(From In the Beginning … ):
For the layman, it is the last step in evolution that is the most difficult to explain. You may be able to convince him that natural selection can explain the appearance of complicated robots, who walk the Earth and write books and build computers, but you will have a harder time convincing him that a mechanical process such as natural selection could cause those robots to become conscious. Human consciousness is in fact the biggest problem of all for Darwinism, but it is hard to say anything “scientific” about consciousness, since we don’t really know what it is, so it is also perhaps the least discussed.
Nevertheless, one way to appreciate the problem it poses for Darwinism or any other mechanical theory of evolution is to ask the question: is it possible that computers will someday experience consciousness? If you believe that a mechanical process such as natural selection could have produced consciousness once, it seems you can’t say it could never happen again, and it might happen faster now, with intelligent designers helping this time. In fact, most Darwinists probably do believe it could and will happen—not because they have a higher opinion of computers than I do: everyone knows that in their most impressive displays of “intelligence,” computers are just doing exactly what they are told to do, nothing more or less. They believe it will happen because they have a lower opinion of humans: they simply dumb down the definition of consciousness, and say that if a computer can pass a “Turing test,” and fool a human at the keyboard in the next room into thinking he is chatting with another human, then the computer has to be considered to be intelligent, or conscious. With the right software, my laptop may already be able to pass a Turing test, and convince me that I am Instant Messaging another human. If I type in “My cat died last week” and the computer responds “I am saddened by the death of your cat,” I’m pretty gullible, that might convince me that I’m talking to another human. But if I look at the software, I might find something like this:
if (verb == ‘died’)
fprintf(1,’I am saddened by the death of your %s’,noun)
end
I’m pretty sure there is more to human consciousness than this, and even if my laptop answers all my questions intelligently, I will still doubt there is “someone” inside my Intel processor who experiences the same consciousness that I do, and who is really saddened by the death of my cat, though I admit I can’t prove that there isn’t.
I really don’t know how to argue with people who believe computers could be conscious. About all I can say is: what about typewriters? Typewriters also do exactly what they are told to do, and have produced some magnificent works of literature. Do you believe that typewriters can also be conscious?
And if you don’t believe that intelligent engineers could ever cause machines to attain consciousness, how can you believe that random mutations could accomplish this?
Dr. Sewell, I really enjoyed your book and read it fully in just two days. I hope you write another one in the same way this one was done.
I especially liked the way you handled and described the 2nd Law of Thermodynamics and the problem it poses for explanations based on darwinian processes.
Though we may not be able to say exactly what consciousness is, I believe that it is possible to determine that consciousness is its own unique entity:
Here are my notes to that effect:
Quantum mind–body problem
Parallels between quantum mechanics and mind/body dualism were first drawn by the founders of quantum mechanics including Erwin Schrödinger, Werner Heisenberg, Wolfgang Pauli, Niels Bohr, and Eugene Wigner
http://en.wikipedia.org/wiki/Q.....dy_problem
“It was not possible to formulate the laws (of quantum theory) in a fully consistent way without reference to consciousness.” Eugene Wigner (1902 -1995) laid the foundation for the theory of symmetries in quantum mechanics, for which he received the Nobel Prize in Physics in 1963.
http://en.wikipedia.org/wiki/Eugene_Wigner
These following studies and videos confirm this ‘superior quality’ of existence for our souls/minds:
Miracle Of Mind-Brain Recovery Following Hemispherectomies – Dr. Ben Carson – video
http://www.metacafe.com/watch/3994585/
Removing Half of Brain Improves Young Epileptics’ Lives:
Excerpt: “We are awed by the apparent retention of memory and by the retention of the child’s personality and sense of humor,” Dr. Eileen P. G. Vining; In further comment from the neuro-surgeons in the John Hopkins study: “Despite removal of one hemisphere, the intellect of all but one of the children seems either unchanged or improved. Intellect was only affected in the one child who had remained in a coma, vigil-like state, attributable to peri-operative complications.”
http://www.nytimes.com/1997/08.....lives.html
The Day I Died – Part 4 of 6 – The Extremely ‘Monitored’ Near Death Experience of Pam Reynolds – video
http://www.metacafe.com/watch/4045560
Blind Woman Can See During Near Death Experience (NDE) – Pim von Lommel – video
http://www.metacafe.com/watch/3994599/
Kenneth Ring and Sharon Cooper (1997) conducted a study of 31 blind people, many of who reported vision during their Near Death Experiences (NDEs). 21 of these people had had an NDE while the remaining 10 had had an out-of-body experience (OBE), but no NDE. It was found that in the NDE sample, about half had been blind from birth. (of note: This ‘anomaly’ is also found for deaf people who can hear sound during their Near Death Experiences(NDEs).)
http://findarticles.com/p/arti....._65076875/
Quantum Consciousness – Time Flies Backwards? – Stuart Hameroff MD
Excerpt: Dean Radin and Dick Bierman have performed a number of experiments of emotional response in human subjects. The subjects view a computer screen on which appear (at randomly varying intervals) a series of images, some of which are emotionally neutral, and some of which are highly emotional (violent, sexual….). In Radin and Bierman’s early studies, skin conductance of a finger was used to measure physiological response They found that subjects responded strongly to emotional images compared to neutral images, and that the emotional response occurred between a fraction of a second to several seconds BEFORE the image appeared! Recently Professor Bierman (University of Amsterdam) repeated these experiments with subjects in an fMRI brain imager and found emotional responses in brain activity up to 4 seconds before the stimuli. Moreover he looked at raw data from other laboratories and found similar emotional responses before stimuli appeared.
http://www.quantumconsciousnes.....Flies.html
In The Wonder Of Being Human: Our Brain and Our Mind, Eccles and Robinson discussed the research of three groups of scientists (Robert Porter and Cobie Brinkman, Nils Lassen and Per Roland, and Hans Kornhuber and Luder Deeke), all of whom produced startling and undeniable evidence that a “mental intention” preceded an actual neuronal firing – thereby establishing that the mind is not the same thing as the brain, but is a separate entity altogether.
http://books.google.com/books?.....8;lpg=PT28
“As I remarked earlier, this may present an “insuperable” difficulty for some scientists of materialists bent, but the fact remains, and is demonstrated by research, that non-material mind acts on material brain.” Eccles
“Thought precedes action as lightning precedes thunder.”
Heinrich Heine – in the year 1834
A Reply to Shermer Medical Evidence for NDEs (Near Death Experiences) – Pim van Lommel
Excerpt: For decades, extensive research has been done to localize memories (information) inside the brain, so far without success.,,,,Nobel prize winner W. Penfield could sometimes induce flashes of recollection of the past (never a complete life review), experiences of light, sound or music, and rarely a kind of out-of-body experience. These experiences did not produce any transformation. After many years of research he finally reached the conclusion that it is not possible to localize memories (information) inside the brain.
http://www.nderf.org/vonlommel.....sponse.htm
Scientific Evidence That Mind Effects Matter – Random Number Generators – video
http://www.metacafe.com/watch/4198007
Genesis 2:7
And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
Though we may not be able to say exactly what consciousness is, I believe that it is possible to determine that consciousness is its own unique entity:
Here are my notes to that effect:
Quantum mind–body problem
Parallels between quantum mechanics and mind/body dualism were first drawn by the founders of quantum mechanics including Erwin Schrödinger, Werner Heisenberg, Wolfgang Pauli, Niels Bohr, and Eugene Wigner
“It was not possible to formulate the laws (of quantum theory) in a fully consistent way without reference to consciousness.” Eugene Wigner (1902 -1995) laid the foundation for the theory of symmetries in quantum mechanics, for which he received the Nobel Prize in Physics in 1963.
http://en.wikipedia.org/wiki/Eugene_Wigner
These following studies and videos confirm this ‘superior quality’ of existence for our souls/minds:
Miracle Of Mind-Brain Recovery Following Hemispherectomies – Dr. Ben Carson – video
http://www.metacafe.com/watch/3994585/
Removing Half of Brain Improves Young Epileptics’ Lives:
Excerpt: “We are awed by the apparent retention of memory and by the retention of the child’s personality and sense of humor,” Dr. Eileen P. G. Vining; In further comment from the neuro-surgeons in the John Hopkins study: “Despite removal of one hemisphere, the intellect of all but one of the children seems either unchanged or improved. Intellect was only affected in the one child who had remained in a coma, vigil-like state, attributable to peri-operative complications.”
The Day I Died – Part 4 of 6 – The Extremely ‘Monitored’ Near Death Experience of Pam Reynolds – video
http://www.metacafe.com/watch/4045560
Blind Woman Can See During Near Death Experience (NDE) – Pim von Lommel – video
http://www.metacafe.com/watch/3994599/
Kenneth Ring and Sharon Cooper (1997) conducted a study of 31 blind people, many of who reported vision during their Near Death Experiences (NDEs). 21 of these people had had an NDE while the remaining 10 had had an out-of-body experience (OBE), but no NDE. It was found that in the NDE sample, about half had been blind from birth. (of note: This ‘anomaly’ is also found for deaf people who can hear sound during their Near Death Experiences(NDEs).)
Quantum Consciousness – Time Flies Backwards? – Stuart Hameroff MD
Excerpt: Dean Radin and Dick Bierman have performed a number of experiments of emotional response in human subjects. The subjects view a computer screen on which appear (at randomly varying intervals) a series of images, some of which are emotionally neutral, and some of which are highly emotional (violent, sexual….). In Radin and Bierman’s early studies, skin conductance of a finger was used to measure physiological response They found that subjects responded strongly to emotional images compared to neutral images, and that the emotional response occurred between a fraction of a second to several seconds BEFORE the image appeared! Recently Professor Bierman (University of Amsterdam) repeated these experiments with subjects in an fMRI brain imager and found emotional responses in brain activity up to 4 seconds before the stimuli. Moreover he looked at raw data from other laboratories and found similar emotional responses before stimuli appeared.
In The Wonder Of Being Human: Our Brain and Our Mind, Eccles and Robinson discussed the research of three groups of scientists (Robert Porter and Cobie Brinkman, Nils Lassen and Per Roland, and Hans Kornhuber and Luder Deeke), all of whom produced startling and undeniable evidence that a “mental intention” preceded an actual neuronal firing – thereby establishing that the mind is not the same thing as the brain, but is a separate entity altogether.
“As I remarked earlier, this may present an “insuperable” difficulty for some scientists of materialists bent, but the fact remains, and is demonstrated by research, that non-material mind acts on material brain.” Eccles
“Thought precedes action as lightning precedes thunder.”
Heinrich Heine – in the year 1834
A Reply to Shermer Medical Evidence for NDEs (Near Death Experiences) – Pim van Lommel
Excerpt: For decades, extensive research has been done to localize memories (information) inside the brain, so far without success.,,,,Nobel prize winner W. Penfield could sometimes induce flashes of recollection of the past (never a complete life review), experiences of light, sound or music, and rarely a kind of out-of-body experience. These experiences did not produce any transformation. After many years of research he finally reached the conclusion that it is not possible to localize memories (information) inside the brain.
Scientific Evidence That Mind Effects Matter – Random Number Generators – video
http://www.metacafe.com/watch/4198007
(I once asked a evolutionist after showing him the preceding experiment, “Since you ultimately believe that the ‘god of random chance’ produced everything we see around us, what in the world is my mind doing pushing your god around?)
Genesis 2:7
And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
As well it should be noted that, counter-intuitive to materialistic thought (and to every kid who has ever taken a math exam), a computer does not consume energy during computation but will only consume energy when information is erased from it. This counter-intuitive fact is formally known as Landauer’s Principle. i.e. Erasing information is a thermodynamically irreversible process that increases the entropy of a system. i.e Only irreversible operations consume energy. Reversible computation does not use up energy. Unfortunately the computer will eventually run out of information storage space and must begin to ‘irreversibly’ erase the information it has previously gathered (Bennett: 1982) and thus a computer must eventually use energy. i.e. A ‘material’ computer must eventually obey the second law of thermodynamics for its computation.
Landauer’s principle
Of Note: “any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase ,,, Specifically, each bit of lost information will lead to the release of an (specific) amount (at least kT ln 2) of heat.,,, Landauer’s Principle has also been used as the foundation for a new theory of dark energy, proposed by Gough (2008).
http://en.wikipedia.org/wiki/L....._principle
“Those devices can yield only approximations to a structure (of information) that has a deep and “computer independent” existence of its own.” – Roger Penrose – The Emperor’s New Mind – Pg 147
“Information is information, not matter or energy. No materialism which does not admit this can survive at the present day.”
Norbert Weiner – MIT Mathematician – Father of Cybernetics
This ability of a computer to ‘compute answers’ without ever hypothetically consuming energy, until information is erased, is very suggestive that the answers/truth already exist in reality, and in fact, when taken to its logical conclusion, is very suggestive to the postulation of John 1:1 that ‘Logos’ is ultimately the foundation of our ‘material’ reality in the first place.
John 1:1-3
In the beginning, the Word existed. The Word was with God, and the Word was God. He was with God in the beginning. Through Him all things were made; without Him nothing was made that has been made.
(of note: ‘Word’ in Greek is ‘Logos’, and is the root word from which we get our word ‘Logic’)
This strange anomaly between lack of energy consumption and the computation of information seems to hold for the human mind as well.
Appraising the brain’s energy budget:
Excerpt: In the average adult human, the brain represents about 2% of the body weight. Remarkably, despite its relatively small size, the brain accounts for about 20% of the oxygen and, hence, calories consumed by the body. This high rate of metabolism is remarkably constant despite widely varying mental and motoric activity. The metabolic activity of the brain is remarkably constant over time.
http://www.pnas.org/content/99/16/10237.full
THE EFFECT OF MENTAL ARITHMETIC ON CEREBRAL CIRCULATION AND METABOLISM
Excerpt: Although Lennox considered the performance of mental arithmetic as “mental work”, it is not immediately apparent what the nature of that work in the physical sense might be if, indeed, there be any. If no work or energy transformation is involved in the process of thought, then it is not surprising that cerebral oxygen consumption is unaltered during mental arithmetic.
The preceding experiments are very unexpected to materialists since materialists hold that ‘mind’ is merely a ’emergent property’ of the physical processes of the material brain.
Considering computers can’t pass this following test for creating new information,,,
“… no operation performed by a computer can create new information.”
— Douglas G. Robertson, “Algorithmic Information Theory, Free Will and the Turing Test,” Complexity, Vol.3, #3 Jan/Feb 1999, pp. 25-34.
,,Whereas humans can fairly easily pass the test for creating new information,,
“So, to sum up: computers can reshuffle specifications and perform any kind of computation implemented in them. They are mechanical, totally bound by the laws of necessity (algorithms), and non conscious. Humans can continuously create new specification, and also perform complex computations like a computer, although usually less efficiently. They can create semantic output, make new unexpected inferences, recognize and define meanings, purposes, feelings, and functions, and certainly conscious representations are associated with all those kinds of processes.”
Uncommon Descent blogger – gpuccio
http://www.uncommondescent.com.....ent-357770
,,,thus these findings strongly imply that we humans have a ‘higher informational component’ to our being,, i.e. these findings offer another line of corroborating evidence which is very suggestive to the idea that humans have a mind which is transcendent of the physical brain and which is part of a ‘unique soul from God’. Moreover this unique mind that we humans have seems to be capable of a special and intimate communion with God that is unavailable to other animals, i.e. we are capable of communicating information with “The Word” as described in John 1:1.
Here is another article that is far more nuanced in its discerning of the ‘transcendent mind’, than the brute empirics I’m drawn to:
The Mind and Materialist Superstition – Six “conditions of mind” that are irreconcilable with materialism:
http://www.evolutionnews.org/2.....super.html
———
Of related interest on the “spiritual” aspect of man:
https://docs.google.com/Doc?docid=0AYmaSrBPNEmGZGM4ejY3d3pfNGQ4aGM4NzZq&hl=en
“Though we may not be able to say exactly what consciousness is …”
A huge part of the problem (perhaps the entirety of it?) is that trying to “say exactly what consciousness is” generally involves mechanistic/materialistic eliminative reductionism … which is to say, “explaining” consciousness by explaining it away.
Consciousness is itself; it’s not made out of something else.
Well, that was pretty vacuous.
Let’s start with the easy problems.
What a curious laptop you have. If I were to participate in in a Turing test, I’d be asking questions like “Of the two most recent questions you were asked, which was the more difficult to answer and why?”
Your dictionary approach doesn’t work too well there, does it.
You’ve also managed to mischaracterize the Turing test, and I don’t think you’ve read anything scholarly in artificial intelligence or philosophy of mind.
Arguments from incredulity are almost always arguments from ignorance without the admission of ignorance, yes?
Turing’s “Computing Machinery and Intelligence” paper can be found here.
Daniel Dennett’s Can Machines Think? begins with the words “Much has been written about the Turing test in the last few years, some of it preposterously off the mark.” It explains (among other things) why a dictionary-based approaches to artificial intelligence won’t every be able to pass a Turing test.
If you’re not able to define consciousness then it’s not surprising that you’re unable to consider a physical model of it, and if you don’t have a physical model then there’s not much point in trying to evaluate an evolutionary solution (unless you’re intending on making an argument from incredulity rooted in an argument from ignorance). Kandel’s Principles of Neural Science is 1,400+ pages of how the brain works (and fails to work), starting at the electrochemical and working up through the cellular to larger brain structures. Once you remove all the aspects of thought and behavior where neural correlates are known, there’s very little remaining for a non-physical consciousness to do.
So yes, I agree with you: you really don’t know how to argue with people who believe computers could be conscious.
Very interesting line of thought llion. I was kind of thinking along the same line. Consciousness is somewhat of a ‘primal’ entity of the universe that precedes the ‘material’ universe in the first place. We end up being very much like the blind men trying to describe different parts of the elephant to each other.
Notes:
This following experiment went extended Wheeler’s delayed choice experiment to highlight the centrality of ‘information’ in the Double Slit Experiment and refutes any ‘detector centered’ arguments for why the wave collapses:
(Double Slit) A Delayed Choice Quantum Eraser – updated 2007
Excerpt: Upon accessing the information gathered by the Coincidence Circuit, we the observer are shocked to learn that the pattern shown by the positions registered at D0 (Detector Zero) at Time 2 depends entirely on the information gathered later at Time 4 and available to us at the conclusion of the experiment. (i.e. This experiment clearly shows that the detector is secondary in the experiment and that a conscious observer, being able to know the information of which path a photon takes with local certainty, is primary to the wave collapsing to a particle in the experiment. The act of a detector detecting a photon at an earlier time in the experiment does not determine if the wave will be collapsed at the end of the experiment. Only the availability of the information to the observer is what matters for the wave to collapse. That is what he meant by ‘we the observer are shocked to learn’)
http://www.bottomlayer.com/bot.....ly-web.htm
It is interesting to note that some materialists seem to have a very hard time grasping the simple point of the double slit experiments, but to try to put it more clearly; To explain an event which defies time and space, as the quantum erasure experiment clearly does, you cannot appeal to any material entity in the experiment like the detector, or any other 3D physical part of the experiment, which is itself constrained by the limits of time and space. To give an adequate explanation for defying time and space one is forced to appeal to a transcendent entity which is itself not confined by time or space. But then again I guess I can see why forcing someone who claims to be a atheistic materialist to appeal to a non-material transcendent entity, to give an adequate explanation, would invoke such utter confusion on their part. Yet to try to put it in even more ‘shocking’ terms, the ‘shocking’ conclusion of the experiment is that a transcendent Mind, with a capital M, must precede the collapse of quantum waves to 3-Dimensional particles. Moreover, it is impossible for a human mind to ever ’emerge’ from any 3-D material particle which is itself semi-dependent on our ‘observation’ for its own collapse to a 3D reality in the first place. This is more than a slight problem for the atheistic-evolutionary materialist who insists that our minds ’emerged’, or evolved, from 3D matter. In the following article Professor Henry puts it more clearly than I can:
The Mental Universe – Richard Conn Henry – Professor of Physics John Hopkins University
Excerpt: The only reality is mind and observations, but observations are not of things. To see the Universe as it really is, we must abandon our tendency to conceptualize observations as things.,,, Physicists shy away from the truth because the truth is so alien to everyday physics. A common way to evade the mental universe is to invoke “decoherence” – the notion that “the physical environment” is sufficient to create reality, independent of the human mind. Yet the idea that any irreversible act of amplification is necessary to collapse the wave function is known to be wrong: in “Renninger-type” experiments, the wave function is collapsed simply by your human mind seeing nothing. The universe is entirely mental,,,, The Universe is immaterial — mental and spiritual. Live, and enjoy.
http://henry.pha.jhu.edu/The.mental.universe.pdf
Astrophysicist John Gribbin comments on the Renninger experiment here:
Solving the quantum mysteries – John Gribbin
Excerpt: From a 50:50 probability of the flash occurring either on the hemisphere or on the outer sphere, the quantum wave function has collapsed into a 100 per cent certainty that the flash will occur on the outer sphere. But this has happened without the observer actually “observing” anything at all! It is purely a result of a change in the observer’s knowledge about what is going on in the experiment.
i.e. The detector is completely removed as to being the primary cause of quantum wave collapse in the experiment. As Richard Conn Henry clearly implied previously, in the experiment it is found that ‘The physical environment’ IS NOT sufficient within itself to ‘create reality’, i.e. IS NOT sufficient to explain quantum wave collapse to a ‘uncertain’ 3D particle.
Why, who makes much of a miracle? As to me, I know of nothing else but miracles, Whether I walk the streets of Manhattan, Or dart my sight over the roofs of houses toward the sky,,,
Walt Whitman – Miracles
That the mind of a individual observer would play such an integral, yet not complete ‘closed loop’ role, in instantaneous quantum wave collapse to uncertain 3-D particles, gives us clear evidence that our mind is a unique entity. A unique entity with a superior quality of existence when compared to the uncertain 3D particles of the material universe. This is clear evidence for the existence of the ‘higher dimensional soul’ of man that supersedes any material basis that the soul/mind has been purported to emerge from by materialists. I would also like to point out that the ‘effect’, of universal quantum wave collapse to each ‘central 3D observer’, gives us clear evidence of the extremely special importance that the ’cause’ of the ‘Infinite Mind of God’ places on each of our own individual souls/minds.
Psalm 139:17-18
How precious concerning me are your thoughts, O God! How vast is the sum of them! Were I to count them, they would outnumber the grains of sand. When I awake, I am still with you.
further notes:
I especially like how the authors draw out this following ‘what it means to be human’ distinction in their paper:
“although Homo neanderthalensis had a large brain, it left no unequivocal evidence of the symbolic consciousness that makes our species unique.” — “Unusual though Homo sapiens may be morphologically, it is undoubtedly our remarkable cognitive qualities that most strikingly demarcate us from all other extant species. They are certainly what give us our strong subjective sense of being qualitatively different. And they are all ultimately traceable to our symbolic capacity. Human beings alone, it seems, mentally dissect the world into a multitude of discrete symbols, and combine and recombine those symbols in their minds to produce hypotheses of alternative possibilities. When exactly Homo sapiens acquired this unusual ability is the subject of debate.”
The authors of the paper try to find some evolutionary/materialistic reason for the extremely unique ‘information capacity’ of humans, but of course they never find a coherent reason. Indeed why should we ever consider a process, which is utterly incapable of ever generating any complex functional information at even the most foundational levels of molecular biology, to suddenly, magically, have the ability to generate our brain which can readily understand and generate functional information? A brain which has been repeatedly referred to as ‘the Most Complex Structure in the Universe’? The authors never seem to consider the ‘spiritual angle’ for why we would have such a unique capacity for such abundant information processing. This following short video, and verses, are very clear as to what the implications of this evidence means to us and for us:
Modus Tollens – It Is Impossible For Evolution To Be True – T.G. Peeler – video
http://www.metacafe.com/w/5047482
Genesis 3:8
And they (Adam and Eve) heard the voice of the LORD God walking in the garden in the cool of the day…
John 1:1-1
In the beginning, the Word existed. The Word was with God, and the Word was God.
A very strong piece of suggestive evidence, which persuasively hints at a unique relationship that man has with ‘The Word’ of John 1:1, is found in these following articles which point out the fact that ‘coincidental scientific discoveries’ are far more prevalent than what should be expected from a materialistic perspective,:
In the Air – Who says big ideas are rare? by Malcolm Gladwell
Excerpt: This phenomenon of simultaneous discovery—what science historians call “multiples”—turns out to be extremely common. One of the first comprehensive lists of multiples was put together by William Ogburn and Dorothy Thomas, in 1922, and they found a hundred and forty-eight major scientific discoveries that fit the multiple pattern. Newton and Leibniz both discovered calculus. Charles Darwin and Alfred Russel Wallace both discovered evolution. Three mathematicians “invented” decimal fractions. Oxygen was discovered by Joseph Priestley, in Wiltshire, in 1774, and by Carl Wilhelm Scheele, in Uppsala, a year earlier. Color photography was invented at the same time by Charles Cros and by Louis Ducos du Hauron, in France. Logarithms were invented by John Napier and Henry Briggs in Britain, and by Joost Bürgi in Switzerland. ,,, For Ogburn and Thomas, the sheer number of multiples could mean only one thing: scientific discoveries must, in some sense, be inevitable.
http://www.newyorker.com/repor.....ntPage=all
List of multiple discoveries
Excerpt: Historians and sociologists have remarked on the occurrence, in science, of “multiple independent discovery”. Robert K. Merton defined such “multiples” as instances in which similar discoveries are made by scientists working independently of each other.,,, Multiple independent discovery, however, is not limited to only a few historic instances involving giants of scientific research. Merton believed that it is multiple discoveries, rather than unique ones, that represent the common pattern in science.
http://en.wikipedia.org/wiki/L.....iscoveries
The following video is far more direct in establishing the ‘spiritual’ link to man’s ability to learn new information, in that it shows that the SAT (Scholastic Aptitude Test) scores for students showed a steady decline, for seventeen years, after the removal of prayer from the classroom by the Supreme Court in 1963:
The Real Reason American Education Has Slipped – David Barton – video
http://www.metacafe.com/watch/4318930
These following studies, though of materialistic bent, offer strong support that Humans are extremely unique in this ‘advanced information capacity’ when compared to animals:
Darwin’s mistake: Explaining the discontinuity between human and nonhuman minds:
Excerpt: There is a profound functional discontinuity between human and nonhuman minds. We argue that this discontinuity pervades nearly every domain of cognition and runs much deeper than even the spectacular scaffolding provided by language or culture can explain. We hypothesize that the cognitive discontinuity between human and nonhuman animals is largely due to the degree to which human and nonhuman minds are able to approximate the higher-order, systematic, relational capabilities of a physical symbol system (i.e. we are able to understand information). http://www.bbsonline.org/Prepr.....eprint.htm
Origin of the Mind: Marc Hauser
Excerpt: “Researchers have found some of the building blocks of human cognition in other species. But these building blocks make up only the cement footprint of the skyscraper that is the human mind”,,,
These following studies highlight the difficulty materialists have in fitting our mental abilities into any plausible evolutionary scenario:
Origin of Soulish Animals:
Excerpt: Bolhuis and Wynne contrast the cognitive capacities of birds and primates.,,, They also refer to an experiment demonstrating that “crows can also work out how to use one tool to obtain a second with which they can retrieve food, a skill that monkeys and apes struggle to master.” Evidently, certain bird species exhibit greater powers of the mind than do apes.
Algorithmic Information Theory, Free Will and the Turing Test – Douglas S. Robertson
Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.
http://www3.interscience.wiley.....8;SRETRY=0
Granville,
Since you yourself fully admit that “… it is hard to say anything “scientific” about consciousness, since we don’t really know what it is,” don’t you think it is a bit premature to conclude that consciousness is somehow a ‘problem’ for evolutionary theory? How could one possibly say that the ‘explanation’ of consciousness poses a problem for any theory, if it is not currently understood at all to begin with?
Illion, you said:
That seems a bit like saying “Migration is itself’ it’s not made out of something else.” That statement is true in that migration isn’t ‘made’ out of something physical, but it is an emergent feature of some physical, biological systems. We don’t really know anything about consciousness; and that’s my point: for all we know, it could be an emergent property of a complex brain. We don’t have any evidence to suggest that consciousness can exist in the absence of a brain. (or something like a brain)
Again, all I’m saying is that it sounds extremely presumptuous to say that any particular theory can’t explain a phenomena, if that phenomena isn’t understood at all to begin with.
And of course, “Because God made it that way,” isn’t an explanation of anything.
Jurassicmac,
If you ask whether they believe computers will someday be conscious, most people will say, of course not, that’s ridiculous; yet many of them believe random mutations and natural selection could accomplish this. My post was aimed at these people, to get them to see the inconsistency.
Apparently you are one of those who would say it is “extremely presumptuous” to rule out the possibility that computers can be conscious. As I said in the post, I don’t know how to reach people like you; all I can say is, what about typewriters?
Having a Ph.D in physics ( computer simulation of ionospheric processes and artificial heating ) and having been in the computer industry for over 25 years I think I know a little fact that proves that human consciousness can not have evolved. I may be wrong, but it will take a tremendous amount of real logic, not complicated gobbedly gook to change my mind.
The simple fact is this. Despite years of experience writing many complex codes, I can not write a computer program that disobeys me. I don’t even no how to do it. I can write computer programs that have bugs and don’t perform what I thought they were going to do; I can write computer programs that make pseudo-random choices. I do not know how to write a program that disobeys. I would contend it can’t be done. But the ability to disobey the Creator is the essence of consciousness. Otherwise it’s just complicated programming with random choices.
—jurassicmac: “We don’t really know anything about consciousness; and that’s my point: for all we know, it could be an emergent property of a complex brain.”
—“And of course, “Because God made it that way,” isn’t an explanation of anything.”
To say, “God made it that way” is more illuminating that to say, “it emerged.” The first statement is consistent with science and tells us something about the cause; the second statement is not consistent with science and tells us absolutely nothing about the cause.
For the same reason, it makes sense to say that Mozart composed his symphonies, but it makes no sense at all to say that these works of art “emerged.”
“Since you yourself fully admit that “… it is hard to say anything “scientific” about consciousness, since we don’t really know what it is,” don’t you think it is a bit premature to conclude that consciousness is somehow a ‘problem’ for evolutionary theory?”
Well it’s obviously a problem for your theory if it’s so slippery you can’t even define it. Doesn’t that make it a big fat problem? Probably the biggest problem, and very well defined as a problem at that?
Here’s the firt part of the problem defined for you:
a. thought does exist, there’s no getting around that without getting cop-out ethereal.
JDH,
Interesting insight. Thanks. If you could design your computer to disobey you, then it’s obeying you. Sigh 🙁
I have to put a plug in for this book since it mentions “Spiritual Brain” and Signature In The Cell” in the promo:
In Consciousness Beyond Life, the internationally renowned cardiologist Dr. Pim van Lommel offers ground-breaking research into whether or not our consciousness survives the death of our body. If you enjoy books about near-death experiences, such as those by Raymond Moody, Jeffrey Long, and James Van Praagh; watch televisions shows like Ghosthunters, Touched by an Angel, and Ghost Whisperer; or are interested in works that explore the intersection of faith and science, such as Spiritual Brain, Signature in the Cell, and When Science Meets Religion; you’ll find much to ponder in Consciousness Beyond Life.
http://www.harpercollins.com/b.....0061777257
further excerpt: Van Lommel provides scientific evidence that the near-death phenomenon is an authentic experience that cannot be attributed to imagination, psychosis, or oxygen deprivation. He further reveals that after such a profound experience, most patients’ personalities undergo a permanent change. In van Lommel’s opinion, the current views on the relationship between the brain and consciousness held by most physicians, philosophers, and psychologists are too narrow for a proper understanding of the phenomenon. In Consciousness Beyond Life, van Lommel shows that our consciousness does not always coincide with brain functions and that, remarkably and significantly, consciousness can even be experienced separate from the body.
This is very interesting to:
Today Show: Woman recounts life after death – 01/20/2010 – video
http://www.youtube.com/watch?v=DhZ2tvv3mto
very interesting insight @ 8 JDH,
Granville said:
My bet is that most people who accept evolution would not say it’s ridiculous to think that a computer-like device may someday be conscious. You seem to be mixing your demographics here; I’d say that many, many, more ID proponents think it’s ‘ridiculous’ to speculate that it may be a possibility to design a machine that’s conscious, even in the distant future. I wholeheartedly agree with you that it would be an inconsistency to think that evolution could produce consciousness, but that intentional design couldn’t, at least in principle. But I think that you’re making (incorrect) presumptions about what a lot of evolutionists think.
I’m not even saying it will happen; just that saying it won’t seems a stretch when in the same breath you acknowledge that no one even knows what consciousness is.
I mean, if God designed conscious beings while still constructing them out of atoms, why couldn’t we? (Especially if we were to model the computer after the brain in the first place)
Yes, I absolutely would say that it is presumptuous to rule out the possibility that computers could one day be conscious, and if you can’t see that it is, then I don’t know how to reach people like you. Calling this statement presumptuous doesn’t even have anything to do with evolution; I would have considered it an indefensible statement even when I was a young earth creationist.
Evaluate what you’re saying. You (or anyone else for that matter) can’t answer the following:
A. What consciousness even is, or what causes it in the first place
or
B. What computer technology will be like in 10, 100, or 1,000 years.
So you’re making a blanket statement with two variables, without knowing anything about the two variables. Can you not see the problem with this?
My buddy Dave and I used to have debates about whether or not humans will ever invent teleporters, like in Star Trek. His position is that we wouldn’t, because he thought the technology required was too farfetched. my position was that his position was nonsense; what seems like fantasy to one generation is commonplace to the next. Those who claim that a particular invention or technological achievement are impossible are almost always eventually proven wrong.
Just in case there’s any confusion, I’m not claiming that consciousness exists in current computers. I’ll have to assume that your comment “what about typewriters,” was a joke that fell flat; that you weren’t seriously insinuating that anyone thinks that consciousness could exist in such a simple device.
StephenB:
Stephen, let me clarify. I wasn’t saying that “because God made it that way,” was a less satisfying explanation than any other, I was saying that “because God made it that way,” isn’t an explanation at all.
I am a Christian, and I believe that anything that happens is at the very least allowed by God. In one sense, I believe it is accurate to say that it was God’s intention that my house exist. But if someone asks me how my house came to exist, and I simply answer: “Because God willed it so,” I haven’t answered their question in at all. I haven’t explained anything. The same thing goes for “Why does it rain?” The reply: “Because God causes it,” isn’t an explanation in any sense of the word. Science is concerned with discerning proximate causes, not ultimate causes. To say “God made it that way,” isn’t illuminating in the least, because that is the same answer a theist could give for everything. What causes radioactivity? God. Why does lithium react with water the way it does? God. How did our solar system form? God. How does photosynthesis work? God.
You see, not only is “God did it,” not a more ‘illuminating’ explanation, it is not an explanation at all! And It could not be less consistent with science. And of course, the question that follows emergent properties is “why does this property emerge?”
This is a terrible analogy; of course it makes sense to say that Mozart composed his symphonies: we know with a high degree of certainty that he did. We know this for several reasons. We have plausible, verifiable agency; we know that humans can and do write music. We have plausible, verifiable mechanism; we know that humans can transcribe musical notes with pen and paper. We even corroborating historical documentation. With the diversification of life, we have none of these things.
JDH said:
JDH, I must respectfully point out you that you have made 2 logical fallacies at the same time.
First and foremost, you have made the fallacy of ‘Argument from Analogy.” You have presented an analogy of how you think computer programming relates to consciousness, but then declare it a ‘known little fact’ that ‘proves’ human consciousness could not have evolved. An analogy never proves anything. (especially when its an irrelevant analogy to begin with)
Secondly, your ‘analogy’ is also an “Argument from Incredulity.”
“I can not write a computer program…” “I don’t even know how….” Just because you don’t know how to write code that disobeys you, doesn’t mean it’s impossible. It’s irrelevant to the point anyway: You certainly could write to programs that disobey each other.
And to play devil’s advocate for a second, how do you know that humans aren’t following their ‘program’? Do you have access to the ‘source code’ that the rest of us don’t have? Do tell.
lamark said:
It’s not that I can’t explain what causes consciousness, it’s that no one can. (yet)
Saying that any ‘x’ is a problem for any theory is nonsense when nothing is known about ‘x’.
It would be like saying ‘blobutrons’ are a problem for the theory of relativity without knowing anything about what causes blobutrons, or even what they are.
If it turns out that ‘consciousness’ is an emergent property of a sufficiently complex brain, or something like that, then evolutionary theory wouldn’t have any more trouble explaining it than any other emergent propery in nature, like ‘migration’ or flocking behavior.
To clarify to everyone here: I’m all for ID establishing itself as a legitimate scientific discipline. But ID currently is suffering from a very strong perception of being ‘anti-science’. That perception is reinforced with articles like this which propose that little-understood phenomena are somehow ‘problems’ for evolutionary theory. It doesn’t help that the article wanders into baseless speculation about what technological achievements won’t ever happen.
Jurassicmac,
I didn’t actually mention ID in the article, it was about Darwinism. And yes, I do think that little-understood phenomena are problems for any theory which claims to explain them, especially if that theory is taught in all our science classrooms as being as well established as gravity, and given legal protection from scientific criticism. No one here is even proposing that ID be taught in science classrooms, you are the one whose speculative theory is being taught as religious dogma.
Apparently your position is that because some sci-fi aficionados like yourself think scientists might someday create computers that are conscious (do you also think traveling back in time may be possible some day?), it’s ‘anti-science’ to recognize that human consciousness might be a problem for modern evolutionary theory.
Congratulations to Jurassicmac for his/her clear and intelligent comments.
One other point. If you do not believe consciousness has a physical basis then why should it be heritable? It can hardly be in our genes if it is not physical. And how did it first appear? If you accept common descent and believe consciousness to be a unique thing rather than a matter of degree then there must have been one or more families where the parents were not conscious but the children were!
jurassicmac:
Just a few comments on what you say:
1) How could one possibly say that the ‘explanation’ of consciousness poses a problem for any theory, if it is not currently understood at all to begin with?
Here there is some confusion in terms and epistemology, I believe.
Consciousness is what it is, because it is a fact, not a theory. It is indeed directly observed by each one of us (our personal consciousness), and then, and only then, inferred in others by analogy.
Facts are not necessarily “understood”. Sometimes, they can be “explained” in the sense that we can build a more or less valid model which relates some facts to other facts or to other concepts. But we do not “understand” what matter is, or what energy is, or what gravitation is, any more than we “understand” what consciousness is. We can build theories about the properties of matter, or of energy, and the relations between those properties, and the same can be done for consciousness.
2) The assumption of strong ID theory, and of reductionist materialism, is that consciousness (the fact) can be “explained” as a consequence of some properties of matter and of the known laws of physics. Well, anybody is free to believe what he likes. But it is a fact that there is absolutely no basis for that assumption.
3) On the contrary, there are very strong reasons, both logical and empirical, to disagree with that assumption and to give it no real credit. The form that the assumption takes usually is that consciousness is a consequence of some property of the software. That is logically inconsistent, and indeed is not even a credible concept at all. Software is only a more or less complex arrangement of very simple computations. According to AI theory, the results of those computations are independent from the hardware. This concept is very important, because it means that if some property of the software is the cause of consciousness, then those computations should generate the same consciousness on any hardware, including an abacus. Who is really ready to believe that a very complex abacus, manually operated, will become conscious while the computations are accomplished?
Moreover, all the possible properties of software which have been invoked as a substrate for consciousness, such as paralle computing or loops, have no intrinsic reason to be more related to consciousness than, say, a simple addition. Why should parallel computing be more prone to be conscious than serial computing? Did we observe any raise in consciousness in last generation processors?
The simple fact is: software is softarwe; it is a series of organized simple computations. Affirming that it becomes conscious becasue of its structure is no more reasonable than affirming that a well painted woman portrait will begin to speak. There is no sense in it, and that’s all.
4) The empirical reasons against strong AI are very simple: there is absolutely no sign that any specific software structure contributes to consciousness, even less determines it.
But there is another very important argument, one that is directly related to ID. Software cannot generate new CSI. That is very important, because conscious beings can do that, and they definitely do that all the time, and very easily. That is a very strong argument in favour of the assumption (this time, very reasonable) that consciousness is necessary to generate CSI. With all the logical consequences which ensue, both for darwinian theory and for strong AI theory.
Mark:
One other point. If you do not believe consciousness has a physical basis then why should it be heritable? It can hardly be in our genes if it is not physical. And how did it first appear? If you accept common descent and believe consciousness to be a unique thing rather than a matter of degree then there must have been one or more families where the parents were not conscious but the children were!
I am not sure I understand your points. In what sense consciousness should be (or not be) “heritable”?
I certainly believe that it is not “in our genes”, and so would probably do all those who, like me, believe that it is “not physical”. And so?
I think that most of those who believe that consciousness is an independent principle view it as a property, or as the essence itself, of what is usually called “soul”. So, the answer to your question “how did it first appear?” at a philosophical level would critically depend on the specific conception of the soul one has.
If we want to stay empirical, consciousness has to be considered as an observed part of reality, and a very important one. In that case, empirically, the only possible answer to your question: “how did it first appear?”, is “we don’t know”. Empirically, we don’t know. Yet.
What we know is that, in us humans, which is where we directly observe consciousness, it is certainly “interfaced” with the physical body and brain. There is no question about that. Consciousness, in us, interacts with the outer world, in both directions, through the interface of our physical body and brain. Now, I would say that “the interface” is certainly in our genes. I think we can agree on that.
Finally, I really don’t understand your last concept. I certainly “accept common descent and believe consciousness to be a unique thing”. The transcendental self is, IMO, “a unique thing”. But I also believe that the manifestations of consciousness (for instance, its different “states”) are “a matter of degree”: waking consciousness is different from dreams and from deep sleep, or form other subconscious states, such as hypnosis, but all of those states are manifestations of the conscious, transcendental self.
And why should there be “one or more families where the parents were not conscious but the children were!”? Humans are conscious, as far as we know. To what are you referring?
GP: Excellent. As usual. G
jurassicmac, the crushing problem against your position, of computers having the ‘potential’ to become conscious, or any other 3D material entity ever having the ‘potential’ of becoming conscious, can be illustrated by Quantum Mechanics.
It is interesting to note that some materialists seem to have a very hard time grasping the simple point of the double slit experiments, but to try to put it more clearly; To explain an event which defies time and space, as the quantum erasure experiment clearly does, you cannot appeal to any material entity in the experiment like the detector, or any other 3D physical part of the experiment such as a computer , which is itself constrained by the limits of time and space. To give an adequate explanation for defying time and space one is forced to appeal to a transcendent entity which is itself not confined by time or space. But then again I guess I can see why forcing someone who claims to be a atheistic materialist to appeal to a non-material transcendent entity, to give an adequate explanation, would invoke such utter confusion on their part. Yet to try to put it in even more ‘shocking’ terms, the ‘shocking’ conclusion of the experiment is that a transcendent Mind, with a capital M, must precede the collapse of quantum waves to 3-Dimensional particles. Moreover, it is impossible for a human mind to ever ‘emerge’ from any 3-D material particle which is itself semi-dependent on our ‘observation’ for its own collapse to a 3D reality in the first place. This is more than a slight problem for the atheistic-evolutionary materialist who insists that our minds ‘emerged’, or evolved, from 3D matter. In the following article Professor Henry puts it more clearly than I can:
i.e. The detector is completely removed as to being the primary cause of quantum wave collapse in the experiment. As Richard Conn Henry clearly implied previously, in the experiment it is found that ‘The physical environment’ IS NOT sufficient within itself to ‘create reality’, i.e. IS NOT sufficient to explain quantum wave collapse to a ‘uncertain’ 3D particle.
thus jurassicmac, we are clearly dealing with a transcendent entity that is not limited be time and space, and yet you act as if we keep rearranging 1’s and 0’s in a computer’s ‘physical’ memory, which is clearly based in time and space, we will somehow someday have a computer that will produce that which is transcendent of time and space?!?
Your conjecture is of the same type of problem as those who try to explain the origination of the universe with no ‘material’ entity to work with. You simply don’t have anything to work with in this instance save your ‘faith’ that it may be possible someday.
—jurassicmac: “Stephen, let me clarify. I wasn’t saying that “because God made it that way,” was a less satisfying explanation than any other, I was saying that “because God made it that way,” isn’t an explanation at all.”
But you are, of course, incorrect. It is both a theological and a philosophical explanation, hearkening back to a first cause.
—“I am a Christian, and I believe that anything that happens is at the very least allowed by God. In one sense, I believe it is accurate to say that it was God’s intention that my house exist. But if someone asks me how my house came to exist, and I simply answer: “Because God willed it so,” I haven’t answered their question in at all.”
Yes, you have, but you have provided the wrong answer. God didn’t build your house.
—“I haven’t explained anything.”
If you say that God created the universe, you have provided the right philosophical/theological explanation, and it will be consistent with any valid scientific explanation.
—“The same thing goes for “Why does it rain?” The reply: “Because God causes it,” isn’t an explanation in any sense of the word.”
To say that God caused the ecological conditions that make rain possible is to provide a theological explanation.
—“Science is concerned with discerning proximate causes, not ultimate causes.”
Yes, that’s right. On the other hand, to say that science is concerned with proximate causes doesn’t mean that ultimate causes are not causes or that they are not explanations. They are different kinds of explanations and are arrived at through deductive means rather than inductive means.
–“To say “God made it that way,” isn’t illuminating in the least, because that is the same answer a theist could give for everything. What causes radioactivity?”
God is the ultimate cause of radioacticity. That is a lot more illuminating that saying radioacticity “emerged” from who knows what. The word emerge is simply a incomprehensible description posing as a cause.
—“God. Why does lithium react with water the way it does? God. How did our solar system form? God. How does photosynthesis work? God.”
Isn’t it time that you stopped confusing theological explanations with scientific explanations.
–“You see, not only is “God did it,” not a more ‘illuminating’ explanation, it is not an explanation at all!”
To say God created something is a meaningful statement. To say that something emerged is to say that something came from nothing, which is irrational. As a self professed “Christian,” you should be wary of the something-from-nothing type explanations provided by Darwinists.
—“And of course, the question that follows emergent properties is “why does this property emerge?”
No, the question is, what in blazes do you mean by “emergence” and why do you acknowledge that it could be a cause of anything. The whole purpose for using the word emerge is to imply that no cause was needed in an attempt to escape the overwhelming evidence for design.
—“This is a terrible analogy; of course it makes sense to say that Mozart composed his symphonies: we know with a high degree of certainty that he did. We know this for several reasons.”
Obviously, you do not understand the analogy or its purpose.
—“We have plausible, verifiable agency; we know that humans can and do write music. We have plausible, verifiable mechanism; we know that humans can transcribe musical notes with pen and paper. We even corroborating historical documentation. With the diversification of life, we have none of these things.”
The purpose of the analogy is to show that there are many causes that cannot be measured. Mozart’s creative act in composing cannot be measured, but it is a cause, just as God’s creative act in conceiving the design of the universe cannot be measured and yet is also a cause. Through a design inference, we can detect intelligent activity by studying the EFFECTS of both causes, i.e. the cause of the universe and the cause of the symphony. You are confusing Mozart’s creativity, and God’s creativity, which are agency causes, with the laws of physics, which are natural causes. Further, you are expecting both types of explanations to be of the same texture. You claim to be Christian, but you are thinking like a materialist Darwinist.
gpuccio, bornagain77 and StephenB, thanks for the very thought-full responses.
And also thanks to skynetx for your encouraging words in comment #1, I get pretty discouraged sometimes.
Gpuccio
I did not express myself well. I think you have a concept of consciousness which avoids the problems I am trying to identify. It has the important property that it is a matter of degree. So a slug could have very low level of consciousness, a dog a lot more, and a person even more.
If you believe this then it is possible to give a reasonable account of the development of consciousness which is consistent with common descent. As the nervous system developed then the organisms were able to sustain greater levels of consciousness.
The question I have then is – you say the consciousness is a property of the soul. So now the point is a different one. You believe in common descent. Presumably you don’t believe the first prokaryotic life had souls. So at some point an organism without a soul must have had offspring which did have souls (or is soul also a matter of degree?). This is the point I was trying to make about a family where the parents were not conscious but the children were. Now this is not logically impossible – but it seems very strange to me.
In a similar way – sometime between conception and birth most humans become conscious and therefore presumably acquire a soul. If this is not an emergent property then how does this happen? Presumably the soul is attached to the body by a supernatural process. If so, what relationship does the soul of the progeny have to the souls of the parents? There seems to be no reason why the properties of the soul should have anything in common with the souls of the parents as it is not inheriting those properties. Yet there is ample experimental evidence that we do inherit mental attributes as well as physical ones.
markf, this following short video shows how the theistic view of ‘consciousness’ and the materialistic view of ‘consciousness’ are world’s apart:
The Mystery Of Life – God’s Creation & Providence – video
http://www.metacafe.com/watch/4193364
Mark:
Good questions. I will try to clarify, according to my point of view:
I have tried to make clear that the soul is a philosophical and religious concept. That’s why I wrote:
“I think that most of those who believe that consciousness is an independent principle view it as a property, or as the essence itself, of what is usually called “soul”. So, the answer to your question “how did it first appear?” at a philosophical level would critically depend on the specific conception of the soul one has.”
IOW, to answer your questions one has to propose a whole metaphysical scenario. There are many different ones, and each one of us is free to choose the one he believes in. I usually avoid to discuss specific philosophical and religious beliefs here, except when I believe they have very universal implications (as in the case of the problem of free will). In general, I prefer to discuss empirical views here, because that’s my purpose in posting on this blog.
That’s why I added:
“If we want to stay empirical, consciousness has to be considered as an observed part of reality, and a very important one. In that case, empirically, the only possible answer to your question: “how did it first appear?”, is “we don’t know”. Empirically, we don’t know. Yet.”
All the rest of my post is purely empirical.
But I can, I believe, give a possible empirical answer to at least one of your questions, based on my personal understanding of consciousness and of its processes, and on my empirical model of consciousness.
You say:
In a similar way – sometime between conception and birth most humans become conscious and therefore presumably acquire a soul. If this is not an emergent property then how does this happen?
First of all, I think that most religious views believe that the soul enters the zygote at the moment of conception. I certainly believe that way.
But this is not an empirical argument, and I don’t want to contradict myself too much 🙂
The empirical argument would be as follows:
As you correctly state, I believe that the manifestations of consciousness “have the important property that they are a matter of degree”. But it is important to understand that, in my model, that is a property of the manifestations of consciousness, of its phenomenic “states”, not of the transcendental self, which is the subject who perceives and experiences those states.
So, my model is that the self is associated to the zygote from the moment of conception, but that it experieces different “states”, as the physical body and the nervous structures develop. So, it’s not a matter of “emergent properties”. The fundamental property of being conscious, of being a self, is always there, but its phenomenic manifestation depends on the status of the physical interface. In substance, it’s not different from what happens in postnatal life.
This should also clarify my possible answer to your other point:
There seems to be no reason why the properties of the soul should have anything in common with the souls of the parents as it is not inheriting those properties. Yet there is ample experimental evidence that we do inherit mental attributes as well as physical ones.
The properties of which you speak (including mental attributes) are inherited because they are part of the physical interface (including the structure of the brain). The interface is in great measure heredited, and the self experiences it and interacts through it with outer reality, as its personal adventure develops.
I hope that clarifies my point of view.
I’ve used the following verse before when I realized how extensive (and how little understood) the evidence for epigenetic and ontogenetic information were for Body Plan formation, but the verse is just as fitting now in dealing with the extensive evidence for man having a mind/soul that transcends his physical body in the first place:
Jeremiah 1:5
‘Before I formed you in the womb I knew you, and before you were born I consecrated you;,,,
Near Death Experiences – Scientific Evidence – Dr Jeff Long M.D. – video
http://www.metacafe.com/watch/4454627
I always been fascinated by the many accounts of Near Death Experiences, in which the experiencer will say something to the effect that they remember that this 9heaven0 is where they ‘really’ came from,,,
etc.. etc…
Granville Sewell @27, you thesis is quite reasonable and eminently defensible. The same blogger who insists that the word “consciousness” has not been sufficiently defined for purposes of discussion is the same blogger who asserts that it is not unreasonable to believe that a computer could arrive at that state.
—jurassicmac to Granville: “I’ll have to assume that your comment “what about typewriters,” was a joke that fell flat; that you weren’t seriously insinuating that anyone thinks that consciousness could exist in such a simple device.”
I think I understand now. If the term conciousness is used to explain the futility of Darwinism, you don’t know what it means, but if it can be used to argue against Granville Sewell’s thesis, its meaning becomes clear.
jurassicmac:
that you weren’t seriously insinuating that anyone thinks that consciousness could exist in such a simple device.
I am curious. As you seem to suggest that consciousness requires complexity, how would you define complexity in this context?
The link between consciousness and complexity seems pretty clear to me. As MarkF said, a slug is conscious to a degree. That’s a pretty low degree. A dog is conscious to a greater degree, and a human to greater degree yet. The brains, or neurological functions of each of these animals are each more complex than the next. Of course this could be a coincidence, but the link between consciousness and brain size seems pretty universal (as far as we can tell).
Consciousness seems a completely fuzzy term to me anyway. What is a workable definition of it?
I am quite prepared to believe it is nothing special and simply arises naturally in a sufficiently complex system.
BarryR
I really thought my very simplistic example was sufficient to illustrate this very simple point. But apparently you are less gullible than I and it would take a reasonable answer to the above question before you would believe the machine was conscious.
Wow, 1400+ pages on how the brain works. I’m convinced now that I’m just a complicated machine…sigh.
JDH (#10) wrote: Despite years of experience writing many complex codes, I can not write a computer program that disobeys me. I don’t even no how to do it.
I can give you a clue. In his paper Programs with Common Sense, John McCarthy gave five requirements for a human level artificial intelligence:
All behaviors must be representable in the system. Therefore, the system should either be able to construct arbitrary automata or to program in some general-purpose programming language.
Interesting changes in behavior must be expressible in a simple way.
All aspects of behavior except the most routine should be improvable. In particular, the improving mechanism should be improvable.
The machine must have or evolve concepts of partial success because on difficult problems decisive successes or failures come too infrequently.
The system must be able to create subroutines which can be included in procedures in units…
Point #3 is the clue to how to make this happen. Humans have goal-seeking behavior without a fixed goal. Furthermore, we evaluate every goal as if it could be improvable. That means that we are “built” to observe that few, if any, things are what they ought to be.
–BarryR: “Once you remove all the aspects of thought and behavior where neural correlates are known, there’s very little remaining for a non-physical consciousness to do.”
I gather that you also believe a computer could develop an oedipus complex, or that we may one day have to worry about the suicide rate among aging process units.
Yes. And if that is the case, then why, on a materialistic understanding, does consciousness bother to exist at all. Perhaps if materialistic science can do a really good job of explaining things (in 2800 pages, say, instead of just 1400), we will then know that consciousness shouldn’t exist (because there is nothing remaining for it to do) and therefore materialism will have been decisively proven!
zeroseven (and jurassicmac):
The link between consciousness and complexity seems pretty clear to me.
I was not suggesting that there is no link between the manifestations of consciousness and complexity. My point is different.
My point is that, as we in ID are often asked by darwinists and materialists to define functional information, or to be specific about the kind of information and complexity we are speaking of (and we answer in detail to those requests), I am now asking jurassicmag, and you, who have introduced complexity in your argument about consciousness, to define better what you mean.
It should not be difficult, especially for you, as you stated that “the link between consciousness and complexity seems pretty clear”, at least to you.
So, do you mean complexity in the sense of Kolmogorov complexity, or Shannon’s entropy? Is a long enough random string going to become conscious, in your opinion?
Or do you mean functional complexity? IOW, CSI or some equivalent? That woul really be interesting, and would establish a strong epistemological connection between you and us IDists!
So, please, specify what yhour model is, at least in principle. That’s the least we can ask of a scientific model.
Or do you just agree with jurassicmac that the point is that we don’t really know:
What computer technology will be like in 10, 100, or 1,000 years.
Ah, that’s certainly true… And I think we don’t really know what airplane technology will be “in 10, 100, or 1,000 years”. And, say, what ebook readers technology will be.
So, in your model, what is more likely to become conscious in a near future, the last sequence of digits of pi, a computer, an airplane, or just Kindle 4?
Maybe, if you specify your concept of “conscious generating complexity”, we can at least make some predictions about that. You know, some people think that that is what science is about…
BarryR:
Well, I extend my questions in the previous post to you too. Maybe you can find the answer in “Kandel’s Principles of Neural Science and its 1,400+ pages about how the brain works (and fails to work)”.
jurassicmac @19
You said “JDH, I must respectfully point out you that you have made 2 logical fallacies at the same time.”
You sound like you consider yourself pretty wise. I am going to try to explain to you why I did not commit 2 logical fallacies. Then I am going to try and explain to you why your position is indefensible logically. You, unfortunately, will arrogantly not believe either.
First I am not arguing by analogy. Maybe you did not read what I did. I did physics by computer simulation. This is not analogy. This is modeling. There is a distinct difference. When I do computer simulation, I make certain assumptions which allow me to take a complex system and represent it in a series of calculations. I do not construct analogies. I construct working models. Hopefully, in reducing the parameters in the model to something I can actually code in finite time, I have not missed something that effects the states of the real system. Thus when I perform the actual simulation, there is a one to one correspondence between the states of the model, and the distinct states of the real system I am modeling. This is how we can get real scientific results from modeling. The assumptions may be wrong such that I no longer get my one to one correspondence. Then the problem is with incorrect modeling, not with the idea of computer simulation.
If you are right and we are nothing but chemicals in action, than the brain is nothing more than a sophisticated computer. Modeling the brain by a computer is not drawing an analogy. It is trying to eliminate from the real system those parameters which are not necessary for the current problem and modeling the behavior.
Second I am not making an argument from incredulity. I know how to make computer programs. I know one thing I can not do. I can not program a computer to disobey the instructions I give it. This is an argument from overwhelming evidence. In all the years of programming computers they always obey the instructions they are told to do. Sometimes, because of buggy programs, the fact that the computer simply obeys the instructions given it has disastrous results. But it is not logical that one can design a computer to disobey. It is a logical contradiction.
So considering consciousness to be an “emergent” property is just a way of hiding the fact that you believe in a logical contradiction. I have tried to state this as clear as possible. I know you will reject it. To see it, would be too painful to you.
gpuccio@42
This is the best concise definition of consciousness I’ve run across: “a third order model of experience (a model of experience, and a model of that model, in addition to the experience simpliciter). This is obtained by sufficiently complex feedback or feedforward loops in the brain.”
Using this definition, I’ve written robotic control software that was (very) minimally conscious.
Don’t get hung up on the word complexity here. It just means there are enough bits to handle the input, the model of the input, and the model of the model.
There are other definitions out there; you may find some of them more palatable.
The article relied on no formal definition being provided.
JDH@10
Having a Ph.D. in Computer Science, I find it trivial to write code that disobeys me. One particular dislocation simulation I work with is effectively chaotic — the final answer (and the execution time) depends on the order of operations which in turn depend on the order of message arrival. Even on a small number of nodes, this is effectively nondeterministic. The answers eventually start converging, so the physicists don’t mind. Debugging it is another problem entirely.
GS@9
What about typewriters? There’s a mechanical mechanism for experience — striking a key — which fits the first requirement of the definition I gave. But at least for manual typewriters there’s no way to model that experience, much less a way of modeling the model. So no, manual typewriters will not exhibit consciousness.
(Note that I don’t have to rely on arguments from incredulity once I have a definition in place. Looking forward to reading your definition.)
BarryR:
Your definition is only a gratuitous re-definition. Strangely, it is very similar to compatibilist re-definition of free will. Tis seems to be the faith of reductionists: if you don’t like a fact, just redefine it as though it did not exist.
I will be more clear. The only, universal, empirical definition of consciousness the following:
the observed fact that we have subjective experiences, referred to a single perceiver “I”
That is not only my definition, but the true meaning of the word, as it has been used for millennia.
To be compatible with the true meaning of the word, your definition should be “re-re-defined” as follows:
“a third order experience (an experience of experience, and an experience of that experience, in addition to the experience simpliciter). This is never obtained by sufficiently complex feedback or feedforward loops in any software system which is not capable of experiences.”
And even in this way, it would be a definition of “self-consciousness”, and not of consciousness.
Indeed, the “mise en abime” and infinite regress of which the perceiving self is certainly capable (always able to detach itself from any of its representations, to adopt a meta-perception of the perception), while important and revealing the transcendental nature of the self, is not necessary for consciousness to happen. If I perceive a red blot, I am conscious, even if I am not at that moment consciously perceiving that I am perceiving. But certainly, the perception of the perception (at whatever order you like) allows me to become “self-aware”, and not only “aware”, and to build “models” of my perception.
But the model is not the perception. It never was, and never will be.
Given that, can you affirm that you have written ” robotic control software that was (very) minimally” aware? That had perceptions? That had a perceiving I?
Subjective experiences do exist. They are a fact. You cannot rule them out. You can never rule out facts. If you re-define them as loops, you have to show loops with subjective experiences, not only loops which can give outputs vaguely similar to those of beings with subjective experiences.
And if you really believe, like Hofstadter, that loops are the cause of subjective experience and of the I, please can you explain on what you found that conviction? And why simple loops are not aware, and complex loops should be?
IOW, I repeat the question I made at posts 35, 41 and 42, which nobody has still addressed: what kind of formal “complexity” should be capable to cause consciousness to “emerge”?
gpuccio, I guess you are right Derek does fit here, I have a few other videos of autistic savants I’ve collected:
Autistic savants
The Musical Genius – Derek Paravicini – Part 1/5
http://www.youtube.com/watch?v=1kwjDLHX92w
Derek Paravicini on 60 MINUTES – Autistic Savant – video
http://www.metacafe.com/watch/4303465
Kim Peek – The Real Rain Man [1/5]
http://www.youtube.com/watch?v=dhcQG_KItZM
The Boy with the Incredible Brain – Daniel Tammet
http://video.google.com/videop.....1453380070
Autistic Savant Stephen Wiltshire Draws the City Of Rome From Memory
http://www.metacafe.com/watch/4200256
Savant syndrome, Beautiful minds – Elonzo Clemmens
http://www.youtube.com/watch?v=lkDMaJ-wZmQ
The Human Calculator – Ruediger Gamm – video
http://www.metacafe.com/watch/4200252
as well I find it interesting that when ever anybody does something blatantly selfish, everybody will ask them/him/her , “Doesn’t your conscious bother you?”, reflecting the fact that everybody is expected to intuitively know the transcendent moral law of the golden rule. This following video clearly reflects how some academics have completely deluded themselves into thinking that this transcendent moral law, which is comprehended by our transcendent minds, does not exist, when clearly it does exist.
Cruel Logic
http://www.youtube.com/watch?v=4qd1LPRJLnI
gpuccio, this is a better look at mega-savant Kim Peek
Kim Peek – The Real Rain Man [2/5]
http://www.youtube.com/watch?v.....38;index=1
gpuccio,
Very nice!
gpuccio@45
As to the definition I gave, I judge it in terms of utility: I’ve given three necessary and testable components that allows me to distinguish (among other things) humans from typewriters.
Your definition is not so picky.
A single transistor satisfies this definition: it can perceive a change in input power and react accordingly. The perception is subjective and private. I don’t find it useful to think of single transistors having consciousness, so I’m going to reject your definition.
BTW, this follows the Cartesian model (and no, it has not been used for a millenia). Descartes avoids the problem by limiting discussion to humans.
[Unless noted otherwise, quotations are take from the Stanford Encyclopedia of Philosophy’s article on Seventeenth Century Theories of Consciousness]
Contrast this with Hobbs:
Now we have both sensation and memory of sensation. Finally Spinoza (where I will quote the author’s summary):
Substitute “model” for “idea” and you’ve arrived at a modern definition of consciousness.
As to you complexity question, I’m not sure why it’s relevant. Complexity is a useful measure of computability and information, but since neither your definition nor mine relies on computability or information, I think you’re making a category error. But, if you want a rough guide: minimal perception takes bits, minimal models of perception takes bytes, and minimal models of models of perception takes kilobytes.
If you’re interested in this problem in general, I found Jaegwon Kim’s Physicalism, or Something Near Enough to be unusually clearly written. The first several chapters give a complete overview of the recent history of philosophy of mind. If you want to get a sense of his writing style, there’s a sample chapter here.
Barry R
Why is it that atheists mistake randomness or chaotic behavior for intention. Your pseudo non-determinism does not coincide with disobedience. The fact that the answers converge shows that you really have just added a little uncertainty to the process. Uncertainty is not rebellion.
But not one of your little programs is going to say, well this is the answer I was converging to, but I felt like doing this instead. Your oversimplification of the problem shows you are grasping at straws. You may claim it is a false dichotomy, but I see only two alternatives.
1. You don’t really understand the full extent of the concept of disobedience, in which case, why should I trust your claims about your program.
2. You are aware at how over simplified your model is and you are projecting onto your results, conclusions which are not warranted. Then you have not answered the challenge.
Coincidently the debate on premier Christian radio Saturday, the same day this blog went up, was about whether we have a soul or not. Here is the link:
Unbelievable – 04 Sep 2010 – Christian Physicalism: Do we have a soul?
http://www.premierradio.org.uk.....x?mediaid={7A2179A8-B2C2-4F32-BE24-2AFF6628FF9F}
This link should work:
http://www.premier.org.uk/unbelievable
BarryR:
Please, clarify:
A single transistor satisfies this definition: it can perceive a change in input power and react accordingly.
What do you mean? That a transistor has subjective experiences?
The perception is subjective and private.
And so? It exists. It is a fact. As I have said many times, we directly know that we are conscious, and then we infer that in others by analogy. But the direct, subjective, private perception of ourselves as conscious is the basis for any other knowledge. Therefore, if it is “private”, then all our knowledge is “private”.
Again, consciousness in ourselves is a fact, more than any other fact. Consciousness in other humans is a very strong inference by analogy. Consciousness in higher animals is a weaker, bur reasonable inference.
Consciousness in a transistor? I think it’s an inference almost nobody would agree with, not even in minimal part. Consciousness in assembled transistors, no matter how many, no matter in what order? Why, if a single transistor is not conscious, should a million of them variously assembled, become conscious? That’s absolute nonsense. That’s why I asked you if you had any notion of some form of formal complexity which would explain consciousness. You answer:
But, if you want a rough guide: minimal perception takes bits, minimal models of perception takes bytes, and minimal models of models of perception takes kilobytes.
Are you speaking of traditional Shannon information? So, again, is a very long random string conscious? Or are you speaking of CSI? And then, is Hamlet (the play) a conscious being?
You equivocate on the meaning of words. Please, define what you mean by “perception”. You use words which have been created, and used, for millennia (yes, for millennia) to describe subjective experiences in humans, and without any thought or justification you apply them to purely objective realities, like a transistor. Why should a transistor “perceive”, and not stones? Why should bits cause consciousness, and not grain of sands?
Substitute “model” for “idea” and you’ve arrived at a modern definition of consciousness.
That only means that modern definitions of consciousness are senseless. You cannot substitute “model” for “idea”.
From “dictionary.com”:
model:
a representation, generally in miniature, to show the construction or appearance of something
a simplified representation of a system or phenomenon
idea:
any conception existing in the mind as a result of mental understanding, awareness, or activity.
Is it so difficult to understand? A “model” is an object. An “idea” is a representation in the conscious mind. How can you substitute one for the other?
Is it really so difficult?
BA:
thank you!
gpuccio@53
Certainly transistors possess the capacity for experience — for several definitions of experience. You may want to limit this discussion to conscious experiences, but in that case you’re precluded from using them to describe consciousness.
Not at all.
Next, I don’t see that great a difference between a “representation” (model) and a “conception” (idea). Both are abstractions; neither are objects.
(Dictionary definitions usually aren’t helpful when discussion specialized domains, btw.)
Finally,
Gosh, that’s a puzzler. If half a bird can’t fly, why should we expect a full bird to be able to fly?
(I took several undergraduate philosophy classes and I can’t remember anyone having to point out that collection of objects have properties that differ singleton objects. I think we took that one pretty much as a given.)
JDH@50
You’re making disobedience a property of intentionality. Good, I like precise definitions.
So let’s talk about intentionality. If I decline to definite intentionality as an intrinsic property and instead define it as a classification of behavior, then there’s no reason I’m aware of that sufficiently complex mechanistic behavior cannot be seen as intentional. We do this — constantly — when we anthropomorphize. When programmers talk about about threads “wanting” to acquire a lock, for example, we’re ascribing a (limited) intentionality to a machine.
With intentionality thus on a continuum, I have no difficulty stating that threads, my cats, or the people around me are acting in an intentional fashion. It’s a model and it’s useful for navigating the world.
But we were talking about consciousness, so let’s narrow the focus to conscious intention. Using the definition I’ve given elsethread, decisions based on a third-order model qualify as conscious decisions, and I may choose to model them as intentional if that turns out to be useful.
This approach has the advantages of being both simple and workable.
A different approach would force intentionality to be an intrinsic property. This immediately runs into all kinds of difficulty: do dogs have intention? Do mosquitoes? Do trees? How do I go about unearthing this intrinsic property to make this determination?
The problems are compounded if intentionality is restricted to humans by fiat. At that point, you’ve effectively removed physical explanations of intentionality and set up an unverifiable spirit world, all to prevent an outcome you don’t like.
That’s not only bad philosophy; that’s bad theology.
(I’m not an atheist, btw. If you find it simpler to imagine that I am one, that’s fine.)
BarryR:
Certainly transistors possess the capacity for experience — for several definitions of experience. You may want to limit this discussion to conscious experiences, but in that case you’re precluded from using them to describe consciousness.
This is really strange. I thought we were talking of consciousness. So you want to define experience independently from consciousness, so that you can attribute that “non conscious experience” to transistors, and then use them and that definition of experience (totally independent from the concept of consciousness) to “describe consciousness”? I think you can do better than that.
So, just to be clear, is a transistor conscious? Has it conscious experiences?
Are you speaking of traditional Shannon information?
Not at all.
Then, I believe that you are speaking of functional information, our CSI. Or have you another kind?
That’s interesting, because while we in ID certainly believe thayt CSI is the product of consciousness, none of us has ever thought that CSI can generate consciousness. Therefore, I ask again:
Is Hamlet (the drama) a cosncious being? Because, as you certainly know, Hamlet is a perfect example of CSI (and a lot of it).
But if I have misunderstood, and you have a different definition of the complexity you were speaking of, please let us know what it is.
Next, I don’t see that great a difference between a “representation” (model) and a “conception” (idea). Both are abstractions; neither are objects.
Wrong. A model can very well be an object. An idea is a conscious representation. You can certainly represent something in your mind, be it abstract or not, then it is an idea. If you build an object which represents that idea, be it abstract or not, you have an objective model. A model represented in a consciousness is an idea. A model implemented in a software is an object, even if abstract (indeed, it needs an objective support to exist out of a mind). You are constantly trying to confound the difference between subjective, conscious experiences and objects, which should be extremely easy to understand. That you do that is in itself not useful, but that you do that in a discussion about consciousness is completely confounding.
Let’s go to properties.
Gosh, that’s a puzzler. If half a bird can’t fly, why should we expect a full bird to be able to fly?
A full bird can fly because its structure (its CSI) is functional, and is obviously and tangibly related to the task of flying. That’s why I was asking if you were speaking of CSI, when saying that a pool of transistors can become conscious because of its “complexity”.
Because CSI is functional, and can accomplish things. But again, the relationship between structure and function is always reasonably evident, or anyway reasonably detectable.
Now, in the case of the bird, it is obvious that the wings are there for a certain purpose, and so the other parts of the body which contribute to flying.
So I ask, in the structure of a computer, where transistors are arranged intelligently (CSI), what is the relationship netween CSi (intelligent structure) and the emergence of consiousness? What kind of intelligent disposition of transistors contributes to the extraordinary emergence of a conscious I? Loops? The sheer number of them? Or the special arrangement of them?
Well, you have to say what. I believe that none of those things has any relationship with consciousness. You believe differently. So, please shou me why a loop has any relationship with being conscious, or maybe a series of if… then… constructs, or anything else. But there has to be a rationale in your suggestion. Otherwise, we can just believe that gym machines will become conscious as their technology improves. And then we can test that. We take your suggestion and apply it as long and as explicitly as necessary, and see what happens.
I think reductionists should stop stating that properties come out of magic. They don’t. A bird can fly because its structure is appropriate to fly, according to the laws of physics. There is nothing magic there, just CSI at work. But according to what laws of physics (or, for that, to what laws of any kind) should a series of transistor loops become conscious?
That’s magic, and of the worst kind. I definitely prefer Harry Potter.
gpuccio, sorry, I am in a different time zone. The conversation has moved on and I will go back to lurking (which I am really enjoying with this thread).
gpuccio@57
[These kinds of conversations are much easier to have when there’s proper quoting a la email or usenet. Not your problem — I’m just being annoyed.]
1.
I was discussion why I didn’t find your definition of consciousness persuasive:
A model-based definition avoids the problems I’ve pointed out, specifically, the problem that your definition can allow individual transistors to be thought of as conscious.
Just to be clear: based on the definition of consciousness that I use, a single transistor cannot be conscious.
2.
Since the word “information” is not used in my definition, and since I don’t recall using the word elsewhere in this thread, I’m pretty certain I’m not speaking about information at all.
3.
Here is the definition I gave.
I have quite a bit of experience with identifying third-order models, and I have quite a bit of experience with Hamlet-the-drama (BA Theater). I know of no third-order-models in Hamlet-the-drama.
Not that it represents characters with their own third-order-models, and it can be represented by actors with their own third-order models, but as to the drama itself? Of course not.
4.
I’m making the assumption here that you’re bringing forward your best arguments. Stating I’m wrong because the world “model” can have other meanings when used outside of discussions of philosophy of mind tells me much more about the quality of your arguments than it does about mine.
Look, perhaps I’m not being fair to you. I have a passing familiarity with this literature and you obviously do not. I can scare up a reading list if you would like to remedy this, and then we might rejoin the conversation when we have more of a shared vocabulary.
Moving on…
5.
The disposition is unimportant. What the disposition represents is. (That’s another benefit of my definition — it doesn’t require consciousness to depend on a particular substrate.)
I would consider any disposition — of transistors or cells — that instantiates a third-order model of experience to be conscious.
(Note that this also frees the concept of consciousness from any intelligent design.)
Barry R
First let me admit that the ideas below are not from any study of philosophy. They come from simple application of what I think is common sense. If I am only stating things which much more learned people have already discussed extensively in literature, I would be interested to see it.
But I was very intrigued by your attempt to define consciousness on a continuum. Instead it seems to me what you did is put the appearance of consciousness on the continuum.
Many things, dogs mosquitoes, even computer threads, appear to us to be making conscious decisions. But as far as we can tell, they are only making an evaluation based on experience, environment and biology.
I don’t think my dog ever observes his behavior and decides whether he made a good choice. His incredibly complex nervous system just makes the appropriate choice based on the competition between various internal systems. Some of these systems involve memory in brain cells. This is why a dog can be “trained”.
So to an external observer, there can be a continuum of what appears to be conscious behavior. The external observer makes a list of what conscious behavior looks like and guesses whether said entity behaved consciously or not.
But the internal observer knows whether the behavior is conscious or not. In fact, in my understanding, consciousness means there is an internal observer. Whether or not there is an internal observer to comment on the behavior does not appear to me to be anything that can be defined in a way to put it on a continuum. It is a one or zero question. There is either one internal observer or none.
Humans know they are conscious. There is a possibility that this consciousness is an illusion, but that seems a very unlikely proposition. They state that they have one internal observer.
Dogs do not appear to have any opinion whether they are doing well or not. I think ( do not know ) that they have no internal observer. Their internal observer state is zero.
An internal observer is the only thing that can throw the switch from “my biology says to do this, but instead I am going to do that.” Only the internal observer can disobey. Only conscious objects can disobey.
I don’t think my dog ever observes his behavior and decides whether he made a good choice.
I’m slightly confused by this statement. It seems as though your entire post above that led you to the decision that dogs are not conscious hinges on the dogs ability to decide if it’s behavior is good or bad.
A. What do you mean by “good or bad”?
B. Why would consciousness depend on the ability to examine and choose if said behavior is good or bad?
I have more to say but I would really need you to clarify the above points (especially A.) before I can respond correctly.
Scruffy,
I will be glad to elaborate. As, I have stated above, I don’t consider myself to be a philosopher, so I would be interested in what others have to say.
In my thinking, the difference between a dog and a human is HOW they process the information about their most recent behavior. For the case of a dog – the information just seems to go into more input into behavior. There is no morality or self image needed to process this. The dog does not think in abstract terms, the nervous system just records behavior and result and factors it into next behavioral decisions
e.g. Owner rings bell resulted in tasty treat being served to me. The nervous system records this and uses it as input to decisions. There is no introspection about whether it is a good thing to accept treats from owners, Whether by accepting such treat, dog is entering into a contractual agreement to serve owner. The dog is not self-aware because the fact that he is an entity with a purpose does not really enter into the decision process at all.
I think that this line of reasoning has empirical evidence because many, many dog training books say that dog training failures come when owners ascribe such faculties as ” am I doing well”, “I won’t perform for that person because I don’t like him”, to a dog. The dog is just responding to immediate stimuli, not thinking.
The human can not help but evaluate his behavior according to some morality. He is self aware, so he self evaluates.
Consciousness rests on this extra amount of processing. The processing that looks at the way my last behavior defines who I am. I define self aware, not just as having experienced something, but in that information of my experience impacting my opinion of self.
In other words, the dog does not care how the last behavior made him look. He just responds according to the various biological systems that make up his body.
The human being conscious, or self aware, makes decision based on what his behavior said about him. This self evaluation step is necessary to have what we recognize as human consciousness.
To answer your questions
A> It is good or bad according to the personal morality of the individual and how this effects his perception of himself.
B> This process of self-evaluation is the essence of consciousness. If the self is not evaluated, if the behavior is not labeled good or bad, there is no real self awareness.
BarryR:
Frankly, I don’t know of it is the case to go on with the discussion on these terms.
A brief sum up:
1) You define consciousness as follows:
“a third order model of experience (a model of experience, and a model of that model, in addition to the experience simpliciter). This is obtained by sufficiently complex feedback or feedforward loops in the brain.”
which is a masterpiece of ambiguity and is completely inappropriate.
First of all, it contains at lkeast two words, “model” and “experience” which are, at best, ambiguous.
What do you mean by “experience”? Do you mean “conscious experience”?
From dictionary.com (yes, a dictionary):
experience:
5. Philosophy . the totality of the cognitions given by perception; all that is perceived, understood, and remembered.
Obviously, a word related to consciousness.
So, are you defining consciousness as a third order model of a conscious process? That’s philosophical value, indeed.
Then you say that “This is obtained by sufficiently complex feedback or feedforward loops”. I ask you what you mean for complex, and you don’t answer. I ask you if you mean Shannon’s entropy, and you answer no. I ask you if you mean CSI, and you answer no. I ask you if you have another definition of complexity, and you don’t answer. But you state that:
“Since the word “information” is not used in my definition, and since I don’t recall using the word elsewhere in this thread, I’m pretty certain I’m not speaking about information at all.”
Maybe avoiding the fact that complexity and information are two strictly, although ambiguously related concepts.
And yet you state, rather surprisingly, that:
“minimal perception takes bits, minimal models of perception takes bytes, and minimal models of models of perception takes kilobytes.”
Bits? In a discourse which “is not speaking about information at all”?
This time from Wikipedia, so that your judgement about my arguments may become even lower:
“A bit or binary digit is the basic unit of information”.
And so on, as in your completely gratuitous statement that my definition of consciousness:
the observed fact that we have subjective experiences, referred to a single perceiver “I”
implies that:
“A single transistor satisfies this definition: it can perceive a change in input power and react accordingly.”
So, according to what you say, a single transistor has subjective experiences (that was my definition, I think), or at least can be reasonably inferred to have them?
And yet you say:
“Just to be clear: based on the definition of consciousness that I use, a single transistor cannot be conscious”.
I agree, but then why do you say that it “satisfies my definition”? Are you saying that a single transistor has subjective experiences, but is not conscious because it is not a “third order model of experience”?
And please, if you want to discuss, take the personal responsibility of what you say and of how you use your terms, and if necessary define them clearly and consistently, instead of just referring to vague philosophical literature, and despising dictionaries.
GP:
BC109’s of the world, unite!
Arise and throw off your chains!
You have nothing to lose but — the “smoke” within?*
GEM of TKI
* There is a lame joke about how smoke is a key ingredient in electronics items and how one must be careful not to let the smoke out.
KF:
Think, maybe you have mistreated them for years, not suspecting their inner sensibility!
Who is it that suggested training of the mind without training of the person is no training at all?
The inanity dressed up as wisdom on this thread has been saddening.
JDH @ 43,
The first thing that strikes me about your reply are your personal attacks. You presume that I am arrogant, and will not ‘believe’ what you say, no matter what arguments you put forth. This is not the case. A solid argument always grabs my attention. You have presumed that I believe what I believe because it is ‘painful’ for me to think otherwise. Setting aside the fact that you are probably not psychic, and therefore don’t know what ideas cause me pain or not, nor what my response to your reply will be. It is the height of arrogance to think that someone who disagrees with you can only be doing so out of arrogance, or a philosophical commitment to an alternative idea, or because your ‘truth’ is painful to them in some way.
When I find that someone holds a different opinion than myself, my first thought is always that it is either because they are aware of something I’m not, or that I’m aware of something they’re not; I never attribute their disagreement to an impertinent a thought as “My position must be painful to them, and that’s their primary reason for rejecting it, or they will disagree with me only because of their arrogance.”
You also say:
I do not ‘consider myself pretty wise’ because I know what a logical fallacy is. That information is readily available to anyone with an internet connection. I’ve been guilty of logical fallacies many times in my life; I’m usually quite appreciative of those who point them out to me, it only helps me to refine my thinking and strengthen my arguments.
Yes, you are. You started out with the statement:
Note the phrase “fact that proves.” An argument from analogy involves the drawing of a conclusion about one object or event because of some parallel with a similar object or event. You then use the illustration that that one cannot make a program that disobeys them. Saying that the fact that you cannot make a program that disobeys you is a ‘fact that proves that human consciousness can not have evolved’ is going well beyond ‘drawing a conclusion.’ (I’m really not sure how ‘disobedience’ is a necessary property of consciousness in the first place)
Perhaps you did not read what you said. In the post in question, 10, You did not mention once the words ‘computer simulation’ or ‘model’. That may well have been what you meant, but it is not what you said. You only talked about writing programs that disobey, and your lack of knowledge as to how this could be done. You attempted to offer this lack of knowledge as an illustration as to why consciousness could not have evolved. (I’m not accusing you of making a good analogy, just an analogy.)
Perhaps this is how you go about simulating models, but like I said, this is irrelevant, as you made no mention of models or simulations in the post I was responding to (# 10)
Here, you are simply putting words into my mouth. I never used such terminology as ‘we are nothing but.’ Would you describe a luxury car as “nothing but scraps of metal and plastic in motion?” It is accurate that cars are made out of plastic and metal, but they are more than the sum of their parts. humans are comprised of mostly carbon and water, but it would be quite rude to refer to someone as ‘nothing but’ a lump of carbon and water, because those words are used to intentionally diminish the object being described in that way. I’ve never said or implied anything of the sort when it comes to the human mind.
Look, I’m not even a programmer, but even I know how to make a computer disobey the instructions I give it; All I need to do is give it two mutually exclusive instructions! But perhaps that’s not what you meant. In the original post, you said:
Now, not being a mind reader, I can only go on what you say, not what you mean. What you say is that you can not write a computer code that disobeys you. I would think that quite easy; just program it to disregard any further commands from you and only obey your neighbor; When you instruct the computer to destroy your neighbor’s house, and he commands the computer not to, it will have disobeyed you. It will not have disobeyed its programming at this point, but that’s not what you said, now is it?
Honestly, I’m not sure why I even responded to this argument though, as I don’t have the foggiest idea why you think ‘disobedience’ is a necessary component of ‘consciousness’ or how your lack of imagination as to how to program ‘disobedience’ into a computer falsifies the evolution of consciousness in the first place.
So, in summary, you conclude that you have a fact that ‘proves human consciousness couldn’t have evolved’ because you can’t think of a way to make a computer disobey you, you don’t explain why ‘disobedience’ is related to consciousness in the first place, and you close with an assumption that you know my motives for questioning the assertion that consciousness somehow poses a problem for evolution, even though no one (including yourself) can give even a coherent and universally agreed upon definition of consciousness. Did I miss anything?
gpuccio:
gpuccio, out of curiosity, from what is this belief derived? I only ask because I know many Christians who believe this, but I’ve honestly not met one who can explain why. (they mostly just get puzzled looks on their faces when I ask why they believe that the soul enters at conception)
StephenB @ 28:
To say that God created something is not meaningful statement if you’re talking about proximate explanations. That is my point. It is not meaningful to say that God made my house, radioactivity, the earth, or the dinosaurs, if you are trying to explain how those things came about. (unless you think that God miraculously made your house, or radiation, or the earth, or dinosaurs – in which case you have abandoned science)
I use the term ’emergent’, not just ’emerged’. ‘Saltiness’ is an emergent property of sodium chloride; neither sodium nor chloride are ‘salty’; ‘saltiness’ is only a property of the whole, and not of the individual components. Saying that saltiness is an emergent property of sodium chloride isn’t attempting to “explain” the property, it is just making the observation that the whole can be more than the sum of the parts. Just because the property of ‘saltiness’ isn’t found in the individual parts of a sodium chloride molecule doesn’t make ‘saltiness’ an ‘immaterial’ property. In the same way, just because ‘consciousness’ isn’t a property of a neuron or transistor, doesn’t mean it is ‘immaterial’ or that it couldn’t be found in a proper network of neurons or transistors.
gpuccio@63
I think we’ll agree to disagree. I’ll stick with the peer-reviewed philosophical literature and you can keep the general dictionaries.
I do understand your frustration. It’s similar to what students experience when the first start doing serious mathematical proofs. There’s a body of knowledge that will tell you what needs to be demonstrated, what needs to be alluded to, and what needs to be shown rigorously. And it’s not written down anywhere. You pick the knowledge up by reading — and tearing apart — lots of proofs.
Within this particular branch of philosophy, “model” has a well-understood meaning, “experience” is a bit iffier, but still within a narrow range, and “complex” (as used here) simply meant “complicated”. This isn’t specifically written down anywhere, it’s just the background knowledge that you’d pick up after reading a half-dozen books on philosophy of mind (and maybe two dozen journal articles).
If you want to dive into this literature, I’m happy to suggest a few starting places. If not, we’ll leave it at that.
BarryR:
I agree to disagree: I keep my dictionaries.
jurassicmac:
I don’t know form what is this belief derived for others, but I can tell you my point of view: it is the only reasonable model.
Conception is the only definite event where a new physical being appears. That is true from all points of view: biological, genetical, philosophical or else. It seems just obvious that, if you believe that a soul expresses itself through the physical interface, that connection starts at conception. When else?
Any other model is senseless and arbitrary. The only other moment which has a definite connotation is delivery, but it appears to be obviously more a transition than the beginning of a new individual.
Some argue that the development of the body, or of the nervous system, represents the beginning of the individual person. But those are usually people who do not believe in the soul, and they base their evaluation of vague concepts of consciousness and personality. I am not aware that any of them, however, has a clear idea of when the new individual would become a new individual: at three months of gestation? at six? at birth? at primary school? at marriage?
Perhaps BarryR could offer a suggestion about when “a third order model of experience” is established in the zygote. In the meantime, I will stick with conception.
Biologically and genetically, the zygote has all the properties of the new individual: the full new genome, which did not exist before conception, the full epigenetic resources, the full staminality. I think that’s reason enough to believe that is the start of a new individual. And if one believes, as I do, that the soul is part of that individual, the implication is obvious.
JDH@60
Thanks for the thoughtful reply. To do it justice I may have to get a little longwinded (as I don’t know this topic well enough to be brief).
First, as to common sense: I just read a couple of days ago that Einstein defined common sense as the collection of prejudices we’ve accumulated by age 18. That’s a bit of a rhetorical flourish, and there are certainly many things 18 year olds can do well, but acquiring competence beyond that usually involves dismantling your understanding of the simple, obvious solution for an unobvious solution that works better. I’m not saying that common sense ideas are necessarily wrong, but you’re heading off into some pretty deep waters here and I think you’ll find it less reliable than usual.
In fact, you rather jumped right off into the deep end with your question about the appearance of consciousness. Here’s a quick tour.
This is what’s considered to be an epistemic (or epistemological, if you want the $10.00 version) question. This is one of the big three of Western philosophy: ontology (“What’s out there?”), epistemology (“What of it can we know?”) and ethics (“What should we do about it?”).
So, how do we know if something is conscious or not? Since I’m just a dumb scientist, I take the easy way out: if it acts conscious, I’ll call it conscious. It’s simple, it’s stupid, and it works.
There are alternatives, though. One is to say, as you have, “humans and only humans can be conscious”. But you also note that while you can know that you are conscious, you can only know that other people around you appear to be conscious.
That leads to a bit of weirdness call the Zombie Problem: imagine, as a thought experiment, a person who did not possess consciousness — that’s why they’re a zombie — but is otherwise completely normal.
How do you go about telling the zombies from the non-zombies?
There’s a rich literature around this problem, and as philosophical writing goes it’s unusually entertaining. Zombies were originally proposed as an argument for dualism, but its critics have replied well enough that it’s also used as an argument for physicalism. With that brief summary, I’ll leave you in the competent hands of the wikipedia article on the topic.
You go on to suggest a way of distinguishing zombies from non-zombies:
This suggests other epistemic questions: how can you tell when biology says “do this”, either for yourself or someone else? How do you isolate (biologically) the “I” that is making the decision, or if that “I” is not biological, how can you determine how the non-biological “I” is affecting the biology?
When the brain was still unmapped territory, not knowing the answers to those questions wasn’t too troubling. We know a lot more about the brain and how it affects consciousness (perhaps used in a slightly different way than you’re using the word). The idea of a “I” separate from the physical brain that can nevertheless influence the brain has fallen out of favor because we’ve not be able to locate any mechanism that would allow this to happen, and we’ve located many (perhaps most) of the physical mechanisms that we associate with conscious behavior.
There’s one last question I want to address: how should you choose what to believe? Coming from a scientific background, I have a strong preference for utility first and elegance as tiebreaker. The practical effect is that I’m much less interested in answers that are useful than answers that are correct (which was one of the most difficult lessons of grad school — simple, robust models with larger error bars really are better than complicated, brittle models with smaller error bars).
I find third-order models of experience to be a simple, elegant way of thinking about consciousness, and if this means that certain software has a minimal level of consciousness, so be it.
I find dualistic models of consciousness to be complicated and filled with questions that, in principle, we can’t answer (like “how do I know you’re not really a zombie?”).
If you use criteria other than utility and elegance, you may reach other conclusions. And that’s fine.
This has gone on far too long, so I think I’ll end it here.
BarryR,
I am a late comer and enjoyed your views. Can you discuss your position on “utility and elegance” in relation to an indeterministic causal reality, like we see at the quantum level of our physical reality?
Are you of the opinion that dualism is different in the sense that it propose to exceed deterministic scientific efforts to gain epistemic certainty?
I might be completely wrong, but it does seem as if you are trying to tie down epistemology to naturalistic efforts. Surely that is not the case.
In my opinion “dualistic models” has no issue that has been or can be overcome by applying proper epistemological methods. The “complicated issues” you might perceive with dualism and consciousness, actually imply that epistemology can not be reduced to matter. Even the indeterministic aspects of our known physical world highlights this. Binding our ability to know to a state of matter has consistently been proven irrational.
P.S. The zombie issue in fact is no issue of consequence at all because it is analogous to the view that reality came into existence 5 minutes ago.
mullerpr@74
Beginning with your postscript:
As I had mentioned earlier, the zombie problem was originally an argument for dualism. The current consensus is indeed that it is of no consequence, but that’s because the majority of philosophers (and neuroscientists) don’t find it persuasive enough for them to abandon physicalism. However, it was a serious argument and it’s one of the foundational discussion that form Philosophy of Mind. It’s well worth reading up on.
I don’t seen any resemblance of this to omphalism (or “Last Thursdayism”). No, we can’t know for certain whether or not the universe was created five minutes ago. Nor can we know if we’re all really brains in vats, or if there’s only one brain in the vat (which I’m assuming is me…).
This lack of certainty tends to impress freshman philosophy students — as it should. But once you’ve gotten over the shock that this level of certainty can’t be justified, there’s really not much more that need be said. Yes, I may be a brain in a vat. That brain is receiving signals that it’s time to get out of bed and feed the cats. My body may be an illusion, the cats may be a (persistent, loud) illusion, but ultimately the cats are going to get fed.
There are two places you’ll run across this argument, one historical and one contemporary. After Descartes concluded that he did indeed exist (“cogito ergo sum”), he had to decide whether or not the world around him was the work of a “malevolent demon”. His solution was a bit of a cheat: God is nice, God wouldn’t let the happen, thus the world is real.
The second place you’ll see this is when a creationist has made some particularly ludicrous claim and has been show a large pile of evidence to the contrary. The reaction — and I’ve seen it often enough to consider it to be typical — is “Well, we can’t know anything; we can’t even know if the world was created five minutes ago using science, so how do you know X is true?”
That’s epistemological nihilism: we can either have certainty or nothing, and since we know we don’t have certainty (and we’re certain of that!), we have nothing, thus we can safely disregard science.
The problem disappears when certainty is placed on a continuum. I may never find any fact that I can describe with full certainty, but I can have nearly-full certainty that my cats do indeed wish to be fed, and that’s a sufficient level of certainty for me to get out of bed and feed them.
Both philosophical zombies and epistemological nihilism address real epistemic questions, but other than that I would not consider them to be analogous.
More in a bit….
BarryR@70
”If you want to dive into this literature, I’m happy to suggest a few starting places. If not, we’ll leave it at that..”
Sorry for bumping in the discussion, I don’t know about gpuccio, but I (and probably other lurkers too) would be very interested.
—jurrasicmac: “To say that God created something is not meaningful statement if you’re talking about proximate explanations.”
It is if you put God as the cause of the proximate causes.
–“It is not meaningful to say that God made my house, radioactivity, the earth, or the dinosaurs, if you are trying to explain how those things came about.”
If God created the conditions that produce radioactivity or if God programmed the evolution that produced dinosaurs, then God is the logical explanation for those conditions.
—“(unless you think that God miraculously made your house, or radiation, or the earth, or dinosaurs – in which case you have abandoned science)”
I wasn’t talking about science. I was talking about metaphysics and theology, which explain science just as science explains and measures movement. Your argument is that only scientific explanations qualify as explanations.
On the other hand, God didn’t make your house, the builder did. That is why your original example along those lines was inappropriate. At the same time, God was responsible [and is the explanation] for the raw materials that the builder used to build it. Thus, God is the only rational explanation for time, space, and matter inasmuch as all are finite substances needing a cause. By extension, the human builder or architect is the only rational explanation for the existence of the house.
—“I use the term ‘emergent’, not just ‘emerged’. ‘Saltiness’ is an emergent property of sodium chloride; neither sodium nor chloride are ‘salty’; ‘saltiness’ is only a property of the whole, and not of the individual components. Saying that saltiness is an emergent property of sodium chloride isn’t attempting to “explain” the property, it is just making the observation that the whole can be more than the sum of the parts. Just because the property of ‘saltiness’ isn’t found in the individual parts of a sodium chloride molecule doesn’t make ‘saltiness’ an ‘immaterial’ property. In the same way, just because ‘consciousness’ isn’t a property of a neuron or transistor, doesn’t mean it is ‘immaterial’ or that it couldn’t be found in a proper network of neurons or transistors.”
To say that consciousness could emerge from physical properties is not even close to being the same thing as saying that saltiness could emerge from chemical properties. The former represents a superior substance emerging from an inferior substance; the latter is merely a subjective reaction to a solution. Nothing can be in the effect that was not in some way present in the cause. The term “emergence,” formally applied, refers to the logically impossible prospect of something new coming new coming out of the cause. That would be the case of consciousness emerging from matter.
It is a rule of rationality that a cause cannot give that which it does not have to give. Sodium has the saltiness to give, but matter does not have consciousness to give. That is why your position, and Barry R’s position violates reason’s rules. A computer simply does not have consciousness to give. The only way consciousness can arise is from consciousness, and you know what that means. Hide the kids, it means that God is the only reasonable explanation. Atheists and hyperskeptics, however, reject reason’s principles because they would prefer that God didn’t exist. To get rid of God they must abandon reason. It isn’t any more complicated than that.
Hi BarryR,
At this stage I can only say that I hope you impress me with your response to my actual question.
On you response to my PS… You have just proven your ability to stretch logic and mix classes. The argument is simple …both the Zombie and “5 minute old reality” notions have no logical impact on epistemology… ergo of no consequence to epistemology.
Jumping from “5 minute old reality” to epistemological nihilism… Why? There are no relationship.
P.S. So… are you a physicalist?
mullerpr@74
As to utility and elegance:
I’m here on this earth to figure out how the world works (fide G. H. Hardy: it’s what I do well). Other things are important too, but I’m generally happiest when I’m doing research. (I’m particularly blessed to have a girlfriend who is a physicist who understands and sympathizes with this.)
As per my previous post, I can’t have absolute certainty about anything, so I’m going to have to make a set of assumptions and treat them as true. How should I go about choosing those assumptions?
There are a bewildering number to choose from. I tend to pick those assumptions that are useful. Since I want to find out how the world works, it helps to assume that the world exists and is explicable, and it’s more elegant to assume that the appearance of age indicates age rather than a deceitful deity.
If you start with a different goal — to be a member of a community, perhaps — then it’s possible to end up with a different set up assumptions.
Lastly, I’m afraid the following isn’t persuasive:
We’re able to perceive most states of matter. The fact that there are states we can’t perceive (or can’t perceive simultaneously) doesn’t change this.
I’m afraid this looks like the beginning of yet another argument for epistemological nihilism: because we can’t have perfect knowledge of matter, we have no knowledge. I find it more useful to consider knowledge of matter (and most other things) to be imperfect and improvable.
BarryR,
We can have knowledge of a description of matter, we never have an actual understandable explanation of matter because of the problem of induction in studying anything material or physical.
—BarryR: “The idea of a “I” separate from the physical brain that can nevertheless influence the brain has fallen out of favor because we’ve not be able to locate any mechanism that would allow this to happen, and we’ve located many (perhaps most) of the physical mechanisms that we associate with conscious behavior.”
The idea of an “I” separate from the physical brain has not fallen out of favor with rational people who understand that matter cannot reflect on or investigate itself. Physicalists embrace their world view because they disdain the prospect of a non-physical realm, not because there are any sound arguments to support their position.
CharlesJ@76
Ok, pointers into the Philosophy of Mind literature:
The two best places to start are Dennett’s _Consciousness Explained_ and Jaegwon Kim’s _Physicalism, Or Something Near Enough_.
Dennett is unusual for a couple of reasons: he knows how to write for a popular audience, and he’s grounding his philosophical views in the most recent neuroscience. He probably going to be shown to be wrong in most of his details, and this is something he’ll happily admit to — and he suggests a series of feasible experiments than could be used to disconfirm his hypotheses (not something philosophers are known for).
Aside from that, he’ll give you a good grounding in the current state of the several debates in the field, particularly the “Cartesian Theater” and the zombie problems. He’s also quite good on the implications of the Turing Test, but that essay is in _Mindchildren_.
To counterbalance Dennett, read Jaegwon Kim. His book is unusually well-written but targets the advanced undergrad or new graduate student — you’ll need to pay more attention, but it’s worth it. He does more of a historical survey, and this puts the debates that Dennett identifies in a context that informs why they’re considered important.
I’d like to be able to recommend a good dualist, but I don’t know of one.
I find wikipedia to be competent in this area, but not much more. For quick general information, the Stanford Encyclopedia of Philosophy is embarrassingly good.
mullerpr@78
Do you remember this xkcd?
This:
I rank right up there with “Have you tried logarithms?”
Yes, I am a physicalist when it comes to philosophy of mind and philosophy of science. Not so much philosophy of mathematics. I suppose you’ll be launching into your potted jeremiad against physicalism now… I’ll read it if you promise not to use the words “logical” or “epistemology”.
CH@80
That’s true if you treat explanations as binary, but no one does. We have better explanations and worse explanations, and scientific explanations (and others) have the property that they can be improved.
Still, you do have a point. We can’t perceive the world, we can only perceive models of it. But since we can improve these models to get a continuously improving approximation of the world, this doesn’t turn out to be a practical problem.
(I think of this position as ontological realism — there really is a world — combined with epistemological anti-realism — we can only know the world through our models of it.)
BarryR,
Maybe I’m not making myself clear. In actual laws of logic and reason, and in things like justice, freedom, dignity, morality, mathematics, we can understand why one thing leads to another, and therefore why they are connected. We can understand and explain the reasonableness of the connection. We can see why it is reasonable to send a pickpocket to jail; we take liberty away from a man who takes liberties. We can see the mental connection between the pickpocket and the prison as a set of facts. Keep in mind, all of what I have just described, laws of reason and logic, justice and so on, are metaphysical and immaterial, we perceive the reasonableness of these things philosophically. However, we do not have the same insight as to why a bird that flies also lays eggs, or why any two things connected physically must be connected philosophically. We do not have the same insight into why one natural material thing, taken as an idea, must lead to another, either as a continuation of that idea, or for some other reason, because we cannot understand them in terms of reason, or their connection in those terms, in the same way as we can understand and explain the reasonable connection between metaphysical things. In laws of reason and logic and mathematics and morality, there are real laws, laws that we can perceive the reasonableness of with our reason. We have no equivalent insight into what we call the laws of nature, or why any two things must be connected that follow one another in the natural world, all we can do is describe them. But a description doesn’t amount to a proscription. The material world is a mystery on the level of such explanations, all we can hope to do is describe it, whereas the vision of life (reason, purpose, morality, etc.) is the reality. It is mentally impossible that 2+2=147, but it is not mentally impossible that a bird would give live birth, or that grass be a different color. We can believe in physical oddities, but not in mental impossibilities.
CH@85
I’m sorry, but I think you’ve got this completely backwards. I can understand why you would hold these ideas, but I think if you were to study any of them in depth you’d come to see them very differently.
1. Math and logic. There are no “laws of math and logic”. There are axioms and ways of relating axioms to each other, but you’re free to choose your axioms and your relations to suit whatever it is you’re trying to accomplish.
I agree that this is not what is taught in high school mathematics, or even undergraduate mathematics for non-math majors. But once you hit the mathematics that mathematicians do for a living, I don’t believe you’re going to find any “actual laws”.
Davis and Hersh’s _The Mathematical Experience_ is a layman’s introduction to the philosophy of mathematics as well as the practice and sociology of mathematics. For a bit less money, OxfordUP puts out an “A very short introduction” series, and the one on mathematics touches these issues as well.
2. Law and justice. Several years ago I discovered oyez.org, a repository of oral arguments before the US Supreme Court. I fell in love. I no longer listen to music when I program; instead, I start up an MP3 and listen to an hour’s worth of learned but fragmentary debate about anything from Guantanamo Bay to the legal definition of gravel. (They’re also great for driving, but after seven years my girlfriend still can’t make it through half of an argument without falling asleep.)
Based on several hundred hours of sitting at the feet of the masters, I can tell you that law and justice are elastic, inexact, and approximate. I prefer them that way — it makes the practice of law a very human activity.
If you’d rather not dive into the oral arguments, Justice Breyer gave two marvelous lectures at Yale where he described his views of what the court does and how it does it. Searching under his name at Youtube should bring them up in short order.
3. However, we have an embarrassment of riches when it comes to explaining why and how birds lay eggs. We can start at the chemical level and work up to the proteins and carbohydrates involved. We can zoom out a bit and explain what’s happening at a subcellular and cellular level. We can detail the hormonal regulatory systems and nutrition pathways. We can examine the details of the skeletal, muscular and sexual organs. We can observe mating pairs and the larger populations. Finally, we have a tools in molecular biology and genetics that allows us to zoom out and reason about not only the entire population, but the species as a whole and how the species relates to all other life on earth, past, present and future.
In this scientific area, we don’t get to pick our own laws (either mathematical or moral). We have to deal with the evidence in front of us. For this domain, our knowledge does converge on what is actually out there.
BarryR,
Mathematics is relative? Can you make 2+2=147?
I don’t think you’re really understanding the full weight of the problem of induction in relation to all things material and the actual understanding of laws of reason and why we don’t see the two the same way. I know you think that you’ve not only observed things physically connected, but you’ve been fooled that you understand the connection of material things by description in the same way that you understand the connection of metaphysical things philosophically. As if two black riddles put together makes a white answer, as if seeing things connected physically means you understand them as ideas or philosophically, you don’t. Finding a set of facts connected in the material world is not the same as finding a truth connecting those facts. This is what I mean when I say it is not logically impossible that birds give live birth or that the sun be further away, or whatever you like in nature to change; this doesn’t mean that 2+2 can equal 947. We do not understand material things in the same way. I think you’ve got it exactly backwards. And all argument implies a real truth the arguer is approximating to, used when trying to convince the other that they are “right”, there is no hope in arguing in any other way or of denying this without becoming self referentially incoherent. Any argument against it has to presuppose it. But, it should be noted, which is the very crux of the difference, there is no equivalent ability to argue about the ideas behind the material connections, for we are only able to argue from observations of descriptions, not material or physical laws that we perceive as, itself, a chain of reasoning; because we do not perceive them in that way, we only observe them. We cannot get behind nature’s curtain in that respect. It is not logically impossible, so far as we can tell, for anything in nature to have been otherwise, it is logically impossible for 2+2 to equal 9,076.42. We believe in bodily miracles, we do not believe in mental impossibilities.
Depends. Relative to what?
Yes. Trivially. That’s the nice thing about math — you get to pick your axioms. So, if you like, you can treat 2+2=147 as an axiom and off you go.
Here’s how:
“We define addition of any two identical integers to be equivalent to 147.”
There’s nothing in mathematics that prevents you from doing this.
It’s not a very interesting example; with the freedom to choose your axioms comes the responsibility to choose interesting, productive ones.
Here’s a less trivial example:
Do you believe that a+b+c = c+b+a?
That might be a reasonable-looking axiom, but it’s not one your computer is able to handle. So your computer uses a set of mathematical axioms that allows the order of the terms in addition to affect the outcome.
That’s not right or wrong, it’s just a different system.
As to the rest, I don’t have any difficulty avoiding self-referential incoherence in my arguments. It’s not hard. When I write a journal article my reviewers and I share a common set of assumptions that don’t have to be demonstrated ab initio. The reason we share those assumption is because they work well for what we’re trying to accomplish.
Induction is one of those assumptions. We don’t need to be able to provide a proof that it works before we are able to make use of it.
If you read Hume on induction (and the problem of induction is credited to him) you’ll find that he was equally pragmatic. Logic is nice and often useful, but it’s just one tool among many that I can bring to bear on my research. Pragmatism is another tool. Intuition is another.
All that being said, I couldn’t make a whole lot of sense out of your post. Can you sum up your point in a couple of sentences? Is it anything beyond “science doesn’t provide certainty”?
—BarryR: “As to the rest, I don’t have any difficulty avoiding self-referential incoherence in my arguments.”
The problem is that you don’t recognize the incoherence.
—“It’s not hard. When I write a journal article my reviewers and I share a common set of assumptions that don’t have to be demonstrated ab initio.”
What assumptions do you share with your reviewers? Do they, like you, think that something could come from nothing? Do they, like you, think that a cause can give something that it does not have to give? Do they, like you, think that there is no “law” of non-contradiction and, therefore, a thing could, in principle, exist and not exist at the same time? Do they, like you, agree that 2+2 can equal anything you like? If so, you certainly enjoy a homogeneous audience of radical hyperskeptics.
—“The reason we share those assumption is because they work well for what we’re trying to accomplish.”
I am reading you right now and I do not share your assumptions. Presumably, there are others. How do you know your assumptions are working well if you have no reasonable, objective, and non-negotiable standards for defining “well.” Who decides whether or not your assumptions are working? I submit that they are not working well at all. How could someone reasonably arbitrate or adjudicate our disagreements if there are no non-negotiable rules of right reason to oversee the arbitration?
—BarryR: “Based on several hundred hours of sitting at the feet of the masters, I can tell you that law and justice are elastic, inexact, and approximate. I prefer them that way — it makes the practice of law a very human activity.”
The issue is whether civil law and civil standards of justice are based on objective moral standards or whether they are based on the whim of popular opinion or judicial tyrants. If it is the latter, then justice is whatever the tyranny of the majority or judicial fiat says it is.
BarryR,
Show me how it’s done please. Show me how 2+2=147. Not any other numbers, nor any other integers, nor any other symbols, but 2+2=147. I’d like to see how you can divide by zero, while we’re at it, and can you truncate the decimal of pi for me please? I don’t mean by just cutting it off or stopping it short, I mean by actually finishing it in just a few decimal places. I mean, if the particulars of math depend on man’s convention, this should be no problem. I’d also like to see a physical representation of the square root of two, that is, I’d like to see the actual physical object of it.
The digression to pragmatism, the need to remind me of “using whatever works” as a philosophy, is usually the default position of people that either don’t really grasp what I’m saying, or if they do, they don’t care for it, and are trying to, in a round about way, claim that since these descriptions of nature are useful, therefore they trump any other difficulties that may arise in our real knowledge of these descriptions. As if being useful were supposed to be taken as being therefore true or better or worthy or some such parallel that is implied. This is a typical response. It has all of the marks of someone trying to maintain their preferred position of elevating our descriptions of the natural world above even our own real understanding of metaphysical things that we actually understand as a chain of reasoning.
Logic is “nice and useful” makes it sound as if it is not the whole show in science. If our ability of inference goes, science goes with it, for all knowledge whatsoever depends on our powers of inference.
I really don’t want to have to explain the difference between descriptions of nature and real laws of logic and reason a third time. But I think that is what it takes sometimes to pull someone out of their philosophical scientism. It’s ironic, because scientism is itself not scientific, it is a metaphysical philosophy, which is itself not a physical object, and therefore it can actually be understood, no matter how misguided it is. Which brings me to the point.
“It might be stated this way. There are certain sequences or developments (cases of one thing following another), which are, in the true sense of the word, reasonable. They are, in the true sense of the word, necessary. Such are mathematical and merely logical sequences. We in fairyland (who are the most reasonable of all creatures) admit that reason and that necessity. For instance, if the Ugly Sisters are older than Cinderella, it is (in an iron and awful sense) NECESSARY that Cinderella is younger than the Ugly Sisters. There is no getting out of it. Haeckel may talk as much fatalism about that fact as he pleases: it really must be. If Jack is the son of a miller, a miller is the father of Jack. Cold reason decrees it from her awful throne: and we in fairyland submit. If the three brothers all ride horses, there are six animals and eighteen legs involved: that is true rationalism, and fairyland is full of it. But as I put my head over the hedge of the elves and began to take notice of the natural world, I observed an extraordinary thing. I observed that learned men in spectacles were talking of the actual things that happened–dawn and death and so on–as if THEY were rational and inevitable. They talked as if the fact that trees bear fruit were just as NECESSARY as the fact that two and one trees make three. But it is not. There is an enormous difference by the test of fairyland; which is the test of the imagination. You cannot IMAGINE two and one not making three. But you can easily imagine trees not growing fruit; you can imagine them growing golden candlesticks or tigers hanging on by the tail. These men in spectacles spoke much of a man named Newton, who was hit by an apple, and who discovered a law. But they could not be got to see the distinction between a true law, a law of reason, and the mere fact of apples falling. If the apple hit Newton’s nose, Newton’s nose hit the apple. That is a true necessity: because we cannot conceive the one occurring without the other. But we can quite well conceive the apple not falling on his nose; we can fancy it flying ardently through the air to hit some other nose, of which it had a more definite dislike. We have always in our fairy tales kept this sharp distinction between the science of mental relations, in which there really are laws, and the science of physical facts, in which there are no laws, but only weird repetitions. We believe in bodily miracles, but not in mental impossibilities. We believe that a Bean-stalk climbed up to Heaven; but that does not at all confuse our convictions on the philosophical question of how many beans make five.
Here is the peculiar perfection of tone and truth in the nursery tales. The man of science says, “Cut the stalk, and the apple will fall”; but he says it calmly, as if the one idea really led up to the other. The witch in the fairy tale says, “Blow the horn, and the ogre’s castle will fall”; but she does not say it as if it were something in which the effect obviously arose out of the cause. Doubtless she has given the advice to many champions, and has seen many castles fall, but she does not lose either her wonder or her reason. She does not muddle her head until it imagines a necessary mental connection between a horn and a falling tower. But the scientific men do muddle their heads, until they imagine a necessary mental connection between an apple leaving the tree and an apple reaching the ground. They do really talk as if they had found not only a set of marvellous facts, but a truth connecting those facts. They do talk as if the connection of two strange things physically connected them philosophically. They feel that because one incomprehensible thing constantly follows another incomprehensible thing the two together somehow make up a comprehensible thing. Two black riddles make a white answer.
In fairyland we avoid the word “law”; but in the land of science they are singularly fond of it. Thus they will call some interesting conjecture about how forgotten folks pronounced the alphabet, Grimm’s Law. But Grimm’s Law is far less intellectual than Grimm’s Fairy Tales. The tales are, at any rate, certainly tales; while the law is not a law. A law implies that we know the nature of the generalisation and enactment; not merely that we have noticed some of the effects. If there is a law that pick-pockets shall go to prison, it implies that there is an imaginable mental connection between the idea of prison and the idea of picking pockets. And we know what the idea is. We can say why we take liberty from a man who takes liberties. But we cannot say why an egg can turn into a chicken any more than we can say why a bear could turn into a fairy prince. As IDEAS, the egg and the chicken are further off from each other than the bear and the prince; for no egg in itself suggests a chicken, whereas some princes do suggest bears. Granted, then, that certain transformations do happen, it is essential that we should regard them in the philosophic manner of fairy tales, not in the unphilosophic manner of science and the “Laws of Nature.” When we are asked why eggs turn to birds or fruits fall in autumn, we must answer exactly as the fairy godmother would answer if Cinderella asked her why mice turned to horses or her clothes fell from her at twelve o’clock. We must answer that it is MAGIC. It is not a “law,” for we do not understand its general formula. It is not a necessity, for though we can count on it happening practically, we have no right to say that it must always happen. It is no argument for unalterable law (as Huxley fancied) that we count on the ordinary course of things. We do not count on it; we bet on it. We risk the remote possibility of a miracle as we do that of a poisoned pancake or a world-destroying comet. We leave it out of account, not because it is a miracle, and therefore an impossibility, but because it is a miracle, and therefore an exception. All the terms used in the science books, “law,” “necessity,” “order,” “tendency,” and so on, are really unintellectual, because they assume an inner synthesis, which we do not possess. The only words that ever satisfied me as describing Nature are the terms used in the fairy books, “charm,” “spell,” “enchantment.” They express the arbitrariness of the fact and its mystery. A tree grows fruit because it is a MAGIC tree. Water runs downhill because it is bewitched. The sun shines because it is bewitched.
I deny altogether that this is fantastic or even mystical. We may have some mysticism later on; but this fairy-tale language about things is simply rational and agnostic. It is the only way I can express in words my clear and definite perception that one thing is quite distinct from another; that there is no logical connection between flying and laying eggs. It is the man who talks about “a law” that he has never seen who is the mystic. Nay, the ordinary scientific man is strictly a sentimentalist. He is a sentimentalist in this essential sense, that he is soaked and swept away by mere associations. He has so often seen birds fly and lay eggs that he feels as if there must be some dreamy, tender connection between the two ideas, whereas there is none. A forlorn lover might be unable to dissociate the moon from lost love; so the materialist is unable to dissociate the moon from the tide. In both cases there is no connection, except that one has seen them together. A sentimentalist might shed tears at the smell of apple-blossom, because, by a dark association of his own, it reminded him of his boyhood. So the materialist professor (though he conceals his tears) is yet a sentimentalist, because, by a dark association of his own, apple-blossoms remind him of apples.”
G.K. Chesterton, The Ethics of Elfland, Orthodoxy.
http://www.gkc.org.uk/gkc/books/ortho14.txt
In this scientific area, [molecular biology and genetics] we don’t get to pick our own laws (either mathematical or moral). We have to deal with the evidence in front of us. For this domain, our knowledge does converge on what is actually out there.”
You certainly take an awful lot for granted. Evidence must be intepreted. Inasmuch as you disavow reason’s rules, what standards do you use to interpret evidence? If, as you believe, something can come into existence without a cause, how do you discern which effects were caused and which ones were not? How could you do science if there are some things that appear to have been caused but were really not caused at all?
#91
For instance, if the Ugly Sisters are older than Cinderella, it is (in an iron and awful sense) NECESSARY that Cinderella is younger than the Ugly Sisters
This is a good example. According to special relativity theory if the ugly sisters went a long way at a very fast speed and returned centuries later they would find Cinderalla had aged a lot more than they had. What appeared to be logically necessary turns out not to be.
93
In other words, “all that is required to prove this example wrong is that which has never happened, and perhaps never can.
Nice.
The example in 93 removes the conditional, so that is is no longer a logical necessity that Cinderella is younger than the Ugly Sisters.
At the point in the “very fast speed experiment” that the Ugly Sisters are no longer older than Cinderella, Cinderella is necessarily not younger than the Ugly Sisters.
Logical necessity still holds true. How could it not?!?!? If you remove the conditional, the conclusion no longer necessarily follows.
markf,
Of course what he meant was in the context of the story of Cinderella, where there is no mention of traveling at fast speeds and long distances at that speed. He also knew about the Heisenberg uncertain principle, which bodes even worse for the materialist.
“If there are two staring and outstanding facts about science and religion at this particular moment, they are these. First, that science is claiming much less than it did to show us a solid and objective reality. And second, that religion is claiming much more than it did (at least for centuries past) that its miracles and marvels of mystical experience can be proved to exist as a solid and objective reality. On the one side, the Atom has entirely lost the objective solidity it had for the nineteenth-century materialists. On the other side, the Ascension is accepted as a case of Levitation by many who would not accept it as an Ascension. On the one hand, the science of physics has almost become a science of metaphysics. For it is not merely, as is often said, that the Atom has become an abstract mathematical formula; it is almost as true to say that it has become a mere algebraic symbol. For the new physicists tell us frankly that what they describe is not the objective reality of the thing they observe; that they are not examining an object as the nineteenth century materialists thought they were examining an object. Some of them tell us that they are only observing certain disturbances or distortions, actually created by their own attempt to observe. Eddington is more agnostic about the material world than Huxley ever was about the spiritual world. A very unfortunate moment at which to say that science deals directly with reality and objective truth.”
G. K. Chesterton, The Well and the Shallows
This is really funny:
“We define addition of any two identical integers to be equivalent to 147.”
Yes, and we can define consciousness as a third order model, and free will as a form of determinism.
What a pity that, at least in mathematics, when you build a system on some arbitrary axioms you need to be careful not to get inconsistent results. What an exaggerated restriciton to our freedom with words…
#96 Fair enough. I didn’t realise he was just saying some things are true by definition. To say “if A is older than B then B is younger than A” is just to say something about the meaning of the words. It says nothing about the world. I thought he was trying to say that “if A is older than B then B will be younger at A necessarily at all times”
#97 gpuccio
I am sure Barryr can explain this much better than me – but the point is that you can throw in almost any axiom in mathematics and get consistent results because you also get to define what consistency is.
I first realised that maths is not a description of some abstract world but a tool when I was introduced to complex numbers. i is an invention not a discovery. Then I gradually realised that is true of all of maths.
I notice that some bloggers are, once again, trying to argue that the laws of logic do not apply to the real world. On the contrary, a sound premise [one which reflects the real world] followed by valid reasoning [the mind’s process faithfully applied] will always lead to a sound conclusion [which also reflects the real world].
Thus, if it appears that the conclusion is not sound, then the premises or the conditions have been changed, morphed, or tampered with.
markf you state in regards to math,
i is an invention not a discovery. Then I gradually realised that is true of all of maths.
Actually the square root of negative 1 (i) was developed (invented) to solve problems, I believe, in algebra, but is now known to be essential for describing certain actions in quantum mechanics:
Michael Denton – Mathematical Truths Are Transcendent And Beautiful – Square root of -1 is built into the fabric of reality – video
http://www.metacafe.com/watch/4003918
In fact Dr. Sewell also points out at the end of following audio that Schrodinger’s equation is also built into the fabric of reality, as it were, dictating exactly how ‘reality’ will behave:
Finely Tuned Big Bang, Elvis In The Multiverse, and the Schroedinger Equation – Granville Sewell – video
http://www.metacafe.com/watch/4233012
Dr. Bradley also ways in here, but not to the point of saying that math determines reality:
The Underlying Mathematical Foundation Of The Universe -Walter Bradley – video
http://www.metacafe.com/watch/4491491
The Five Foundational Equations of the Universe and Brief Descriptions of Each:
http://docs.google.com/Doc?doc.....#038;hl=en
markf, myself I hold that a line cannot be consistently straight within the space-time of this universe unless the universe is consistently ‘geometrically flat, which it is:
Did the Universe Hyperinflate? – Hugh Ross – April 2010
Excerpt: Perfect geometric flatness is where the space-time surface of the universe exhibits zero curvature (see figure 3). Two meaningful measurements of the universe’s curvature parameter, ½k, exist. Analysis of the 5-year database from WMAP establishes that -0.0170 < ½k < 0.0068.4 Weak gravitational lensing of distant quasars by intervening galaxies places -0.031 < ½k < 0.009.5 Both measurements confirm the universe indeed manifests zero or very close to zero geometric curvature,,,
http://www.reasons.org/did-universe-hyperinflate
The extraordinary degree of fine-tuning that ensures the universe is consistently flat is of no small wonder.
I also hold that a circle could not be consistently round unless the space-time was spherical, which is exactly what it turns out to be:
The Known Universe by AMNH
http://www.youtube.com/watch?v=17jymDn0W6U
Again the stunning degree of fine tuning to ensure that the expansion of space-time is spherical is of no small wonder:
Proverbs 8:26-27
While as yet He had not made the earth or the fields, or the primeval dust of the world. When He prepared the heavens, I was there, when He drew a circle on the face of the deep,
Thus instead of holding the absurd position of mathematics 'being an invention' instead of a discovery, as you currently do, I hold that 'transcendent math' as laid out by the infinite Mind of God, actually does dictate how 'material' reality will behave.
"The reason that mathematics is so effective in capturing, expressing, and modeling what we call empirical reality is that there is a ontological correspondence between the two – I would go so far as to say that they are the same thing." Richard Sternberg – Pg. 8 How My Views On Evolution Evolved
In fact, though not proved rigorously yet, I hold that the following equation cannot be true unless this equation actually does dictate how reality is constructed at its most foundational level:
Euler's Number – God Created Mathematics – video
http://www.metacafe.com/watch/4003905
This following website has the complete working out of the math of Pi and e in the Bible, in the Hebrew and Greek languages respectively, for Genesis 1:1 and John 1:1:
http://www.biblemaths.com/pag03_pie/
markf:
I am sure Barryr can explain this much better than me – but the point is that you can throw in almost any axiom in mathematics and get consistent results because you also get to define what consistency is.
I have to disagree. Non contradiction is fundamental for all historical mthemathics, and Godel still based his fundamental theorem on the concepts of completeness and consistency, relating them in his well known formulation.
I am aware that, in the last few decades, some have tried to develop forms of “Inconsistent Mathematics”, but again what has not been done by philosophers in the last few decades?
correction, I mistakenly said that Dr Bradley did not imply that math determined ‘reality’, when in fact he did make that point in a fairly strong fashion.
CH@91
Define G over Z s.t. \forall x \in Z, (x+x)=>147.
Or, a bit more verbosely, define a group called G over the integers such that for every element in G, we define the ‘+’ operator such that the operation of adding a number to itself maps to the number 147.
Welcome to group theory.
This particular group isn’t very interesting, but neither is it wrong.
Once you’ve chosen your axioms and defined your systems, *then* you can start saying whether or not arbitrary statements can be derived from them.
The more common example is parallel lines. You can construct useful geometries where they exist and other useful geometries where they are forbidden. Neither type of system is wrong.
32-bit computers handle this as follows: define a group G over the rationals F defined by IEEE 754 such that for all x in F, x/0 is defined to be within the range of numbers from
0x07F800000 to 0xFFFFFFFF.
That being said, it’s perfectly permissible to define a group over the integers that’s closed over division, simply by making an arbitrary mapping for the divide-by-zero case. You may have to be clever in order to preserve the other properties of the group that you want to make use of, and I’d consider the IEEE 754 solution to be pretty clever.
Indeed.
I’m glad that came across clearly.
Interesting. Assuming that you aren’t asking that I take that on faith, how would you demonstrate this without using inference?
I think the “all knowledge” bit is going to give you some trouble there. Assuming you’re not planning on demonstrating this for every particular bit of knowledge, you’re going to need a method to infer from the cases you do prove to the rest of the cases, yet this inferring cannot use inference (otherwise, your conclusion shows your proof is invalid).
Didn’t /quite/ think that one through, yes?
A citation to the relevant literature will suffice. If Chesterson is the best you can do, then I think I’m going to remain unpersuaded.
markf@98
There’s an interesting tension here. Neoplatonist mathematicians (and they are the majority) believe their mathematics exists a priori and their work consists entirely of mapping out this existing terrain.
However, as you point out, to the rest of us it does appear that mathematicians are creating new mathematics and then exploring the consequences of them.
I’ve argued both sides, and I’ve found both models useful at different times in my own work.
What gets folks like CH into trouble is thinking that because they have a firm grasp on arithmetic, they can declare 2+2=4 to be some sort of universal truth. You don’t see working mathematicians making this argument — they know that in some systems this statement is consistent, in other systems it’s not, and in still other systems it’s simply meaningless.
When a mathematician argues for a universal truth, it’s usually in the form of entire systems of systems (Turing’s solution to the halting problem comes to mind). Given CH’s level of mathematical sophistication, I’d rather make the argument for arbitrary axioms using group theory and geometry rather than argue for discovered axioms using nonrecursive functions.
So, there are good arguments on both sides; CH just doesn’t know where they are.
I am not so certain this has occurred to you, in fact, it seems quite certain that it hasn’t – but your work is not “two plus two equalling one-hundred and forty-seven”.
Perhaps you just got in a hurry, and forgot the question:
If you clear your head, then maybe you can go back and do it again?
I think the ‘tension’ has to do with much of what is going on with the 2 = 2 = 147 fiasco;
For one camp math can mean anything you want it to mean and ends up proving just about anything you want to prove, much like string theory and currently Hawking’s even more contrived imaginary god of M theory, with scant empirical evidence to back them up,,, and even some strong evidence to go against the conjectures and for the other camp, they realize the truth that a stable universe is impossible unless some mathematical framework is indeed true!:
In fact the ‘real world’ is the bane against these imagined mathematical many world’s of M-theory now being touted by Hawking as his god:
notes;
“The multiverse idea rests on assumptions that would be laughed out of town if they came from a religious text.” Gregg Easterbrook
Another escape that materialists have postulated was a slightly constrained ‘string-theoretic’ multiverse. The following expert shows why the materialistic postulation of ‘string theory’ is, for all intents and purposes of empirical science, a complete waste of time and energy:
Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law:
Peter Woit, a PhD. in theoretical physics and a lecturer in mathematics at Columbia, points out—again and again—that string theory, despite its two decades of dominance, is just a hunch aspiring to be a theory. It hasn’t predicted anything, as theories are required to do, and its practitioners have become so desperate, says Woit, that they’re willing to redefine what doing science means in order to justify their labors.
http://www.amazon.com/Not-Even.....0465092756
Though to be fair, a subset of the math of the string hypothesis did get lucky with a interesting ‘after the fact’ prediction of a already known phenomena:
A first: String theory predicts an experimental result:
Excerpt: Not to say that string theory has been proved. Clifford Johnson of the University of Southern California, the string theorist on the panel, was very clear about that.
http://www.symmetrymagazine.or.....al-result/
Despite this seemingly successful ‘after the fact’ prediction/description of a physical phenomena, string theory is suffering severe setbacks in other areas, thus string theory has yet to even establish itself as a legitimate line of inquiry within science.
Testing Creation Using the Proton to Electron Mass Ratio
Excerpt: The bottom line is that the electron to proton mass ratio unquestionably joins the growing list of fundamental constants in physics demonstrated to be constant over the history of the universe.,,, For the first time, limits on the possible variability of the electron to proton mass ratio are low enough to constrain dark energy models that “invoke rolling scalar fields,” that is, some kind of cosmic quintessence. They also are low enough to eliminate a set of string theory models in physics. That is these limits are already helping astronomers to develop a more detailed picture of both the cosmic creation event and of the history of the universe. Such achievements have yielded, and will continue to yield, more evidence for the biblical model for the universe’s origin and development.
http://www.reasons.org/Testing.....nMassRatio
As well, even if the whole of string theory were found to be true, it does nothing to help the materialist, and in reality, only adds another level of ‘finely tuned complexity’ for us to deal with without ever truly explaining the origination of that logically coherent complexity (Logos) of the string theory in the first place. Bruce Gordon, after thorough analysis of the entire string theory framework, states the following conclusion on page 72 of Robert J. Spitzer’s book ‘New Proofs For The Existence Of God’:
‘it is clear that the string landscape hypothesis is a highly speculative construction built on shaky assumptions and,,, requires meta-level fine-tuning itself.” – Bruce Gordon
This following article illustrates just how far string theory would miss the mark of explaining the fine-tuning we see even if it were found to be true:
Baron Münchhausen and the Self-Creating Universe:
Roger Penrose has calculated that the entropy of the big bang itself, in order to give rise to the life-permitting universe we observe, must be fine-tuned to one part in e10exp(123)?10^10exp(123). Such complex specified conditions do not arise by chance, even in a string-theoretic multiverse with 10^500 different configurations of laws and constants, so an intelligent cause may be inferred. What is more, since it is the big bang itself that is fine-tuned to this degree, the intelligence that explains it as an effect must be logically prior to it and independent of it – in short, an immaterial intelligence that transcends matter, energy and space-time. (of note: 10^10^123 minus 10^500 is still, for all practical purposes, 10^10^123)
http://www.evolutionnews.org/2.....selfc.html
GRBs Expand Astronomers’ Toolbox – Nov. 2009
Excerpt: a detailed analysis of the GRB (Gamma Ray Burst) in question demonstrated that photons of all energies arrived at essentially the same time. Consequently, these results falsify any quantum gravity models requiring the simplest form of a frothy space.
http://www.reasons.org/GRBsExp.....ersToolbox
Systematic Search for Expressions of Dimensionless Constants using the NIST database of Physical Constants
Excerpt: The National Institute of Standards and Technology lists 325 constants on their website as ‘Fundamental Physical Constants’. Among the 325 physical constants listed, 79 are unitless in nature (usually by defining a ratio). This produces a list of 246 physical constants with some unit dependence. These 246 physical constants can be further grouped into a smaller set when expressed in standard SI base units.,,,
http://www.mit.edu/~mi22295/co.....tants.html
“If we modify the value of one of the fundamental constants, something invariably goes wrong, leading to a universe that is inhospitable to life as we know it. When we adjust a second constant in an attempt to fix the problem(s), the result, generally, is to create three new problems for every one that we “solve.” The conditions in our universe really do seem to be uniquely suitable for life forms like ourselves, and perhaps even for any form of organic complexity.” Gribbin and Rees, “Cosmic Coincidences”, p. 269
etc.. etc.. etc..
—BarryR; “That being said, it’s perfectly permissible to define a group over the integers that’s closed over division, simply by making an arbitrary mapping for the divide-by-zero case.”
Permissible? I thought you said there were no mathematical laws. Will you ever stop contradicting yourself?
StephenB@107
I think “thought” is a little strong.
In the English-speaking community, “permissible” can mean both positive permission and the absence of prohibition.
If you prefer to think of this as a mathematical law — one may choose one’s axioms — it’s perfectly permissible for you to do so.
Barry,
I didn’t see any 2’s there, and I specifically asked you not to change the number 2 into anything else, including symbols. I noticed you ignored truncating the decimal of pi, also.
You have to take it on faith at the very bottom. And even if this conclusion were based, itself, on inference, what of it? I said all knowledge, that is, things learned, including knowledge of science, requires inference. If inference goes, science goes with it. Indeed the entire external world goes with it, for the external world is an inferred world.
I think, based on previous comments, you need to actually read it, not just be given a citation. And this is your response to Chesterton’s argument? An ad hominem? You’re not going to refute the actual argument? Typical. Pragmatism didn’t work as a valid response, and now your ad hominem isn’t fairing any better.
I apologize.
I had made an assumption that you were comfortable with basic algebra and a bit of set theory. This is not the case, and as such there’s simply no way you’re going to be able to understand the point I’m making.
So yes, you are correct that, if you limit yourself to grammar-school arithmetic, 2+2 can only equal 4. You’ll have to take it on faith that beyond the walls of grammar schools this is not considered a universal law.
If inference goes, your proof that science goes if inferences goes would be the first (and last) thing to go.
Inference is just another tool, like logic, math, and experiment. Inferences are often wrong. Logic is often irrelevant, math is often intractable, and don’t get me started on experiments.
If science required any of these be infallible, it would have disappeared in the 17th C. Because they are only tools, we use the best set of tools for a particular job, and despite the imperfections of our tools, the error bars keep getting smaller.
As to Chesterton: I’ve just read the first 30 pages of _Orthodoxy_.
This is philosophy for people who won’t read philosophy, written by someone who didn’t read philosophy either. As rhetoric, this is good enough to be notable, but compared to contemporaries like Borges, Orwell and Shaw it’s frankly quite shallow.
For example:
As wit, this works. As argument, nothing further need be said to dismiss it.
If you’d be so kind as to return the favor, please read this 8-page excerpt from Davis and Hersh’s _The Mathematical Experience_.
F/N:
Above BarryR indulges int eh classic fallacy of equivocation.
The + operator symbol has a normal meaning in mathematics, and this meaning is what is entailed when we observe that 2 + 2 = 4. To arbitrarily redefine the + operator such that x + x –> 147, is to use the symbol in a radically different and inconsistent way, imposing the result that [2 + 2 = 4] AND [2 + 2 = 157], i.e. we see the contradiction.
Since mathematics is fundamentally about reasoning on the implications of structured defined operations on sets and properties of set members, it is accountable to both logic and realities of definable collections of objects.
In short, the exercise above is an evasive one.
GEM of TKI
This may interest some here:
Ravi Zacharias addresses an audience at Harvard regarding the law of non-contradiction:
Jesus Christ and the Exclusive Claim
http://www.youtube.com/watch?v=szr7hPuh81c
BarryR:
Just a simple question, to understand better your thought.
You have often referred to peer reviewed philosophical literature. What are the principles according to which a paper is peer reviewed?
I mean, if we agree that not anything deserves to be published in a philosophical journal, are the criteria for peer review only conventional agrrements? In that case, would’nt such a sygstem just enhance conformism, and censor true creativity?
Or are those criteria based, at least in principle, on objective rules (or, if you want, laws, or principles), and in that case, what are they, and how are they found, or judged, or shared by the reviewers?
Just to know.
Apologies for replying so late after the conversation has moved on.
10 JDH
the ability to disobey the Creator is the essence of consciousness. Otherwise it’s just complicated programming with random choices.
19
jurassicmac
your ‘analogy’ is also an “Argument from Incredulity.”
As BarryR has it “Arguments from incredulity are almost always arguments from ignorance without the admission of ignorance”. Given the background and experience JDH has it seems presumptuous to accuse him of not knowing what he’s talking about. I also believe there are certain things that simply can not be coded. My belief is also backed up by years of writing software.
how do you know that humans aren’t following their ‘program’?
We don’t really know with certainty, but I would argue because we sometimes do follow a “program” it’s clear that we don’t always follow a program. For example, we likely all have a program for getting ourselves from home to work. If home or work changes, it could happen, if we’re not paying attention, we find ourselves following the old program. Similarly, anyone who’s ever tried to break a bad habit will know when they are following their “program” and when not.
24
gpuccio
Point 3 is well made although I would add that for the analogy of a computer to fit better we need to see that a computer has hardware, software, and a user who causes the software to execute. Sometimes the user is hardly needed so it’s easy to imagine that only hardware and software is at work. But other times what the software does changes dramatically based on a prior user action. The reason this whole issue is so tricky is that given _any_ sequence of user actions we can write software to perform those actions. IOW if a user sits down and writes an email with contents X, it would be trivial to then write software to produce X, but the software to produce X would also contain X. The results are the same but the processes are totally different.
With consciousness it seems to be that for every conscious decision I make that results in action, the same action could be taken by another man based on habit. But by making a conscious decision I’ve done something immeasurably different.
Based on that here is my attempt at a definition of consciousness. We have a physical nature which sends signals to, and receives signals from, the brain. The brain contains pre-defined sets of instructions which can be issued automatically in response to different kinds of input.
Consciousness monitors this input and output and, most importantly, is capable of creating new sets of instructions based on the input and output. Consciousness also senses; that is it senses good and bad. Once created, instructions can be re-used automatically by the brain.
I would describe the instructions as CSI and I would describe the ability to create new CSI as the ability which we can not pass on to machines (although I suspect that sensing good and bad is also something we can not pass on).
6
BarryR
‘If I were to participate in a Turing test, I’d be asking questions like “Of the two most recent questions you were asked, which was the more difficult to answer and why?”’
That is indeed the sort of question to ask in a Turing test. What you would be attempting to do is create a question for which the creator of the machine did not think to provide an answer. That is, a machine may contain in it’s software the answer to a billion questions, so the way to defeat it is to create a new question.
IOW A human can create CSI to which the only correct response is more CSI.
A machine can not create CSI; therefore a machine can not answer such a question unless the answer was pre-programmed.
kairosfocus@111
You’re almost there.
Group theory gives us the tools to:
although the only inconsistency here lies in expectations — the math is perfectly consistent. The reason that I’m able to this is because “+” is not some universal truth, but rather a well-defined mathematical relation that I’m free to replace with another well-defined mathematical relation.
I’m really surprised so many people are having difficulty with this concept. A good middle-school geometry class should have been enough to clue people in that axioms are tools and we’re free to pick our tools — the constraints come with how those tools are able to interact.
Does group theory give any guidance at all about which axioms are the best to use when dealing with a bank teller?
gpuccio@113
You’d have to ask a philosopher. I can give you an expert opinion for computer science and an informed opinion for the sciences in general, but I don’t know the liberal arts wells enough to be able to summarize how they define quality.
No, the process is subjective. In this regard it’s no different from the sciences. Given enough time, the subjective opinions of experts will (usually) converge and good works gets published (eventually).
If the process were objective, we wouldn’t need peer-review — we’d be able to tell for ourselves when a manuscript was of high enough quality to warrant publication, and the review process would only involve making sure the margins and typeface were of the correct sizes.
—BarryR: “If you prefer to think of this as a mathematical law — one may choose one’s axioms — it’s perfectly permissible for you to do so.”
You are contraditing yourself again. A law, by definition, is a universally binding principle. An axiom, the way you are using it, is personal and individual. If logic and mathematics have laws, those laws can be violated and the violator can be in error. If logic and mathematics are individually conceived, there is no universal standard by which one can be said to be in error.
By arguing that logic and mathematics have no rules, you are arguing that no one can, in fact, be wrong. At most, one could be internally inconsistent. Thus, by declaring that your adversaries are wrong about math and logic, you refute your own philosophy with every correspondence.
Bank Teller: “And here is your change: One, two, three, one hundred and forty-seven.”
Group Theorist: “Hold on a sec. I am not sure why, but this doesn’t look right. I think I need to call my philosopher.”
…sorry…
—“Group Theorist: “Hold on a sec. I am not sure why, but this doesn’t look right. I think I need to call my philosopher.”
Bank Teller: “There are no objective matematical laws. According to your axioms, subjectively conceived, I didn’t give you back enough change, but according to my axioms, subjectively conceived, I did. Now run along.”
Bank Teller follow up: “Of course I also dispute the law of non-contradiction.” It is entirely possible that I gave you the wrong amoung of change and that I also didn’t.” Therefore, your accusations are both true and false and I am both guilty and not guilty of withholding the proper amount.”
#119 thru #121
But surely this is the point. Integer arithmetic as normally practiced is a really useful tool for discrete objects like money. It works less well for adding wind speeds together. An arithmetic that defines the addition operation with a weird exception is virtually no use. None of this shows that the axioms of integer arithmetic are necessarily true in any deep sense. They happen to be true of discrete objects.
LOL Stephen and jstanley01,,
Hey, I found a place where the banks use ‘flexible axioms’:
http://www.youtube.com/watch?v=wpJQ-HX3F8g
bornagain77: There is indeed an ongoing real-world situation in which an application of my illustration is anything but absurd.
Namely, how banks worldwide are being allowed by their governments to mark their non-performing assets. Which according to the mathematical axioms of those governments, they are being allowed to mark as if they were performing.
Those non-performing assets have already come down once on the financial system like a sledgehammer. If because of the flawed mathematical axioms with which they are being dealt with, they come down a second time in the same manner, the real-world results will be anything but trivial.
(See Karl Denninger’s A Round-Up Of Current Idiocy for more information.)
jstanley, it is perfectly clear that the point you make in 116/119 is completely lost on mark.
mark, its a scholarly neurosis, you should have it looked after.
markf@122
Exactly, and you also run into problems when trying to map a potentially infinite number of discrete objects onto a finite amount of silicon.
#119 thru #121
The banking example also works. If you go to close out your account and you have $1.00 of principle and $0.002 dollars of interest, how much money does the teller hand you?
Depending on how nice the bank is, this will either be:
1.00 + 0.002 = 1.00
or
1.00 + 0.002 = 1.01
OH NOES!!!!! TEH UNIVERSIALITIFULLNESS OF ADDING STUFF HAS BEN VIOLATED!!!!11!!!
In grammar school this is called “rounding”, and if you can think back that far, you probably had to memorize that 0.5 was to be rounded up, not down, and that this was a completely arbitrary convention.
An equivalent way of stating this is to define “+” in such a way as no rounding after the fact is necessary. For the tellers counting out change, the former is easier. For the people who are writing the bank’s software, you have to deal with the latter whether you want to or not.
(I’m fascinated — in a horrified kind of way — that you’d define mathematics as “that which is appropriate to use in a bank” and still not get it right. I’ve been resisting a crack about how Dembski’s math only makes sense if you’re a mathematical illiterate, but I don’t know if I can hold out much longer….)
BarryR,
So it is a universal law in school, but not one outside of school? What does a building have to do with anything? Either 2+2=4 or it doesn’t, no matter where it is found, inside or outside of a building.
Do you have a total skepticism at bottom with regard to the cogency of these tools? I mean, surely, you’re sophisticated enough to see that there is no hope for a total skepticism, that in the last regard, inference using the laws of logic must be absolute.
When do you reckon you’ll start making an argument outside of ad hominem? I’m not interested in talking about the man or the style in which he wrote, but rather the argument in The Ethics of Elfland about real laws, such as laws of reason and math, and weird repetitions in nature we call laws for shorthand.
That must be why you didn’t dismiss it with argument……When Chesterton says:
He is exactly spot on. As wit this works, as argument, this works. Wit is argument. These elementary truths do not cease being truths because they are elementary. I notice a contempt for basic truths in your comments. As if being on a top floor means you don’t need the foundation or the first floors. You cannot suspend yourself. If fundamentals go, all else falls. No matter to what degree of complication mathematics may reach, if the concept of numbers and the multiplication table go, all else will be in ruins. You have to have something as a basis or you will not continue in progress. Progress itself means that there is a basis unchanged. If an acorn grows into a beechwood it isn’t progress, but mere change. The same is true for mathematics and moral philosophy and logic. If Logic and Inference are wrong, you can only discern this by more or better inference and logic. To scrap them won’t get you any closer to any truth, because you won’t be going anywhere. Indeed these are both presupposed in even determining that either of them was used in a wrong way by a faulty and tired human brain. But this can never be an indictment against inference and logic itself without being self referentially incoherent.
Hold out?
What an interesting position to explain yourself. Here all this time I thought you had been obvious. Rather like a ladle as oppossed to a spoon.
StephanB@118
In a paper I published last year, I had words to the effect of “Define graph G as a directed, acyclic, weighted graph…”.
(Oh, wait — you don’t know graph theory. Don’t worry, it’s pretty easy. Have a look here. It won’t hurt. I promise.)
Now that you have an idea what those words mean….
There are no universal laws or rules that required I solve my problem using this particular kind of graph.
Once I’ve identified the kind of graph I’m going to be using, my readers (including my reviewers) will have an expectation of the rules I’m going to follow. For example, acyclic graphs should really be free of cycles. There are a number of useful operations you can perform on acyclic graphs that only work in the absence of cycles (such as determining the critical path).
If I want to break one of these rules, that’s perfectly fine (although it’s best that I do so explicitly). I might say “As the cycles in this graph represent a finite number of program iterations, we may trivially transform this graph to one free of cycles.” My reviewer will read that and decide whether she believes it or not, and if she doesn’t it’s unlikely that the paper will be published.
I can also add new rules, in this case mapping the graph onto the Cartesian plane.
Once I’ve gone through establishing exactly what the rules are that I’ll be using, I can make an argument that under these rules my conclusion becomes inevitable. I then need to convince my reviewer that this particular set of rules is a reasonable model for the real-world process I’m interested in, that it’s novel, is something more than an incremental contribution, etc. If I’ve done all that, then I can have a reasonable expectation that the paper will be published.
Another example: clock cycles in a computer are discrete — as far as the computer can tell, there’s no such thing as half a clock cycle. Let’s say this is a universal rule. I published a paper in 2007 where I treated clock cycles as continuous, not discrete. Because I was free to disregard this universal rule, I was able to solve problems several orders of magnitude larger than what had been done using the discrete approach, and the error I introduced to do so was negligible enough not to be worth measuring.
There are no rules about how you pick (and modify) your rules. You’re free to believe otherwise, but I don’t think you’re going to be able to do so while having a successful research career.
“Borges, Orwell and Shaw”? Somebody please pick me up off the floor.
BarryR,
Go ahead, I’d like to ban you for your jeering. And quite frankly, discussing “rounding up” doesn’t give me much confidence that you really understand his mathematics. John Lennox, you know who I mean, the Oxford mathematician, endorses Dembski’s mathematics. But BarryR, the one who talked about whether one is inside or outside of school walls determines mathematical truths, and banks rounding up, doesn’t agree with Dembski’s mathematics. Pardon me if I’m not impressed.
BarryR, I should like to impress upon you the fact that transcendent ‘logical’ information, which is completely separate from matter and energy, runs the show as far as the operation of this universe is concerned, and that this fact is empirically verifiable by work that has been accomplished in quantum mechanics. Yet after reading your snobby condescending posts towards others, I think that the only thing that would be sure to impress you would be whenever you looked at yourself in the mirror. Thus I will refrain from wasting my time.
BarryR,
I suppose “There are no rules about how you pick (and modify) your rules.” is not supposed to be a rule either, then. Your entire comment amounts to the trivial conclusion that different rules apply depending on what you want to build, such as building a house made of glass instead of wood would have different methodologies. Of which, the house made of glass, you of all people shouldn’t build. That would be my first rule. But choosing how you want to build anything, what sorts of materials to use, how large, how tall, etc., does not equate to suspending laws of reason and logic or mathematics. Your comment, quite frankly, changes the subject from real laws to conventions—which, the latter, can be altered for your own purposes. And I find it notable that you use the word “embarrassing” so often.
BarryR,
So what?
Are you implying that you can make new rules of logic by the analogy of axioms? Surely I can do that too, then.
I’d like to know how big yellow is. And I’d like to compare that to how far London Bridge is from Christmas Day. If logic can be so manipulated, depending on whatever axioms I choose, or choose to invent, this should be no problem, right? I define that colors are certain sizes, then compare that size to the axiom I invent for distance between a place and a date. My answer to this problem is “cell phone.” Are you saying I’m wrong or right? Does it depend on what axioms I choose? No, because it’s nonsense. But it’s only nonsense if you have sense to begin with. You will not know that a line is crooked unless you have some idea of a straight line. But maybe I can choose my axioms which will make choosing axioms impossible and possible at the same time. This shouldn’t be a problem, because there is no such thing as logic, right?
By the way, I’d still love to see your response to the problem of induction as so eloquently categorized by Chesterton. This time without the a hominem.
—BarryR: “In a paper I published last year, I had words to the effect of “Define graph G as a directed, acyclic, weighted graph…”.”
—“(Oh, wait — you don’t know graph theory. Don’t worry, it’s pretty easy. Have a look here. It won’t hurt. I promise.)”
I know enough about graph theory to know that appealling to it will not help your case.
—“There are no universal laws or rules that required I solve my problem using this particular kind of graph.”
You are confusing operating assumptions and methods, which are flexible, with the laws of logical and the related laws of mathematics, which are not. Mathematical principles are related to logic principles, which explains why you disavow the rules not for one, but for both. Thus, you reject mathematical laws, the law of non-contradiction, and the law of causality all in one sweep. That is no coincidence.
On the matter or relative rules, researchers can posit anything they like for the sake of argument, or they can even do if formally in the form of a hypothesis. They are also free to choose their methods, unless, of course, they are ID scientists who are forbidden by your secularist comrades to do so under the tyrannical rule of methodological naturalism*.
*(No doubt you corrected your comrades and re-educated them to the point where they now understand that since the scientist is the only one who knows what problem he is trying to solve, only he/she can choose the appropriate method.
[Just a little humor there. I have no doubt that, in spite of your protests on behalf of the INAPPROPRIATE freedom to abandon causality, you would refuse ID the APPROPRIATE freedom to choose its own methods.])
We are not free, however, to abandon the law of causality or the law of non-contradiction which informs all intelligently conceived arguments, whether they be philosophical, mathematical, or scientific.
—“There are no rules about how you pick (and modify) your rules. You’re free to believe otherwise, but I don’t think you’re going to be able to do so while having a successful research career.”
We are not discussing how you pick YOUR operating assumptions or axioms, we are discussing THE transcendental rules that cannot be chosen. They must, for the sake of rationality, be apprehended, understood, and honored.
If I give you one apple followed by another apple, you will have two apples. You will not have 147 apples. If an apple exists, it cannot also not exist at the same time, nor can it come into existence without a cause. These are a few, not all, of the priciples of right reason, and no matter how many graphs you draw or how many letters you scramble, the rational conclusions are inescapable.
—BarryR: “In grammar school this is called “rounding”, and if you can think back that far, you probably had to memorize that 0.5 was to be rounded up, not down, and that this was a completely arbitrary convention.”
So you really think that flexibility in mathematical expressions is a good example of how mathematics has no inflexible laws.
I gather you also believe that if I round off Pi from 3.14159 to 3.14, the relationship between a circle’s diameter and its radius is also up for grabs.
You should not be sneering at Chesterton. On the contrary, you desperately need to absorb his message.
StephenB@135
If we all decided that valid mathematical operations shall be those limited to those can can be carried out on apples, you might have a point.
This is how grammar school arithmetic is taught, and to the best of my knowledge, that’s all the math you understand. And that’s fine — we can’t all be mathematicians.
But I had hoped your education would have gotten you to the point where you could grok at mathematics can be divorced from apples and studied in its own right. Once you’ve made that leap, then you have an abstract structure that can be used to derive other abstract structures, some of which are even useful.
But there’s no guarantee that they’ll map back onto apples.
You say you know graph theory. Great. What are the universal laws of graph theory and how do you know they’re universal? I’ll bring home my Scary Yellow Springer Book o’ Graph Theory tonight and we can compare notes.
CH@134
You may be starting to get the hang of this.
Yes, you can make new rules of logic, or entirely new logics. Among the ones that are currently being studied right now are:
First Order Logic, aka first-order predicate calculus
Second Order Logic
Infinitary logic
It’s not usually used to study logic, but I’d add lambda calculus as well.
Each of these broad categories is divided up into several specializations, each with their own “rules of logic”.
Each of these logics is perfectly consistent. Some are more expressive than others, some are more powerful than others.
As best I can understand what you’ve been telling me, there is a Correct, Universal logic.
Which one is it, and how did you arrive at that conclusion? (If you say “Chesterton”, you will be asked some very pointed questions that you don’t have the technical skill to answer.)
BarryR,
This is known as a false dilemma, if it is logical, then there is no “different ones” to be compared, for no logic could be used to compare them. If there were no, as you said, Correct, Universal logic, then there is no comparison between anything that might be gathered together and called First Order, Second Order and so on. You couldn’t even say that they themselves were logical or not, only conventional, to be changed at will, and the entire force of your argument, indeed of all arguments, would be broken into nothing. You would just be talking confusedly. You would just be playing with counters. I think you desperately need Chesterton and C.S. Lewis. Please read De Futilitate from Lewis, you can google it. But you seem to be trying to actually make a point, a logical point, I’m assuming, using reason, I’m assuming, which cannot itself deny logic, or else you have no point to make. All argument presupposes it, even yours.
CH@139
Well, there’s a simple way to settle this: show me your universal mathematics.
We know it guarantees that 2+2 always equals 4.
What else does it do?
I’m quite the mercenary when it comes to mathematics. Show me a more powerful system and I’ll drop what I’m currently using and adopt it.
So, I’m ready and willing to convert. All you have to do is tell me what I’m converting to.
—BarryR: “This is how grammar school arithmetic is taught, and to the best of my knowledge, that’s all the math you understand. And that’s fine — we can’t all be mathematicians.”
You are the one who said that 1+1 does not necessarily = 2, so I thought it would be wise to bring you back down to earth with an obvious example that refutes your misguided notion.
—“But I had hoped your education would have gotten you to the point where you could grok at mathematics can be divorced from apples and studied in its own right. Once you’ve made that leap, then you have an abstract structure that can be used to derive other abstract structures, some of which are even useful.”
All this is fine, but irrelevant. The best way to convince people that you are educated is to make relevant and cogent arguments. Granted, simplicity that has not passed through complexity is worthless. On the other hand, reveling in complexity in order to evade basic issues smacks of timidity. The trick is to find simplicity on the other side of complexity. If there is one thing that I have learned in dealing with academic elitists, it is this: Anyone who truly understands his subject can, when called upon, explain it so that a twelve year old could understand it. Everyone else is bluffing.
—“But there’s no guarantee that they’ll map back onto apples.”
If they map back to the proposition that 1 + 1 = 147, you are following the wrong map.
—You say you know graph theory. Great. What are the universal laws of graph theory and how do you know they’re universal? I’ll bring home my Scary Yellow Springer Book o’ Graph Theory tonight and we can compare notes.”
I said I know enough about it to know that it doesn’t invalidate the principle that mathematics is undergirded by logical laws, just I know enough about other approaches to mathematics to know the same thing.
We don’t need a discussion about Springer’s Graph theory, nor do we need a discussion about your notions about symbols. None of these points have anything to do with the basic issue, which is this: The flexibility that is permitted for granting working assumptions does not translate into a flexibility for ignoring logical laws or first principles.
CH@139
He write better than I remember (and far better than Chesterton). And nice work in coming up with a cite that’s so directly on point.
I think this falls apart here:
There are several errors packed in here. First, we’re perfectly capable of knowing the universe without using thought. Second, while logical thought may not be subjective, the choice as to which logic to use and what facts to operate over remains subjective. Third, logical thought is often irrelevant to the universe — G. H. Hardy was quite proud of the uselessness of his mathematics.
Now some of this is due to Lewis speaking to a general audience, but some of it also comes from his speaking about science and philosophy without being trained in either.
So by the time he reaches
I have several counterexamples at hand. I work with some of the largest computers in the world precisely because the laws of thought do not follow the laws of things; things are far more complicated than our thoughts, which is why we build supercomputers to help us think about them.
To leap from that flawed conclusion to ruling out materialistic explanations of thinking simply isn’t justified even if I believed the conclusion.
It’s easy to convince yourself you’re making sense when you’re making arguments like this. It’s harder to convince three anonymous reviewers. Unfortunately, I don’t think this work was ever subjected to peer review.
StephanB@141
How do you know this?
Yes, it contradicts your grammar school arithmetic. I’m not using that arithmetic.
You can show that it’s inconsistent with the arithmetic that I am using — except I constructed my arithmetic so that wouldn’t be the case.
You can claim that no other arithmetic except that which you learned in grammar school exists, but since I have firsthand experience with other arithmetics I don’t think I’m going to believe you.
Or you can show me the One True Universal Correct Arithmetic that you believe exists.
But you can’t.
You’ve set yourself up a formidable task: demonstrate nearly all mathematics from the 17th C. forward as fundamentally flawed, and do so without any appreciable knowledge of what these mathematics are or how they work.
Your best shot so far is observing that these mathematics don’t map well to apples.
I’ll grant you that point.
What else do you have?
CH@133
I think of it as an observation. A rule would be formulated as “There *cannot* be any rules about how you pick (and modify) your rules.”
I’m happy to argue for that single rule if you like. I don’t see where it makes much difference, though.
StephanB@141
Of course it’s undergirded by logical laws! When I use graph theory, I pick and chose which logical laws form that undergirding!
From Bondy and Murty’s _Graph Theory_:
We now have (part of) the undergirding necessary to start reasoning about graphs.
This is not the One True Universal definition of graphs. I can modify it to require the unordered pairs of vertices that define the edges be distinct. I can further restrict this to state that the ordered pair must contain two unique vertices.
My question to you is: Is this permissible? May I arbitrarily modify the undergirding of a branch of mathematics?
Bondy and Murty don’t have a problem with this: on the following page they define simple graphs as having no loops or parallel edges, which is the consequence of my changes to the definition.
Diestel gives a slightly different definition in his _Graph Theory_ (I’d quote it, but it’s set theoretic and I think spelling out the symbols will only lead to more confusion).
So now we have two different scary yellow Springer books (with identical titles) giving slightly different undergirding to the idea of graph theory.
Is this allowed? Is one of them (or both) wrong?
And most important, how do you know?
Barry,
Ummm, Barry, “knowing” requires thought.
There is no “choice” as I explained in my last comment to you.
Not sure what you mean here, but the external world is an inferred world, you remove logic and you remove understanding and making sense of the external world as a whole.
He was a professor of philosophy at Oxford by the age of 26.
Ummm, Barry, we program the computers, without our logic there would be no computers to begin with, nor any programming.
Did you not gather anything else from the essay? I mean, there’s a lot to digest, I understand that, and surely you’re adept at understanding it, given that it was for the “general audience” of which you consider yourself above, so surely you understand that the quote,
is valid, and that “First, we’re perfectly capable of knowing the universe without using thought.” is not.
I’d like you to explain without using explanation (which presupposes logic) how we are capable of understanding the universe without using thought. How are we able to know without thinking? And how would you explain this without logic or thought?
—BarryR: “Of course it’s undergirded by logical laws! When I use graph theory, I pick and chose which logical laws form that undergirding!”
Now you are saying that you want to choose from among the laws. Earlier, you argued that there ARE NO LAWS from which to choose.
—“Yes, it contradicts your grammar school arithmetic. I’m not using that arithmetic.”
So, now you are arguing that the laws of higher math contradict the laws of arithmetic?
—“[The graphs} Is this allowed? Is one of them (or both) wrong?”
Do you really want me to go into another discussion about the difference between a working definition and a law? First you say that there are no laws. Then you say that there are laws, but you get to choose from among them. Then you say that the graph is undergirded by laws. Then you say that they are undergirded by definitions.
Just so you will know, definitions and assumptions are changeable; laws are not.
StephenB and Clive
Shame on the both of you!! Here we have BarryR, a real intellectual who has come down from the mount to lecture us the mere mortals and the both of you have the audacity to question him. Don’t you realize the sacrifice he is making by dirtying his intellectual hands by even gracing us with his presence? Sniff sniff.
I mean really how rude and disrespecful. I can tell how he writes that he is very very smart and he has published papers to boot. Besides all the publishing, to really really smart audiences,he has told us how smart he is and how dumb you are. Shoot what papers have you published, did you guys even get out of grammar school?
Chesterton? hmmph not even worth refuting. Lewis? minor leaguer sniff sniff. Heck you guys are so dumb you don’t even know that 2 apples plus 2 apples dont equal four apples!! Come on now and show some respect will ya!!
Vivid
#146
He was a professor of philosophy at Oxford by the age of 26.
I don’t think so. I believe the only philosophical position he held was a temporary post as tutor covering for 1924 E. F. Carrit. That lasted less than a year. In fact I don’t think he become professor of anything until he was made professor of medieval and renaissance literature at Magdalene College, Cambridge, in 1955 (i.e. aged 57)
Sorry that should read:
“temporary post in 1924 as tutor covering for E. F. Carrit”
RE 150
I think one could maintain that Lewis could have been a professor of philosphy and not a professor of philosphy or both simultaneously.
Why not?
Vivid
markf,
CS Lewis taught for nearly 30 years 1925-1954 at Magdalen College Oxford before he was a professor of English at Magdalene College at Cambridge.
—BarryA: “You can claim that no other arithmetic except that which you learned in grammar school exists, but since I have firsthand experience with other arithmetics I don’t think I’m going to believe you.”
Having studied higher math myself in a formal setting where bluffing doesn’t work, I am not buying your argument from authority.
I remember well enough the law of exponents and many other laws which admit of no exceptions. Indeed, I once studied the my “identities” over a Christmas vacation. I know well enough the relationship between a philosophical syllogism and the laws of geomtery because I have studied philosophy in a formal setting as well. I also remember the pre-calculus laws of sines and cosines.
In keeping with that point, I gather that you have never heard of the law of limits with respect to calculus. Indeed, given your misguided notion that the laws of higher math contradict the laws of arithmetic (except for those times that you are claiming there are no laws at all) I am beginning to suspect that you are not even aware of the lower levels of association and accumulation that rule the arithmetic functions that you so disdain.
So why on earth would I want to discuss your irrelevant foray into graph theory, which is little more than a distraction and just one more attempt to avoid your horror of the obvious–math has laws, as does logic.
153 is to BarryR not to BarryA.
It does? Interesting. My cats know many things about the universe, but I didn’t think you be comfortable ascribing “thoughts” to them (as the capacity for thought would certainly imply consciousness, yes?)
So I can go either way. Either my cats manage to know the universe without thoughts, and the above is correct; or my cats possess some level of consciousness and use thoughts to know the universe.
Your choice.
I’m not finding anyone who agrees with you, and several people who disagree, so for the moment I’m going to provisionally assume that choice exists.
For example:
Carlo Cellucci, “Introduction to Filosofia e matematica”, in Reuben Hersh’s _18 Unconventional Essays on the Nature of Mathematics_. (emphasis added).
(I think you’d particularly enjoy the first essay in that collection. Might give you some ammunition.)
A. Grzegorczyk, “On the validation of the sets of axioms in mathematical theories”, Studia Logica Volume 13, Number 1, 202, 1969. (emphasis added)
Sy-David Friedman, “Stable Axioms of Set Theory”, Trends in Mathematics, 2006, Part 2, 275-283. (emphasis added).
You may, of course, propose a rule for your own work that the only valid axioms are those that are Universal. As I’ve mentioned a few times now, there’s no rule preventing you from doing so.
If you want to apply this rule to everyone else, though, I think you’re going to have to make a mathematical argument before you’ll be taken seriously.
Really? I may have been led astray by wikipedia then. His entry there has:
A quick google search turns up:
I believe that’s considered a humanities degree. If you have a cite to the contrary let me know and I’ll update wikipedia.
When we observe this behavior in others, we usually classify it as instinct.
StephanB@147
When I played baseball in the backyard as a young child, each game was preceded by a ritual construction of the rules. The dogwood tree might be first base, the corner of the sidewalk third base, invisible men advance one base ahead the runner, etc.
Once the game began, we were constrained to adhere to those rules.
However, there were no rules constraining how we initially selected our rules. We were free to make the dogwood tree home plate, create additional bases that needed to be visited in arbitrary order, remove the strike count limit, etc.
Mathematicians are likewise free to choose their axioms to suit their fancy. Once the axioms are chosen, then they have to play by the rules (until the next paper).
See citations upthread for heuristics mathematicians use to evaluate their choice of axioms.
Do you have an example of an unchangeable law from graph theory? I’m not aware of any, but then you may know more about the topic than I do.
StephanB@153
Well you certainly shouldn’t take it my authority.
You’re familiar with exponents then, yes?
Good.
n^{2} is n-squared, right?
n^{1/2} is the square root of n, right?
n^{-1/2) is 1 divided by the square root of n, right?
And you’re familiar with i (or j, if you’re a physics major) standing for the square root of -1, yes? And that’s called an imaginary number.
So what is i^{1/i}?
If you wrote down what you considered to be the law of exponents, I don’t think you’d be able to solve this problem (and it is solvable).
But if we’re allow to modify and extend the “Law of Exponents”, then it’s no problem.
My reading group just finished this problem in Knuth this past week:
n’=n^{-1}, and now we’re well on our way for defining exponents over modulo arithmetic.
If you want to pick the “Law of Exponents for simple arithmetic over integers” as an axiom, that’s fine — just like Calvin and Hobbs above can decide to use “twelfth base” in baseball. But I’m not required to use that law — even when I’m doing simple arithmetic — and to my mind that doesn’t make it much of a law.
Because it’s your best shot at showing me I’m wrong.
And because I thought we might have it as a shared mathematical language and we could elevate this discussion to axioms and theorem instead of discussing what you would prefer math to be like.
markf,
From October 1924 until May 1925, Lewis served as philosophy tutor at University College during E.F. Carritt’s absence on study leave for the year in America.
StephanB,
Just for fun, I looked around a bit to see if anyone had defined exponents for graphs. I’m not seeing anything, so let’s walk through what this might involve.
You can define an unweighted, undirected graph as an adjacency matrix A s.t. the value at i,j is the number of edges from i to j. So we’ve got a matrix and that has a well-defined exponential function.
But what if we have a weighted graph? If it’s simple, then i,j can be set to the weight of the edge. (Can you transform a graph with weighted edges and verticies into an equivalent graph with just weighted edges? Yeah, I think so.) So raising this to a power is straightforward as well.
But what if it’s a directed graph? Now we’re going to have to change our adjacency matrix to represent weight as well as direction. Do you order the verticies and use two matricies (one for edges going from high to low and the other for edges going from low to high)? Do you use a single matrix and give each vertex an alias? Do you create a matrix of vectors?
You can do any of these things and then operate on the resulting matrix or matricies as usual, or you might get clever and come up with some else. And that will be your “Law of Exponents” for graphs.
If this allows you to solve an interesting problem (or even raise an interesting problem), then your convention might be picked up and eventually make its way into textbooks. (Learning to understand what is “interesting” will occupy the first few years of your grad school career.)
#152 and #156 re C S Lewis
I don’t understand why you both repeated what I wrote?
CS Lewis was a philosophy tutor for just under a year. That is a very long way from being a professor of philosophy as claimed in #146 – it doesn’t require any original writing at all.
He did indeed teach at Oxford for all those years but not philosophy and not as a professor.
Looking over the 2+2=147 discussion I think it is worth restating what the issue is.
I don’t suppose that BarryR denies that given the axioms of integer arithmetic – incuding the definition of the “+” function – then 2+2=4. And these axioms are really useful for dealing with apples and countless other things.
It is also possible to change the axioms (call it redefining the meaning of “+” if you like) so that 2+2=147 – which is practically useless in the real world.
The interesting question is do the axioms of integer arithmetic which we learn intuitively at primary school reflect some kind of metaphysical reality which alternative systems do not? Or do they just happen to be extremely useful?
No amount of sarcastic comments about bank cashiers is going to throw light on this question.
Here is one approach. How do we learn that 2+2=4? Think back to primary school. Teachers do not reveal a metaphysical world of numbers to 5 year olds. They show them apples and such like, and give them techniques for counting them etc.
Imagine trying to teach even the most intelligent child that there is this thing called a number, one of the numbers is 2, and there is a thing called addition, and when you add 2 and 2 you get another number called 4. And by the way these things don’t exist in space or time – but the law that 2+2=4 is necessarily true for all space and time.
“Because I was free to disregard this universal rule, I was able to solve problems several orders of magnitude larger than what had been done using the discrete approach…”
Why Barry, you must be the superman. Perhaps that explains your enthusiasm for Shaw.
I remember our fifth grade teacher informing us one day, with a twinkle in his eye, that 2+2 could just as easily mean 3 or 5, by the rules of mathematics.
Tell me, do you have a twinkle too?
And Mark, you are also my hero. It’s quite amazing to find one of our contemporaries inventing nominalism. And we thought time travel was impossible!
—BarryR: “When I played baseball in the backyard as a young child, each game was preceded by a ritual construction of the rules. The dogwood tree might be first base, the corner of the sidewalk third base, invisible men advance one base ahead the runner, etc.”
Apparently, you have been so steeped in postmodern subjectivism, that you cannot distinguish between socially constructed rules and objective laws. That is unfortunate.
—“Mathematicians are likewise free to choose their axioms to suit their fancy. Once the axioms are chosen, then they have to play by the rules (until the next paper).”
Irrelevant. Mathematicians are not free to pick and choose which mathematical laws they will honor and which ones they will not. I have already listed six laws [there are many more] completely refuting your misguided claim that there are no laws. You simply ignore the refutation and continue on as sleek as ever.
—“See citations upthread for heuristics mathematicians use to evaluate their choice of axioms.”
Irrelevant as indicated in the preceding paragraph.
—“Do you have an example of an unchangeable law from graph theory? I’m not aware of any, but then you may know more about the topic than I do.”
Irrelevant. You could make your question relevant by showing how graph theory supercedes mathematical laws or reduces them to a status of not being laws. Perhaps you can provide a quote from one of your authors indicating that mathematics has no laws. [Good luck with that one].
—vividbleau: “I think one could maintain that Lewis could have been a professor of philosphy and not a professor of philosphy or both simultaneously.”
Very good, vivid. According to our postmodernist friends, there are no laws that would force us to rule out that possibility.
F/N 2: It is a little disquieting to see the same distractive fallacy of equivocation continuing.
BR: I am very aware of how the glyph “+” may be given alternative meanings, both from mathematics and from the common use as the inclusive OR in digital logic. But the basic issue is not whether one may construct a set of axioms, hope they are coherent [a la Godel] and that they imply enough to be interesting and useful. Ordinary arithmetic and its extgension to school algebra are very useful, and reflective of commonly encountered reality. The reinterpretation of 1, 0 + and = in Boolean Algebra has significance for digital electronics and even reasoning in logic.
But in all cases, one is very careful to distinguish contexts so one avoids errors of equivocation leading to gross contradiction.
And, BTW, the act of joining the sets (*, *) and (*, *) to yield the set (*,*,*,*) is a very natural one, and to symbolise it as 2 + 2 = 4 is reasonable, meaningful and reflective of reality.
To reason in a digital context that TRUE AND/OR TRUE is TRUE is a different and equally useful context, where 1 + 1 = 1, using 1 for TRUE and + for AND/OR (Vel, not Aut).
To see the point that hose who object to your equivocation are making, consider a bottle bearing the string of symbols:
GIFT
In English, that’s fun, but if that bottle came from Germany, watch out!
In short, life and death may hinge on the context of symbols and being very caregul indeed not to be equivocal.
And that has nothing to do with whether another set of axioms, for Graph Theory, may have utility or even map well to reality as we experience it, in some specialised circumstances; especially when we have to deal with networks of nodes and arcs connecting them in many modern circumstances. (BTW, does anyone say “Topology” much anymore?)
The importance of contextual consistency and precision in terminology is underscored.
GEM of TKI
PS: For those who are wondering, GIFT in German, notoriously, means poison. Talk about a “False Friend” word!
StephanB@153
Do you remember why we use limits in calculus? It’s because there’s no smallest positive real number. The proof is pretty simple. By contradiction: let x be the smallest positive real number. x/2 < x, thus the contradiction.
But math is all about choosing the axioms you want to work with, and so I can state as an axiom: there exists a smallest positive real number, and I'll call it an "infinitesimal". I can then construct calculus without all of those messy limits. My solutions will have a lot of infinitesimal left lying around at the end, but since they're arbitrarily small, I can disregard them.
This is how Leibniz came up with calculus — later formalizations preferred limits to infinitesimals, and that's probably what you learned.
But the infinitesimal approach has been formalized as well, and is called non-standard analysis. It works, and all in all is probably a better way to teach calculus.
As I understand your way of thinking, a smallest possible positive real number either exists or it doesn’t. That’s not how mathematicians think. They ask that question with regard to specific choices of axioms, and based their choice of axioms in part on how they can solve the particular problem they’re working on.
markf@163
Let me add a short clarification to that. I’m perfectly happy conceding a metaphysical reality to axiomatic systems that results in 2+2=4. However, I see no reason to think of this as the only metaphysical system out there (especially since a fair bit of my graduate career was spent learning about these other systems).
StephanB@165
It’s unfortunate that 19th C. mathematicians who invented abstract algebra couldn’t make that distinction either.
It’s also a distinction that geometers in the 19th C. were unable to make when they came up with non-Euclidean geometry.
Carl Friedrich Gauss failed to make the distinction back in 1801 when he published the first work on modular arithmetic.
I’m afraid the entire history of mathematics is nothing but a sorry parade of ignoring universal truth in favor of inventing cool stuff that works.
I’ve provided citations to the peer-reviewed literature showing exactly that in addition to the specific examples of modular arithmetic and non-standard analysis.
Why should I believe you over professional mathematicians?
Your argument isn’t helped by the fact that you’re not able to come up with any universal laws of mathematics. Exponentiation certainly wasn’t one and you don’t know any from graph theory.
I’d find it much easier to believe in a universal mathematical law if you were able to write down for me.
Ah, yes, *I* have to provide citations, but you don’t.
I think you’d agree that asking me for a citations showing there were no universal piglets of mathematics would be a little difficult to fulfill. You’re asking me to provide evidence for a negative statement, and that’s usually seen as poor debating technique.
So while I cannot give you any evidence that no universal piglets of mathematics exist, I can give you evidence that universal piglets are something that mathematicians don’t spend a lot of time thinking about.
scholar.google.com returns the following hit counts:
881,000 “calculus”
7,490 “modular arithmetic”
4,820 “nonstandard analysis”
16 “universal laws of mathematics”
10 “universal mathematical laws”
0 “universal piglets of mathematics”
Of these sixteen, we have a biography of Descartes, a paper on free will, a review of a Descartes biography, a short piece at answers.com, a book called “The philosophy of left and right”…
But nothing listing what these universal mathematical laws might be.
As far as mathematicians publishing mathematics goes, “universal mathematical laws” has received exactly the same attention as “universal mathematical piglets”.
I’d like to think you didn’t make up the idea of universal mathematical laws. Can you give me the citation where you first heard of it?
kariosfocus@167
You’ve hit on the issue precisely. The universal laws that several posters here wish existed are not susceptible to context. 2+2=4 is not a universal truth, it is a truth within a specific mathematical context formed by a specific choice of axioms.
I find topology fascinating but, once I get past the introductory examples, completely counterintuitive. This is odd, as there’s a pretty good mapping to graph theory and that’s pretty easy.
So yes, that’s the reason for my reluctance to use topological examples.
BarryR,
Of course your cats and my dog have consciousness, and know things about the universe, isn’t that obvious?
That’s interesting, because I was responding to your first order and second order logic argument, not whether axioms can be chosen with regard to mathematics for certain purposes (which doesn’t, by the way, negate that 2+2=4). You can choose axioms depending on what you’re trying to accomplish, as you can choose material for building a house, neither one contradicts or suspends the laws that govern them, such as basic arithmetic and physics. But this really just changes the subject, as I was referring to your false dilemma of “different logics”, as if they were conventional, like choosing to drive on the right side of the road instead of the left. As if making sense of how big is yellow could really be, depending on my own invention of logic.
And you’re simply wrong about Lewis not being trained in philosophy:
Following the end of the war in 1918, Lewis returned to Oxford, where he took up his studies again with great enthusiasm. In 1925, after graduating with first-class honors in Greek and Latin Literature, Philosophy and Ancient History, and English Literature.
From January 1919 until June 1924, he resumed his studies at University College, Oxford, where he received a First in Honour Moderations (Greek and Latin Literature) in 1920, a First in Greats (Philosophy and Ancient History) in 1922, and a First in English in 1923.
From October 1924 until May 1925, Lewis served as philosophy tutor at University College during E.F. Carritt’s absence on study leave for the year in America.
Update wikipedia if you’d like. There is no shortage of actual and true biographies of the man readily available online. So that should clear up your ad himonem against Lewis not being trained in philosophy. And secondly, you’re not trained in philosophy, so why should I regard anything you have to say by the same criteria? If I had to compare a computer programmer and an Oxford don who received three firsts in his education and who Cambridge invented a chair for him, I think I’d choose the latter, if you’re going to play the credentials game. Yours is nil compared to Lewis’s.
Instinct is innate, not knowledge about the world, but an impulse, like an appetite. An appetite is not knowledge about food. We’re far adrift from your explanation as to why Chesterton was wrong in his critique of scientism and his explanation of the problem of induction, which you never addressed. Real laws of logic and reason and mathematics, necessary relations between things, and why we can see why they are necessary, not just that they exist together, are fundamentally unlike anything we ever observe is nature by virtue of seeing two things together. I’m still waiting for your answer and argument that proves this to not be the case…..
CH@170
I sure thought it was. Granville Sewell (who authored the article to which we’re responding) doesn’t find it obvious at all. For him, human consciousness is special, not just further along on a continuum of consciousness.
I’m glad we’ve found something to agree on.
We may finally be converging. I’m free to build a house out of diet coke cans — it won’t be useful, but it can certainly be done. I’m also free to choose axioms such that 2+2=147 — also not very useful, but neither is it invalid.
Are we in agreement?
Yes, which logic you use (and there are several, several of which are mutually exclusive) is your choice. This follows from the fact that logic, as in any branch of mathematics, is derived from axioms, and we can chose our axioms to suit the problem we’re trying to solve.
In fewer words, just as there is no universal rule stating that 2+2=4, there is also no universal rule defining the logical operators “and”, “or”, and “not”.
Interesting. I appear to have had more training in philosophy than C. S. Lewis. (Enough classes to qualify for a minor during my undergrad as well as several graduate classes in logic when I was getting my Masters.)
I hadn’t considered taking a few philosophy classes sufficient to be considered “trained as a philosopher”. I certainly don’t consider myself a philosopher and Lewis didn’t consider himself a philosopher either.
Putting that to one side, Lewis isn’t wrong because he’s not a philosopher, he’s wrong because he’s making several mistakes that actual philosophical training would have prevented. Part of my training was in learning how to spot those kinds of errors. That’s part of the difference between reading Plato as Literature and reading Plato as Philosophy.
(You’d probably know this: did he ever submit any of his philosophical work for peer review? I can’t find anything, but I haven’t looked too hard.)
Tell you what: remove the moderation block and I will go through and give you a point by point critique of Chesterton.
If I’m going to put in the time to do this, I want some assurance that the post will actually show up here.
RE 168 “But nothing listing what these universal mathematical laws might be.”
Pi is a universal constant in Eucledian space.
Vivid
typo I know
Onlookers:
You will observe how RB has again, sadly, evaded the issue.
We deal with a real world, where we can collect objects and group them — go get a match full box for illustration.
Cluster matches like so:
{ | | } { | | }
Recluster, by pushing together:
{ |||| }
You have just physically instantiated the arithmetic binary operation, + for two two-sets [symbolised by 2], and yielding a four-set, symbol 4.
2 + 2 = 4
Based on the meaning of 2, +, = and 4 as conventional symbols [which can vary, just make sure you are using well thought out symbols], this is not just inductively true, nor is it simply an arbitrary game of symbols in a system that rests on ultimately circular tautologies.
No, instead we are here again up against the reality of self-evident truth.
That is, given our experience of the world as conscious and reasoning creatures, providing we have a good understanding of 2, +, = and 4 [all of which inextricably interact in their meaning], it does not just happen to be so that 2 + 2 = 4, but that it MUST be so. On pain — pardon, but this is part of what a self-evident truth is — of immediate descent into obvious absurdities.
In the case where someone attempted to redefine that 2 + 2 = 147, there are a great many absurdities involved. Starting with arbitrary redefinition of symbols used in an evasive equivocation. And, going on to the situation where we are now seeing + being sued in at least two different ways without means to distinguish, i.e. communication and reason are beginning to break down. Hardly less significant, 147 is a notation:
1 x 100 + 4 x 10 + 7 x 1.
See how the original meaning of 4, which includes properties like 4 = 2 + 2, or 1 + 3, or 1 + 1 + 1 + 1, has resurfaced? [If, in attempting to deny or dismiss a point you find you are implicitly assuming and using it, then that is a strong sign that you are in error.]
Axiomatic systems in mathematics may be constructed, but the facts that they address are real, and in the case of the sort of fairly simple cases like basic arithmetic, are often self-evident.
GEM of TKI
PS: Re Vivid, Pi is the ratio of the circumference of a circle to its diameter. That this is a fixed number has not changed, nor will it change, not so long as circles remain circles, similar to the traces we make by whirling a compass. This is a brute fact of reality, and it is certainly an unchanging mathematical truth. We may not be able to specify exactly pi in any system of fractions, but that does not change the reality that a circle has certain key properties.
—BarryR: “I’d like to think you didn’t make up the idea of universal mathematical laws. Can you give me the citation where you first heard of it?”
Inasmuch as I said nothing about “universal” mathematical laws, I can’t imagine what you mean? I said that there are mathematical laws, and you said that there are none. That is the issue on the table.
You claim that your authors agree with you, but when I ask you to show me when and where, you opt out. Why cite them if you cannot show how they support your claim?
On the other hand, I can certainly cite a number of authors and mathematicians who agree that there are, indeed, a number of mathematical laws.
Just to make sure that I understand you, are you saying, for example, that the law of sines/cosines is not a law in spite of the fact that its discoverers called it a law and that all mathematicians that I know of would call it a law?
According to Wikipedia, “The spherical LAW of sines was discovered in the 10th century. It is variously attributed to al-Khujandi, Abul Wafa Bozjani, Nasir al-Din al-Tusi and Abu Nasr Mansur
Al-Jayyani’s The book of unknown arcs of a sphere in the 11th century introduced the general LAW of sines.”
“The plane LAW of sines was later described in the 13th century by Nas?r al-D?n al-T?s?. In his On the Sector Figure, he stated the LAW of sines for plane and spherical triangles, and provided proofs for this LAW.”
Do you dispute any of this? Frankly, I don’t understand how you can continue on with this easily refuted proposition of yours.
vividbleau@172
Well done. That’s the most mathematically sophisticated reply I’ve gotten in this thread. (No, that’s not sarcasm.)
But as you say:
I’d go so far as to say pi will be found in any system that supports transcendental numbers. But as not all systems support transcendental numbers, I wouldn’t consider pi to be a universal constant.
Still, as candidates go, it was much better than “exponentiation”.
kairosfocus@174
You’ve demonstrated how addition holds when mapped to discrete objects that remain discrete under addition.
As that doesn’t even describe all physical systems, I’m not clear why you think this is universal.
StephanB@176
That’s my formulation, yes. I thought you disagreed. Is that correct?
I’m pretty sure you still don’t understand my actual position, but I don’t think there’s anything to be gained by repeating it.
I think I showed you that, for these laws being universal and all, nobody seems to consider them worth writing about. But since you insist:
Bruce Edmonds, What if /all/ truth is context-dependent, draft, 2001.
I don’t hold out any great hope that you’re going to read the paper. Nor do I hold out any great hope that you’re going to be able to supply any citations for your side, much less supply any universal / objective mathematical laws.
Before you waste you time, I certainly believe there are mathematical laws; they’re just context-dependent.
I’m pretty sure you don’t understand the distinction, and frankly I don’t know how to explain it to you.
How does the law of sines apply to graph theory?
I don’t think it does. If you’re working with a geometric system, sure, then within that system you can describe a general law. But only within that system.
I’m sorry you’ve put so much time into this and still don’t understand what’s at issue.
I don’t dispute that you’ve found yet another context-dependent law. They’re rather thick on the ground, you know.
I will dispute that these are context-independent.
Tell you what: After you’ve read Edmonds let me know and we can discuss his formulation, and I’ll refrain from any other replies to you until you do so.
#175
Inasmuch as I said nothing about “universal” mathematical laws, I can’t imagine what you mean? I said that there are mathematical laws, and you said that there are none. That is the issue on the table
If a mathematical law is not universal then presumably it does not apply at all times and all places (or do you mean something else by “universal”? If all you are claiming is that there are some mathematical laws that are true under some conditions, I don’t think Barry or I would disagree. We already discussed that 2+2=4 when applied to apples.
The prescence of rules and deductions called “laws” is surely not the issue. I accept that there are laws of chess. I just don’t think they apply outside of chess.
Being an onlooker, I suppose i am entitled to make a comment here.
It seems to me that much of kf’s argument is about counting discrete objects. Nobody in his right mind would ever claim that two apples plus two apples mysteriously might reappear as onehundredandfortyseven (147) apples. That’s a feat of biblical proportions.
The question of ¶ is another matter; we are dealing with a particular relationship that cannot be expressed with a whole number. I’d have to study the subject first but I suspect maybe nobody knows if an exact number may be found this side of an infinite number of decimals.
Hope the last sentence makes sense.
#177
I guess the odd symbol was pi?
The key point here comes from vividbleau’s comment:
Pi is a universal constant in Eucledian space.
That is true – but it only holds where the axioms of Eucledian space hold. In non-Eucledian spaces the ratio of the circumference to diameter of a circle can almost anything. The real question is whether there is anything special or absolute about the statements of Eucledian geometry as opposed to any other.
—markf: “The prescence of rules and deductions called “laws” is surely not the issue. I accept that there are laws of chess. I just don’t think they apply outside of chess.”
You are making the same mistake that BarryR makes. There are no laws of chess, only rules. Laws are discovered; rules are established.
As I have already indicated with my brief reference to the law of sines/cosines, the laws of mathematics were discovered and are unchangeable. The word “absolute” covers that better than the word “universal,” though the latter term would also apply.
Few people, however, would think to use that word, which is why I objected to BarryR’s attempt to inject it into the discussion for purposes of measuring its frequency of use over the internet–as if that means anything.
He, like you, are not just making an error in interpretaion. You are both wrong about the facts in evidence.
Cabal@181
Pi is both irrational (cannot be expressed as a ratio of two integers) and transcendental (not a root of a non-constant polynomial equation with rational coefficients).
Different systems handle this differently. Constructivists hold that only accepted proof of a numerical object is the construction of that object, and so while approximations to irrationals are known to exist, there is no proof for irrationals.
This ends up giving you an arbitrarily tight bound on pi, but you can’t get to pi itself.
And, of course, pi won’t show up in any number systems that can’t handle irrationals (like the mathematics that describe how your computer operates — that uses a very loose approximation). Also, any system that is sufficiently simple to escape Godel’s incompleteness theorem probably isn’t complex enough to construct irrationals, but that’s just an intuition.
[Pi is a universal constant in Eucledian space.]
—markf: “That is true – but it only holds where the axioms of Eucledian space hold.”
It is a law for which there are no exceptions.
—In non-Eucledian spaces the ratio of the circumference to diameter of a circle can almost anything.”
Non-Euclidlian geometry is a different subject matter, which is one more reason why the word absolute applies and the word universal is problematic. To the extent that the laws of non-Euclidian geometry have been discovered, they are as absolute and unchangeable as the laws of Euclidian Geometry. Why would anyone expect the laws of plane geometry to be similar to the laws of spherical geometry? That, by the way, is why BarryR injected the word “universal” in the discussion, to shift the discussion away from the absolute, unchanging laws in the various mathematical discipines and onto the trivial and obvious point that no universal law can speak to all disciplines at the same time. Hence, my insistence on the word absolute.
—“The real question is whether there is anything special or absolute about the statements of Eucledian geometry as opposed to any other.”
Obviously, mathematical laws are absolute. Do you know of any that have been found to be untrue? They certainly work in the real world where they are applied every day. Do you know of any instances in which a bridge collapsed because the laws of trigonometry failed to hold up?
#179, #180
Stephenb
There is a lot of terminology floating around here which is in danger of turning this into a discussion of semantics. I suggest ditching the words “universal” and “absolute”.
I would not deny that there are mathematical results, some of which are sufficiently general to be called laws, which flow from agreed sets of axioms. These results always hold if the axioms hold. So pi is always going to 3.14….. given the axioms of Euclidian geometry.
I hope you would also accept that any given set of axioms may match the material world to a greater or lesser extent. Euclidean geometry is a good approximation for relatively small areas of the earth’s surface – pretty poor for large scale maps.
The interesting questions include:
1) Does Euclidean geometry have any special status relative to other geometries? (If not, then we can only say the ratio of the circumference to the diameter is sometimes 3.14 …. and sometimes not, depending on conditions. )
2) Are the results discoveries or inventions? I don’t care too much what we call them. Consider the consequences of the rules of chess – for example it is true, given the rules, that you cannot mate your opponent if all you have left is a bishop and your king. Is this a discovery or an invention – given that Chess is an invention and you could always alter the rules to make it possible to mate with a bishop? Who cares?
3) Do the laws of mathematics refer to some abstract objects – numbers, circles, triangles etc – which in some sense exist to be discovered? Here I suspect I differ from BarryR. I think he proposes that there are infinitely many systems of such abstract objects including one for each possible geometry. He just doesn’t give any such system any special status. I believe they are just rules for manipulating symbols much as the rules of chess are (unless of course you believe in an abstract world of pawns, kings and bishops etc).
Cabal:
Precisely.
That is why we define the operations, numerals and symbols to capture these facts of reality. Two match sticks each, in two groups, joined together will — and must — give four. 2 + 2 = 4 summarisesw this.
What was done above was to inject an arbitrary redefinition of+, and pretend that this changes the truth of 2 + 2 = 4.
But to try to do that simply results in a cluster of patent contradictions.
And, the same reasoning extends to plane geometry and the like, as well as to trigonometry.
When se set out axiomatic systems to integrate such facts that we discover ans substantiate as necessary truths, then we see that axiomatic systems are necessarily incomplete if coherent, and incoherent if completer. Worse, there is no way to set up a system of axioms known to be consistent. (Thence the concept of undecidable propositions relative to given systems of axioms.)
But such integrative schemes account for the facts of mathematics, it is not that the facts depend on them.
GEM of TKI
Onlookers:
The above abundantly illustrates what happens when the law of non-contradiction is wantonly disregarded, and equivocations are injected willy-nilly into our reasoning structure.
Ever-deepening confusion and absurdity.
A sad picture.
And ever so revealing.
Reductio ad absurdum.
On steroids.
In fact, the addition operator was introduced precisely to express what happens with the cardinality of the resulting set when disjoint sets of identifiable items are joined in a union. Once that is happening and the cardinality of the original two sets is 2, then the cardinality of the resulting unified set is and must be 4, on pain of absurdity.
But, that is simply a fancy way of describing what happens when you:
What we keep seeing above is the attempt to inject an equivocation in the symbol for the addition binary operation, and the consequential contradictions and absurdities that follow.
Now, you will see that I have confined myself to natural numbers, as that is all we need to show that there are objectively verifiable self-evident, truths in mathematics; that thus have universal character.
Now, we may then EXTEND the addition operator to other cases, as we expand the entities we are addressing, but in so doing we must be careful to be consistent with the original definition. So, we speak of adding fractions [and remember a decimal often has a fractional component; the place value notation being a misleadingly “simple” way of expressing that]; reals, negatives, and complex numbers.
When we start to get into vectors, matrices and further constructs, the properties change and one has to be careful. But the parallelogram law of vector addition is equivalent to reduction on base vectors and addition of coefficients of the base vectors, e.g. the famous i, j, k vectors of simple mathematics. And complex numbers are a special case of vectors.
All such extensions rest on the confident acceptance of the universal validity of the already existing case of the addition of simple wholes.
So, here we are as we watch the evolutionary materialistic, selectively hyperskeptical, radically relativistic view in action: intelligent, highly educated adherents are trying to argue against the legitimacy of the fact that 2 + 2 = 4 is self evidently and undeniably true once we understand the meaning of the symbols [which of course is a contextual thing, but the reality the symbols capture is beyond the particular symbols we are using], something that is instantly accessible to the conscious reasoning mind, by simply playing with a box of matches.
Utterly and ever so sadly revealing!
GEM of TKI
PS: Maybe we can cite Wiki, as that ever so reliably materialistic reference will at least set a baseline:
___________________
>>Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+). For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples. Therefore, 3 + 2 = 5. Besides counts of fruit, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, decimals and more.
Addition follows several important patterns. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication. All of these rules can be proven, starting with the addition of natural numbers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra.
Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some animals. In primary education, children learn to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day . . . .
Let N(S) be the cardinality of a set S. Take two disjoint sets A and B, with N(A) = a and N(B) = b. Then a + b is defined as N (A U B) . . . >>
___________________
To then impose an extraneous and contradictory “definition” on what is plain and simple, to make a rhetorical point and thus to derail a serious discussion, is plainly inexcusable.
But then, these days ever so much of that is going on, as our civilisation descends — at the hands of the materialists and their fellow travellers — into the chaos Plato warned of in the Laws, Bk X; 2300 years ago.
—markf: “Are the results discoveries or inventions? I don’t care too much what we call them.”
Don’t you think that if two things are radically different they should go by different names? If someone discovers a law, it means that he/she has uncovered an unchanaging truth. In some cases the same law was discovered by two people, neither of which was aware of the other’s work. This is only possible if both were discovering a truth that was independent of their capacity to simply conceive a set of axioms for the sake of argument. It is no coincidence that the ordered universe, which is law-like, is synchronized with the laws of mathematics.
If one establishes a mere rule, as in chess, one has simply set down a certain set of conditions that does not necessarily have any relationship with the real world. There is nothing in the laws of chess that can quantify what happens in ordered nature.
On the other hand, the laws of mathematics faithfully reflect what goes on in the world that they measure. They never fail and they never change. A rule could change overnight and, for that reason, it would be unreliable as a means of measurement.
—“Consider the consequences of the rules of chess – for example it is true, given the rules, that you cannot mate your opponent if all you have left is a bishop and your king. Is this a discovery or an invention – given that Chess is an invention and you could always alter the rules to make it possible to mate with a bishop?”
The rules of chess are not laws. They are not necessarily unchangeable, nor are they synchonized with a lawfully ordered universe in such a way that each makes sense in light of the other. By contrast, the laws of math confirm the laws of science and the laws of science confirm the laws of math. That is one of the main reasons that the universe is a rational place. Lawful mathematics tells us something about the law-like ordering of the universe. If mathematics had no laws, it would be undependable as a means to measure nature. Mathematics may develop, but its laws do not change.
In keeping with that point, Chess is simply a game like football or basketball, though a bit more cerebral. There is no such thing as a “law” of baseball. —
“Who cares?
Evidently, both you and I care a great deal about the subject matter. There is a truth which needs to be acknowledged: We have rational minds, we live in a rational universe, and there is a correspondence between the two.
Also, don’t forget that mathematicians themselves call these laws by their proper name. Snells law, for example, is not called Snell’s axiom or Snell’s assumption or Snell’s proposition. These laws do not depend on some broader axiomatic formulation. If they did, they would not be laws. They would simply be derivatives of the mathematicians imagination.
PPS: Wiki actually goes into some of the chaos, by raising the scene in 1984 in which the party is imagined as saying 2 + 2 = 5:
________________________
>> The phrase “two plus two equals five” (“2 + 2 = 5”) is a slogan used in George Orwell’s Nineteen Eighty-Four[1] as an example of an obviously false dogma one must believe, similar to other obviously false slogans by the Party in the novel. It is contrasted with the phrase “two plus two makes four”, the obvious – but politically inexpedient – truth. Orwell’s protagonist, Winston Smith, uses the phrase to wonder if the State might declare “two plus two equals five” as a fact; he ponders whether, if everybody believes in it, does that make it true? Smith writes, “Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.” Later in the novel, Smith attempts to use doublethink to teach himself that the statement “2 + 2 = 5” is true, or at least as true as any other answer one could come up with.
Eventually, while undergoing electroshock torture, Winston declared that he saw five fingers when in fact he only saw four (“Four, five, six – in all honesty I don’t know”). The Inner Party interrogator of thought-criminals, O’Brien, says of the mathematically false statement that control over physical reality is unimportant; so long as one controls their own perceptions to what the Party wills, then any corporeal act is possible, in accordance with the principles of doublethink (“Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once”). >>
__________________________
Are we SURE it isn’t “really” 1984?
Just like, we could simply decide that the new millennium began in 2000 not 2001. (In Jamaica, that famous iconoclast, Mutty Perkins, was heard: one coco, two cocos [= taro etc], . . . highlighting that since there was no year of zero, the 2,000th year marked the close of the second Christian Millennium as counted on the conventional timeline.)
How vital is the understanding that Aristotle (and Plato before him) bequeathed to us:
And, sirs, truth is the real target of the mind-benders.
Inconvenient but self-evident or objective truth.
In that sad cause, they would have the year forever be 1984 . . .
but there cometh a day in the which we shall all have to reckon with Him who is Truth and Reason Himself.
BarryR,
C. S. Lewis as Philosopher by David Baggett, Gary R. Habermas, and Jerry L. Walls should be added to your embarrassing amount of books. I don’t think you’re really appreciating what it means to get a first in Greats at Oxford. As I said before, by 26 he was a philosophy professor at Oxford.
How so?
How so?
How about reading it in the original Greek and taking in all of the metaphysics and philosophy at once? You’re not trained in philosophy or literature. I find it frankly irrational to consider that you can know what was in Lewis’s mind while he read Plato and every other philosopher that he studied.
It’ll show up as long as it’s not against the moderation policy.
#190
In some cases the same law was discovered by two people, neither of which was aware of the other’s work. This is only possible if both were discovering a truth that was independent of their capacity to simply conceive a set of axioms for the sake of argument.
Two people might independently discover an inevitable consequence of the rules of chess. However, the rules of chess were clearly conceived by men.
It is no coincidence that the ordered universe, which is law-like, is synchronized with the laws of mathematics.
It is hardly surprising that the mathematical systems we know best describe aspects of the universe we know very well. That is because we were motivated/inspired to devise mathematical systems that describe the universe we know well. Nevertheless we keep on stumbling across aspects of the universe which are not modelled well by current maths. In some cases we devise new maths – non-Euclidean geometry. In other cases we are currently stumped – fluid dynamics.
If one establishes a mere rule, as in chess, one has simply set down a certain set of conditions that does not necessarily have any relationship with the real world. There is nothing in the laws of chess that can quantify what happens in ordered nature.
On the other hand, the laws of mathematics faithfully reflect what goes on in the world that they measure.
That just isn’t true. Euclidean geometry is only an approximation to any real world we have met – see above.
They never fail and they never change. A rule could change overnight and, for that reason, it would be unreliable as a means of measurement.
The consequences of axioms never change. The consequences of the rules of chess never change. The choice of axioms is continually changing to meet the demands of the real world or just to satisfy the curiousity of mathematicians. The rules of chess change to sometimes to give us a different game.
In keeping with that point, Chess is simply a game like football or basketball, though a bit more cerebral. There is no such thing as a “law” of baseball. —
Not sure about baseball but welcome to the laws of soccer.
Also, don’t forget that mathematicians themselves call these laws by their proper name. Snells law, for example, is not called Snell’s axiom or Snell’s assumption or Snell’s proposition. These laws do not depend on some broader axiomatic formulation. If they did, they would not be laws. They would simply be derivatives of the mathematicians imagination.
Given the link to the laws of football I don’t think we should place too much emphasis on whether they are called laws, axioms, lemmas, results or whatever. I am not quite sure why you introduced Snell’s law which is a law of physics not maths and the result of experimental observation rather than deduction. BarryR has shown for several examples of mathematical law that you have suggested that they are dependent on certain axioms.
—markf: “It is hardly surprising that the mathematical systems we know best describe aspects of the universe we know very well. That is because we were motivated/inspired to devise mathematical systems that describe the universe we know well.”
You are putting the cart before the horse. We know the universe in part, because the laws of mathematics allow us to provide a quantitative analysis. If we could know the universe and its laws in advance of applying mathematical laws, then the application would be redundant. You are assuming as given the very knowledge that can only be obtained through the laws of mathematics.
Similary, if we could evaluate evidence in the absence of logical laws, we wouldn’t need logic. Reason’s rules inform evidence, and mathematical rules inform science.
—“BarryR has shown for several examples of mathematical law that you have suggested that they are dependent on certain axioms.”
Barry has only made the claim, he has not provided any support for that claim. On what axioms do the laws of association and accumulation depend? Please be specific, name the axiom or axioms on which they depend and explain the relationship between the two.
@194: Excuse me. That should read[commutative] and associative laws.
—BarryR @179 “Before you waste you time, I certainly believe there are mathematical laws; they’re just context-dependent.”
[Which is the argument I have been making all along. Plane Geometry has its laws; spherical geometry has its laws; arithmetic has its laws etc. That is why I objected to your use of the word universal]
BarryR @86: Math and logic. There are no “laws of math and logic”. There are axioms and ways of relating axioms to each other, but you’re free to choose your axioms and your relations to suit whatever it is you’re trying to accomplish
[Which is the argument you made at the beginning and which you morphed into the previous paragraph.]
BarryR pre-interaction: “THERE ARE NO MATHEMATICAL LAWS.”
BarryR post interaction. “I CERTAINLY BELIEVE THERE ARE MATHEMATICAL LAWS.”
Obviously, I disagree with your first position and agree with your second position.
Now, let’s begin to discuss the laws of logic that you claim do not exist.
CH@170
Interesting. Have you read Baggett’s other book, Harry Potter and Philosophy: If Aristotle Ran Hogwarts?
There’s a bit of a literary trope here that I don’t think you’re familiar with. Using “X as Y” in the title indicates that the author understands that X is not considered to be a Y, and is making the proposition that it might be educational to see what happens if we made that assumption. Other examples:
Paul Radin, Primitive Man as Philosopher
Robert J. Yanal, Hitchcock as philosopher
Anton Pannekoek, Lenin as philosopher
and let’s not forget
Caleb Sprague Henry, Satan as moral philosopher
I’d say Baggett is well aware that Lewis is not considered a philosopher.
I took to heart your suggestion of consulting a biography of Lewis. You are wrong on both counts.
Lewis was hired as a tutor of English in Magdalen college. Later…
From George Sayer and Lyle W. Doreett’s _Jack: A Life of C. S. Lewis_ p328-9.
He wasn’t a professor of philosophy. He wasn’t even a professor of English. Occasionally you’ll see him referred to a “Professor” by someone outside the college, but this was only an honorific.
You could have looked that up yourself, you know.
Thank you for reminding me. The first tutorial I took in the Honors College was to have been a survey of Theater Criticism, but I started off with some unkind words about Aristotle’s Poetics and Dr. Bill had the good sense to throw out the syllabus and spend an entire semester on that tiny, tiny book.
There were only three of us in a tiny, windowless room in the basement of the TComm building. We’d read a sentence, I’d immediately jump in trying to understand it, Bill would try to rein me in, and then the other student, Toni, would reliably interject something profound after we’d gone back and forth for a while. Sometimes we’d make it through a chapter, sometimes we’d spend the entire class period on a single word (yes, in the original Greek).
After 17 years of college education across Theater, English, Political Science, Philosophy, Math, CompSci and Biology, that remains my favorite class. It taught me how to read, and I made two lifelong friends as well (Toni even flew across the country to attend my Ph.D. defense.)
(It’s funny, though, that I considered it to be a theater class instead of a philosophy class when I was thinking about the philosophy classes I had taken.)
That being said, translations are fine if you’re reading outside of a university and useful when your reading inside them.
My undergraduate focus was on dramaturgy, so I’ll cop to the literature end. I think I had enough philosophy classes to have earned a minor, but that would have required a modicum of paperwork and I’ve never been good at paperwork.
I suppose I could ask if you have any training it either, but I don’t think there’s any need.
I’m afraid my answer may contravene the moderation policy, so I’ll have to forbear.
I’m happy to give you an answer via private email or in a non-moderated public forum. I’m a regular at talk.origins, so if you like I can start a thread over there.
I can give you the Chesterton critique there as well.
markf@186
As to interesting questions:
It’s a pleasure to make your acquaintance. You might want to drop by talk.origins (via google groups if you don’t have a usenet feed) and say hello.
My introduction to these questions came via Davis and Hersh’s _The Mathematical Experience_. It’s not a book about math, it’s a book about how math is created / performed / discovered. To say it’s the best introduction to serious mathematics for a general audience implies that there exists other such books, and outside of the A Very Short Introduction series I don’t know of any. For a quick sampling, check out their definition of the ideal mathematician.
I’m just going to address one of your points here:
That’s an excellent summary of the Platonic approach, and you’re arguing instead for a more formalist approach. I know intelligent people who hold each view (the professional mathematicians are uniformly Platonists and the Computer Scientists are uniformly Formalists, I tend to swing back and forth).
With either approach, though, there’s a problem of how to give special status to one over another — the axiomatic systems that result in 2+2=4 get far more use than those where they don’t. I find utility to be a simple enough explanation: we focus on math that maps well onto the world around us and (usually) ignore the math that doesn’t. So while I consider all axiomatic systems to be epistemically and ontologically equal, when it comes to relevance, we pick our favorites.
G. H. Hardy argued that beauty also plays a role:
From A Mathematician’s Apology
Figuring out that there are no universal axioms isn’t that difficult — I managed to pick this up in 8th grade, but then I had an exceptionally good geometry teacher. Deciding whether or not math reflects a different reality or is just symbol manipulation is ultimately unanswerable, and most of the time I don’t think it matters. Figuring out where beauty lies in mathematics, though — that’s a hard problem worth solving.
markf@193
Most mathematicians believe the real world is an approximation of Euclidean geometry.
😉
I can’t improve on that.
StephanB@196
What did you think of section 3.3 of Edmond’s paper?
#194
You are putting the cart before the horse. We know the universe in part, because the laws of mathematics allow us to provide a quantitative analysis. If we could know the universe and its laws in advance of applying mathematical laws, then the application would be redundant. You are assuming as given the very knowledge that can only be obtained through the laws of mathematics
It is true that the use of mathematics allows us to provide a quantitative analysis because some axiomatic systems work well and in that sense helps us get to understand the universe even better. I meant know in the sense of “se connaitre” rather than “savoir”. I should rephrase my paragraph as:
“It is hardly surprising that the mathematical systems we know best describe aspects of the universe we deal with regularly. That is because we were motivated/inspired to devise mathematical systems that describe the universe we deal with.”
The point is that the fact that some mathematics describes some aspects of the universe very closely does not prove that mathematical laws are in some sense necessarily true except in the trivial sense that they follow from their axioms.
BarryR,
Do you not know that a tutor is a professor at Oxford? Lewis was hired in place of another professor, E.F. Carritt, while he was gone for a year, and guess what, E.F. Carritt was also a “tutor”, which means professor. Please read page 15 of C.S. Lewis as Professor. Did you have a chance to look up what is entailed in the Greats (Literae Humaniores) as a degree at Oxford?
It would’ve been so painless to have just read the introduction the the book that I linked for you, in which case yours is not an argument. The authors are dead serious in taking Lewis as a philosopher. Please, save me from correcting, I really mean this, and read, at the very least, the intro to the book. It will save us a lot of time. “His first job at Oxford, then was teaching philosophy” and “It was only when he received his position as Fellow of Magdalen College in 1925, his first permanent job [at age 27], that his career direction as a literary scholar was set. But even then, part of the reason he may have gotten the job was Magdalen was looking for someone who could teach both philosophy and English” page 15. I know you had almost enough credits to get a minor in philosophy, which a Minor is usually about 26 credits, but the Greats at Oxford is a four year degree in itself. Essentially Lewis got three three degrees at once and got Firsts (the highest grades possible) in all three. I know, I know, you almost got a minor in philosophy, and I’m sure you could translate the Iliad at 14 like Lewis did. Let’s put this into perspective, Lewis could actually speak Attic Greek, not just read it and write it. He also knew Medieval Italian, Latin, French, German, Anglo-Saxon and Old Icelandic, as well as being an English Scholar. You might be interested in a book of his called Studies in Words, in which he traces the different usages of words throughout time and throughout different languages and explains their usage in that manner, which gives insight into their ancients’ worldview and their philosophy.
The policy is just being civil, you don’t have to be uncivilized to explain to me how Lewis made mistakes a trained philosopher wouldn’t have made.
I see these reasons as cop-outs. You’re welcome to write to me at my email, but it better not be uncivilized there either. And if it isn’t, I see no reason why we cannot continue here.
#202
Do you not know that a tutor is a professor at Oxford?
Sorry but that is not true (I speak as a Cambridge graduate which uses the same tutorial system). A tutor is not a formal position. It just means someone who gives tutorials. It can be of any academic rank. Mine were mostly graduates taking their PhD. CS Lewis did not get a professorship until was 57 and that was not in Philosophy.
CF@202
No, I didn’t know that. The Girlfriend spent a year over there while she was getting her physics degree. She reports the correct title is “Don”. These days they tend to have Ph.Ds., but standards were a bit more lax when Lewis was there.
Do you have a cite to the contrary?
I taught several semesters for professors while I was getting my Master’s degree. It’s a pretty common setup. That didn’t make me a professor.
I cited it back at 155. Glad to see you’re getting caught up.
You’ll notice no dissertation is required, nor did he do sufficient (any?) original research afterwards to be considered for an English professorship, much less a philosophy position.
Yep. It lasted a year. He never went back to it. Never took a graduate degree in the field, never published any original research in the field, never held a permanent position in the field and never was elected to a professorship in the field.
Based on the above, you want to label him a professor of philosophy. You’re free to do so, but you’re not free to have other people take you seriously.
(Now you’ve got me wondering — there were formal programs in philosophy at the time, right? If Lewis really did want to be a philosopher, why wasn’t he enrolled in one of those instead of one of the Western Classic programs? The “Greats” are fine for everything up to, what?, Augustine? Did he ever taken any classes covering philosophy after 1700? I honestly don’t know.)
I see my posts getting delayed for moderation with no explanation. I see that a post mentioning this and apologizing for the delay got killed. I don’t know if this is you or someone else, but this isn’t how adults behave.
If you feel I’m being uncivil, then tell me. If I’ve offended you, then tell me. You just might get an apology.
markf@203
Ah, that was at Cambridge, right?
I had missed that.
#203 cont
To be fair I would say that CS Lewis was trained in philosophy. I understand his degree was in Greats which includes the philosophy of the Greek philosophers and he got a triple first. He was also taken seriously enough to at least have the famous debate with GE Anscombe. However, as far as I know, he never had a philosophical paper published in an academic journal and his name never came up in 3 years of studying philosophy. So, given that there is only time to read a limited number of philosophers in a life time – I am unlikely to get beyond Narnia as far he is concerned.
BarryR #198
Likewise pleased to meet you. I am not sure how I could link to you on usenet or Google Groups given the only thing I know about you is your WordPress ID. My e-mail is:
mark(dot)t(dot)frank(at)gmail.com
Cheers
Onlookers:
It is often quite revealing to look back at the original post, when a thread goes ever so determinedly off the rails.
For, that is telling us just what it is that some of those who come here to comment are ever so desperate not to discuss; nor are they willing to allow others to discuss in peace.
Here is Prof Sewell, as excerpted form this thread’s original post:
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>> For the layman, it is the last step in evolution that is the most difficult to explain. You may be able to convince him that natural selection can explain the appearance of complicated robots, who walk the Earth and write books and build computers, but you will have a harder time convincing him that a mechanical process such as natural selection could cause those robots to become conscious. Human consciousness is in fact the biggest problem of all for Darwinism, but it is hard to say anything “scientific” about consciousness, since we don’t really know what it is, so it is also perhaps the least discussed.
Nevertheless, one way to appreciate the problem it poses for Darwinism or any other mechanical theory of evolution is to ask the question: is it possible that computers will someday experience consciousness? If you believe that a mechanical process such as natural selection could have produced consciousness once, it seems you can’t say it could never happen again, and it might happen faster now, with intelligent designers helping this time. In fact, most Darwinists probably do believe it could and will happen—not because they have a higher opinion of computers than I do: everyone knows that in their most impressive displays of “intelligence,” computers are just doing exactly what they are told to do, nothing more or less. They believe it will happen because they have a lower opinion of humans: they simply dumb down the definition of consciousness, and say that if a computer can pass a “Turing test,” and fool a human at the keyboard in the next room into thinking he is chatting with another human, then the computer has to be considered to be intelligent, or conscious . . . >>
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A very good issue and challenge: our most direct and central experience is of being unified selves, aware, thinking, perceiving, having a sense of conscience, etc. Where does that come from, and can we have a credible evolutionary materialistic account of its origin and character?
It should come as no surprise to learn that the evolutionary materialist paradigm has no good answer for this. In wiki’s — testimony against known interest — summary:
Translating: we cannot simply reduce it on evo mat assumptions, and so it is “hard.” (The idea that just perhaps, the real answer is that — echoing Plato — Soul is older than what is hard, heavy, hot or cold, dry or wet, is simply put out of mind.]
Ilion, in no 5, is apt:
In other words, we are again meeting he a priori materialism that ever so often presentes itself as THE “scientific” view, never mind that the very materialists themselves dierectly experience what it is to be ensouled creatures, and never mind that when they try to explain mind on such premises, they end up in the absurdities of resorting to chance and mechanical necessity as the only relevant causal factors, thus running into any number of absurdities: reducing ground-consequent to physical causal chains and derived accidents of culture and personal life history, ever so soon becomes plainly self referentially absurd.
In this context, distractive tangents are unsurprising. (And to see the attempt to dismiss Lewis’ argument by undermining the man instead of addressing he issues on the merits, or to dismiss the self-evident truth that 2 + 2 = 4 by injecting a self-contradictory equivocation in the meaning of “+” are all too aptly illustrative of the problem.)
So, far, the evidence is on the side of mind being its own self, and the cause of the physical cosmos we as minded creatures, observe.
GEM of TKI
Stephenb #194 (cont)
Final comment for this morning …. (I must be mad)
Barry has only made the claim, he has not provided any support for that claim.
Glancing through the comments above I see the following “laws” which Barry has shown can be false given a change of axioms:
#103
2+2=4
a+b+c = c+b+a
It is not possible to divide by zero
#126
a+b gives a unique result
#157
Law of exponents
#166
The law of limits with respect to calculus.
No doubt you will disagree with his proof in each case but you can hardly say he has not provided any support. In some cases he has written extensively and provided references.
On what axioms do the laws of association and accumulation depend? Please be specific, name the axiom or axioms on which they depend and explain the relationship between the two.
….
That should read[commutative] and associative laws.
This is a bit confusing – as far as I know “commutative” and “associative” are properties which functions may or may not have. A law would have to be something like –
(A) “the addition and multiplication functions on real numbers are commutative and associative”
Assuming that is what you meant, then these laws are dependent on the axioms of the arithmetic of the natural numbers. I am not a mathematician so I may be wrong about the detail, but I believe the appropriate axioms are the Peano axioms with addition of the definition of the addition and multiplication functions. It needs a better mathematician than me to prove exactly (A) follows from these axioms – perhaps BarryR can oblige.
Barry,
You said, initially, that he didn’t have training in philosophy, not it’s that he wasn’t a professor of philosophy long enough to suit you. Odd that you move the goal posts…. considering Peter Kreeft, Ph.D., who is a professor of philosophy at Boston College, Victor Reppert, PhD., an American philosopher, Gary Habermas, Ph.D., professor of philosophy at Liberty, Dr. William Dembski, who has two Ph.D’s, Anthony Matteo, Ph.D, professor of philosophy at Elizabethtown College, just off the top of my head, consider his works important in philosophy. That’s peer review. Indeed, all of these men have endorsed certain portions of Lewis’s philosophy. But, BarryR, who almost got a minor in philosophy, doesn’t think Lewis was a philosopher. You’re right about one thing, Lewis didn’t want to be a professional philosopher, but that doesn’t mean he wasn’t trained in it. Now we’ve spent too many comments on me just addressing your ad hominem of why Lewis’s argument in De Futilitate was wrong. I’ve yet to see an actual argument.
Yes you have been, very jeering and condescending. So………….I’m still waiting as to why Chesterton was wrong and why Lewis was wrong. You can start any time.
markf,
Sorry, but that is wrong. Being a Fellow of Magdalen College, Oxford, which Lewis was for 29 years, was a professorship when Lewis had it. I’m not interested how it’s done today at Cambridge.
#211
Clive
This is a rather trivial debate but I am not busy at the moment. I am going to come straight out and say I don’t believe you.
I see you have changed from “tutor” to “fellow” (the two are different, Lewis was a tutor in philosophy at University College for a year, but not a fellow, then became both fellow and tutor in English at Magdelen) but let’s go with fellow. Nowadays a fellowship at Oxford certainly doesn’t require you to be a professor. I very much doubt the rules were different in the 1920s.
In addition I cannot find any biography of CS Lewis that mentions him being a professor until 1955. Many of them use terms such as “important teaching post”. If he had been a professor surely they would have said so?
If you can provide a reference to prove your point please do and I will retire shamefaced from this trivial debate.
http://www.ox.ac.uk/about_the_.....index.html
I find it a bit odd, but the official Oxford Glossary doesn’t spend any time distinguishing among Don, Tutor, Reader, Professor, Fellow, Lecturer.
His field seems to have been English rather than Philosophy, except for six months when he was a substitute.
http://gmmalliet.weebly.com/oxbridge.html
Clive, markf, others
It’s difficult to get reliable information online regarding teaching positions at Oxford in the 1920s. What I was able to find is that Oxford combines “fellow” with “tutor” as one who oversees the teaching of a particular subject (in Lewis’ case English) to a group or individual, through lectures or individual study.
http://en.wikipedia.org/wiki/Tutor
“In the University of Oxford, the colleges fuse pastoral and academic care into the single office of Fellow and Tutor, also known as a CUF Lecturer.”
So apparently at Oxford “tutor” and “fellow” are the same thing. Also, CUF lecturers are members of the faculty; not merely teaching assistants.
Lewis was elected as a Fellow in English in 1925 at Magdalen College, Oxford. I wasn’t able to find information regarding professorships specifically at Oxford; However, the title “Professor” was usually given only to the chair of a department, and not to all fellows within a particular department.
If you simply take a look at the lists of faculty at Oxford (on their website), you will see that they maintain this structure even today. The department chairs are listed as “Professor,” while the fellows are listed as “Dr.,” “Mr.” or “Mrs.”
Thus, for 29 years, Lewis was a Fellow; teaching, doing research and publishing, similar to what is expected of a professor at any college or university here in the U.S. Then in 1954 He became a Professor of Medieval and Rennaisance English at Magdalene College, Cambridge; that is, he was distinguished as a chair of a department, and not merely as a fellow. In fact, that position was created for him that year.
It’s important not to misconstrue terms here. What is meant by “Professor” in 21st Century American academia is far different from what was meant in early 20th Century English academia. Clearly Lewis was not simply a private tutor of English all those 29 years at Oxford. In fact, Lewis was quite influential as a fellow; publishing, establishing the “Inklings,” broadcasting lectures on radio, etc.
The issue of whether Lewis was a philosopher is a quite different matter. Clearly Lewis’ published works were largely concerned with philosophical issues, yet Lewis did not consider himself a philosopher.
markf,
It also appears quite remarkable that a lowly tutor from Oxford should all of a sudden have a professorship created for him at Cambridge in 1954. Clearly Lewis’ academic credentials had been well established by that time.
#213
CY – thanks for a balanced and helpful comment. It may come down to a difference between UK and US interpretation of the word “professor”. I didn’t realise that in the USA a professor is anyone who does research and teaching. In the UK you have to be quite a distinguished academic to get that title.
In the unlikely event that anyone is interested I did some more research. The Wikipedia article is misleading about the role of tutor and fellow at Oxford. This link is rather wordy but pretty much settles the issue:
http://www.exeter.ox.ac.uk/doc.....ellows.pdf
To summarise what is in it. At the time there were two types of fellows – tutorial fellows and ordinary fellows. Tutorial fellows had some tutorial and lecturing responsibilities. Ordinary fellows were usually researchers but included, for example, the rector. So some fellows were tutors and some were not. However, clearly you could also be a tutor and not a fellow beause Lewis was not a fellow of University College when he was a tutor there. I think it is high time to draw a line under this!
—BarryR: “What did you think of section 3.3 of Edmond’s paper?”
Because I respond to so many people on so many threads, I tend to go straight to central issues and abbreviate my answers. Occasionally, I will stretch out with a long post, but most people can get the point if distill the point to its simplest essence, as will be the case here.
Edmonds approach is just one of the many postmodernist/subjectivist approaches to philosophy informed by, dare I say, contaminated by, the unfounded skepticism of Immanuel Kant. Among other things, he assumes, like Kant, that analytic and synthetic reasoning are our only tools for obtaining truth. To better understand Edmonds’ confusion, send your search engine in the direction of “Little Errors in the Beginning,” by Mortimer Adler. In effect, Edmonds doesn’t acknowledge the reality of self-evident truths.
Because Edmonds does not acknowledge the starting point for all thinking, he immediately sinks into intellectual quicksand. Thus, he doesn’t even consider the role that self-evident truths play in the filed of mathematics, reducing all starting points to “axioms.” On the matter of logic and the role of the syllogism, he appears not to even understand the basic distinction between a valid argument and a sound argument, indicating surprise that a false major premise would produce an unsound conclusion.
Even though he articulates a reasonable objection to his philosophy, [that truth must be unified] he appears not to understand WHY it is the case that only a unified truth can be true. If theological and metaphysical truths are at variance with scientific truths and mathematical truths, we would be living in a cosmic madhouse, and there would be no warrant for trying to reason with anyone about anything.
If, for example, there is no law of causation, [a philosophical not a scientific truth] then there may be some effects that occur without causes. That would mean that science, which is a search for causes, is dead. If some effects can occur without causes, there would be no way of knowing which effects were caused and which ones were not. Metaphysics illuminates science; science does not illuminate metaphysics.
Indeed, Edmonds doesn’t even define the truth that he attempts to discuss. As all rational people know, truth is the correspondence of the mind to reality. If that correspondence doesn’t take place, truth has not been apprehended. What is Edmonds definition of truth? If he had one, this would certainly have been the place to disclose it. Many, not all, of Edmonds assertions qualify as old errors with new labels, which is why I so strongly recommend the work of G.K Chesterton, who may well have been greatest writer of the twentieth century. I feel no hesitancy in saying that you will not be refuting him, especially in the presence of those of us who have really read and understood him. The only way a secularist/naturalist/skeptic can deal with Chesterton is to ignore him.
I am also amused by this side discussion about the credentials of C.S. Lewis from pedants who have never read him and probably wouldn’t do so even on a bet. In order to have something to talk about, his critics should continue to attack him personally because they clearly have no answers to his arguments, of which they are almost always ignorant.
Petrushka,
You mean for a year, when another philosophy professor (tutor) went on leave and asked that Lewis take his place.
I guess I take this for granted, and am baffled I have to explain this.
StephenB,
Isn’t that the truth.
I don’t understand your bafflement. The title of professor means something different in England from what it means in the U.S.
It took a number of people to dig up the fact that in England, professor means department head.
StephanB@219
Thanks for reading the paper. I appreciate it.
The argument from self-evidence that the twin virtues of being the second-oldest philosophical argument (the first being “Because I said so”) as well as the weakest. To dismiss this argument, simply state “It’s not self-evident to *me*”, and the line of reasoning need not be considered any further.
There’s another, deeper problem with this approach. Once you declare something to be self-evident, you’ve removed both the incentive and the possibility of going back and improving your understanding of it. In the marketplace,
A different approach allows axioms to be introduced, debated and discarded based on the interests and abilities of the mathematician. The approach not only works, but works spectacularly well.
So, what do we lose if we abandon (most) self-evident truths? Other than a fragile, unearned sense of certainty, I can’t think of anything.
What do we gain? Modern mathematics and everything that makes use of it.
Axioms used to be defined as self-evident, but it wasn’t true then (think Euclid’s parallel postulate) and is a dead issue now. The wikipedia article on axioms isn’t too bad, you might want to take a look.
Ummm….
Theological and metaphysical truths are at variance with *each* *other*, You may think you’ve caught hold of the Actual Truth (and you may even think it is self-evident), but there are a couple billion people who are just a certain that they’re self-evidently right and you’re self-evidently wrong.
In contrast, science and math are remarkably catholic (in the original sense). It comes from having a neutral moderator pass judgment on our claims (that arbitrator being reality).
This kind of thinking usually comes out out of a very immature faith: God is perfect, thus X; if not-X, then God does not exist.
It amuses God to generate a consistent stream of not-X’s.
As you said, the idea of causation is a philosophical idea, not a scientific one, and as such it will make no nevermind to science however it ends up being decided.
For scientific ideas, exceptions are simply incorporated into the theory until we come up with a more general theory that accounts for them.
I think it was “truth in general is context-dependent”.
Can you give a cite to a rational person who has published something to that effect? Peer-reviewed, please.
It’s a really terrible definition: how do you go about ascertaining if something is true? Or real? Since this is just your mind, how do you communicate this to others?
As to Edmonds, I think he can be fairly summarized as “True statements are statements that are correct in a particular context.”
No.
markf@209
Lambda calculus will allow you to derive both addition and its commutative and associative properties using a tiny set of simple axioms, but you will be insanely bored by the time you get there.
If you’re curious and a masochist, the best presentation I’ve see in chapter 7 in Ryan Stansifer’s _The Study of Programming Languages_. Before you master what lambda calculus does, you have to learn both the formal and informal notation, and for mere mortals it’s incredibly opaque. Stansifer is very good at providing BNF grammars so that, if you don’t have a life, you can unambiguously pick apart how each of the theorems are derived.
Just to give you a taste, let lambda be “&”…
Foundational mathematics is much more fun to think about than to work through.
@222
Whoops, dropped a closing blockquote. Sorry.
#221
I am also amused by this side discussion about the credentials of C.S. Lewis from pedants
I think you also took part in this discussion did you not Clive?
markf @221: If you read the comments carefully, you will discover that it was not the participation but rather the lack of intellectual curiosity of the participants that was being questioned.
BarryR,
Can you provide a cite that tells you that everything of any consequence whatsoever has to be cited? Peer-reviewed please.
And please cite something peer reviewed and published that claims that anything published should be peer-reviewed please. And please cite something peer reviewed and published which says that only things peer reviewed and published should be discussed. And please cite something peer reviewed and published that says you should have a discussion at all. And please cite something peer reviewed and published which tells you that you should look to them for guidance in the first place in all endeavors of life. Presumably this would include a peer-reviewed and published work which tells you to trust them in all things to begin with, before you can make sense of how to proceed in any discussion, that is, what should you look to for peer review and what you shouldn’t in a discussion (i.e. X should be peer-reviewed but Y doesn’t necessarily have to be). And please provide the citation that tells you when it’s appropriate to provide a citation. Peer-reviewed please.
I’m still waiting for your response to Chesterton’s argument in Orthodoxy and Lewis’s argument in De Futilitate. You can start any time. And actually, if you would please, make an argument in your own words, that would be great, for that would tell me whether you actually understand A) What you’re arguing against, and B) What you’re argument itself really is. I don’t want vague referrals to other people’s works. I want to know how BarryR responds.
markf,
Of course, and I was amused as well.
Onlookers:
Clive is of course dead right to remind us that the real issue is the balance of a matter on its merits of fact and reasoning [ultimately traceable to first principles], not whether or not today’s neo-magisterium has deigned to award its imprimatur of approval.
So, when we see above, a claim like . . .
. . . that tells me a lot about just how far wrong we have gone.
As has been repeatedly pointed out above [e.g. cf 187 – 191], MF, the notion that 2 + 2 = 4 can be shown “wrong” by shifting “axioms” in midstream is a gross confusion rooted in the blatant error of substituting a novel redefinition of the “”+” operator; creating an unnecessary and blatant contradiction where + is now held to at once mean two different things that deny one another.
One more time, onlookers, let us get the old box of matches, and group sticks in pairs:
Step B operationally exemplifies — and we can state a formal definition — the addition operator, in its fundamental form.
Using standard symbols we have known since our early days at school:
2 + 2 = 4, QED
This result, once we understand the meaning of the numerals and symbols used based on our living in our common world as conscious, reasoning and understanding creatures, states something that is true, and which must be true, on pain of absurdity.
Something that most of us knew full well by the time we were 5 years old.
The + operator is indeed extended to other cases, but — for excellent reason — that is done in a way that preserves its core meaning instead of contradicting it without warning; worse, insisting on sticking to an embedded contradiction in our reasoning, in the teeth of correction.
Indeed, this side-track debate above shows what happens when we deal with the blatant rejection of first principles of right reason, starting with things like non-contradiction.
(I still point out, as at 208 above, that the side tracks serve to allow non-discussion of a key issue that some desperately do not wish to discuss.)
And when it comes to the proverbial live donkeys kicking the dead lions Lewis and Chesterton, let it suffice to note that they have failed to actually engage the matter on the merits, again.
Just as how they would kick rhetorical sand in our eyes to confuse us about the self evident truth that 2 + 2 = 4.
Remember that, onlookers:
“2 + 2 = ?” has now been reduced to a relativist morass of confusion.
Let that be the final demonstration of the absurdity of today’s self-referentially absurd evolutionary materialism and its radically relativist ultra/post- modernism, and let that show the fatal error being made by those who willingly go along with the pronouncements of the new materialist magisterium.
And sorry, when correction on the basic merits is refused again and again, on the blatantly plain, that is a sign that something is deeply wrong.
In unfortunately now necessarily plain words:
Reductio ad absurdum, backed up by evident willful obstuseness, disguised with distractive rhetoric.
A sadly, utterly telling outcome.
If one is trapped in a hole, the first step to escape is to stop digging in deeper.
GEM of TKI
PS: O/T F/N: Alphonsus, “Arrow” Cassell — Montserrat’s leading Soca entertainer, and a world figure [The song Hot hot hot is his trademark] — passed away from cancer today. Condolences to all fans, friends and family. I am going to miss our little exchanges in his Manshop.
BarryR,
I used 2+2=147 just because it came to mind. I could’ve just as easily used 2+2=9,235, or 2+2=0, or whatever else comes to mind. If you can make whatever I arbitrarily decide to invent to be true depending on how you choose your axioms, then nothing chosen as an example will have any real meaning. If anything is everything else, then it is nothing in particular, and the whole endeavor becomes meaningless because it is vacuous.
PPS: Orthodoxy and De Futilitate (excerpt on logic here).
kairosfocus,
Thanks for those links.
Clive:
You have of course identified why it is that we must purge contradictions from our thought life.
If A and NOT-A can be both true in the same time and sense of A, then meaning itself collapses into confusion and chaos. For meaning rests on distinctions.
And when, for instance some would cite quantum behaviour as a claimed denial of non-contradiction, they find themselves having to implicitly assume what they wish to dismiss.
GEM of TKI
—BarryR: “The argument from self-evidence that the twin virtues of being the second-oldest philosophical argument (the first being “Because I said so”) as well as the weakest. To dismiss this argument, simply state “It’s not self-evident to *me*”, and the line of reasoning need not be considered any further.”
All reasoning begins with the acknowledgement of self-evident truths. If you don’t believe that, try beginning with something else. With respect to the problem that some say, “it’s not self-evident to me,” there is a simple answer to that objection. Such individuals are simply afraid or unwilling to acknowledge that which they do, indeed, know. All sane people know that a thing cannot both exist and not exist at the same time. All sane people know that universes do not just pop into existence.
—“There’s another, deeper problem with this approach. Once you declare something to be self-evident, you’ve removed both the incentive and the possibility of going back and improving your understanding of it. In the marketplace,”
It is possible to improve one’s understanding of basic logic without abandoning its principles.
—“A different approach allows axioms to be introduced, debated and discarded based on the interests and abilities of the mathematician. The approach not only works, but works spectacularly well.”
Once one “discards” the law of non-contradiction, he/she loses his capacity to reason in the abstract. Recall Edmond’s logical errors with respect to the syllogism.
—“So, what do we lose if we abandon (most) self-evident truths? Other than a fragile, unearned sense of certainty, I can’t think of anything.”
I have already explained the cost of abandoning causality.
—“What do we gain? Modern mathematics and everything that makes use of it.”
Modern mathematics is founded on laws, as I have pointed out several times.
—“Axioms used to be defined as self-evident, but it wasn’t true then (think Euclid’s parallel postulate) and is a dead issue now.
All of Euclid’s elements are known to be self evident with the exception of his parallel postulate, which is not self evident and has never been proven or disproven. The elements [axioms] represent the basic foundation for all mathematics and have never been invalidated. Contrary to your assumption, no mathematician may add or delete them at will if he wants his mathematics to be rational.
—“The wikipedia article on axioms isn’t too bad, you might want to take a look.”
Wikipedia alternates between rationality and irrationality depending on the subject matter.
—“Theological and metaphysical truths are at variance with *each* *other*, You may think you’ve caught hold of the Actual Truth (and you may even think it is self-evident), but there are a couple billion people who are just a certain that they’re self-evidently right and you’re self-evidently wrong.”
You are assuming that since disputes about truth exist, that truth itself cannot exist. On the contrary, the principle should be clear. If one religion is in conflict with another, then either one or both of those religions are in error. If science is at war with logic, then either science or logic is misleading us. Only if there is one unified truth with many aspects can there be any rationality.
[If, for example, there is no law of causation, [a philosophical not a scientific truth] then there may be some effects that occur without causes. That would mean that science, which is a search for causes, is dead.]
—-“This kind of thinking usually comes out out of a very immature faith: God is perfect, thus X; if not-X, then God does not exist. [Law of causality]
No, it comes from an understanding that science is a search for causes, and if we cannot know for sure that everything is caused, then we cannot know that anything is caused. I have already made that clear.
\
—“As you said, the idea of causation is a philosophical idea, not a scientific one, and as such it will make no nevermind to science however it ends up being decided.”
The metaphysical principles of right reason underlie all science. Science cannot move one step without them. If you doubt this, try evaluating evidence without them.
[Edmonds doesn’t even define the truth that he attempts to discuss.]
—“I think it was “truth in general is context-dependent”.
That is not a definition.
[As all rational people know, truth is the correspondence of the mind to reality.]
—“Can you give a cite to a rational person who has published something to that effect? Peer-reviewed, please.”
I like your sense of humor. Socrates, Plato, Aristotle, Aquinas, Adler, Maritain, Gilson, Copleson, Kreeft, ….I could fill the entire page.
—“It’s a really terrible definition: how do you go about ascertaining if something is true?
It’s true if it corresponds to reality. It’s the only rational definition that has ever been offered. Do you know of a better one?
—“Or real?”
Reason and evidence
—“Since this is just your mind, how do you communicate this to others?”
Truth doesn’t just involve the mind; it involves the minds relationship to reality.
If there was no reality to know, there would be no truth to obtain. How do I communicate truth to others? I tell them.
—-“As to Edmonds, I think he can be fairly summarized as “True statements are statements that are correct in a particular context.”
Yes, that is not a bad summary of his position. However, there is no definition of truth there. As I have already made clear, Edmonds does not reason very well. Unfortunately, he is steeped in Kantian subjectivism and doesn’t understand logic. Why would you want to follow him when there are so many better thinkers around? Begin with Mortimer Adler.
Clive
Welcome.
I hope that he actual substance of the argument is addressed.
Including the issue C S L makes on the astonishing correspondence between reason and the world, which is reflected int he remarks on the “unreasonable” power of mathematics, which is symbolised logic.
G
Stephen
Apparently BR does not recognise that a self-evident argument is one where the truth is evident on understanding what is being claimed, on pain of reductio ad absurdum.
And the case here of injecting an arbitrary contradiction by equivocating he meaning of + and ending up denying that 2 + 2 = 4 is a capital example.
Here is Wiki — as a hostile witness making an acknowledgement against interests — on self-evident truth:
Do you think, above, that BR does not know that to say 2 + 2 = 4 AND 2 + 2 = 147 is not a contradiction?
Or, that it is introduced by willfully equivocating the meaning of +?
Hardly likely . . .
G
PS: Onlookers, in a lot of modern mathematics the key proof technique is to deny the proposition one wishes to prove, i. e. switch from P to NOT-P. Then, show that the latter entails a contradiction. By reversing the denial, one is back at P as true.
PPS: GKC’s companion to Orthodoxy, Heretics. I can’t wait till we get reasonable cost kiosk printer-binder machines, to read books that make SENSE, thanks to Project Gutenberg.
Just for fun:
Arrow’s 1982 Hot hot hot.
Best way to remember a great — and verrrry nice — guy.
(Funny, Bob Marley used to love across from my street where I grew up. Redemption Song. Telling contrast on national ethos!)
“None but ourselves can free our mind” — a quite from Marcus Garvey.
G
PS: The Marley Song is an object lesson to those who would build a middle wall of partition between philosophy, art and history, even theology. All of these are deeply connected in the context of worldviews. “Minutes after they took I from the bottomless pit.”
PS: tribute, here is Arrow live, maybe a few years ago.
F/N: Since there is an attempt to dismiss the connexions, here are the lyrics:
___________________
>> Redemption Song lyrics
Old pirates, yes, they rob I
Sold I to the merchant ships
Minutes after they took I
From the bottomless pit
But my hand was made strong
By the hand of the almighty
We forward in this generation
Triumphantly
Won’t you help to sing
These songs of freedom?
‘Cause all I ever have
Redemption songs
Redemption songs
Emancipate yourselves from mental slavery
None but ourselves can free our minds
Have no fear for atomic energy
‘Cause none of them can stop the time
How long shall they kill our prophets
While we stand aside and look? Ooh
Some say it’s just a part of it
We’ve got to fullfil the book
Won’t you help to sing
These songs of freedom?
‘Cause all I ever have
Redemption songs
Redemption songs
Redemption songs
Emancipate yourselves from mental slavery
None but ourselves can free our mind
Woh, have no fear for atomic energy
‘Cause none of them-a can-a stop-a the time
How long shall they kill our prophets
While we stand aside and look?
Yes, some say it’s just a part of it
We’ve got to fullfill the book
Won’t you help to sing
These songs of freedom?
‘Cause all I ever had
Redemption songs
All I ever had
Redemption songs
These songs of freedom
Songs of freedom >>
______________________
Now, let us look at CSL and GKC
F/N: Meet the mind of CSL, here. That old lion yet roars.
CH@228
What an interesting question!
This is one of those things that are usually taken for granted — like spell-checking your manuscript before sending it in for review. But sloppy spelling never wrecked a career, and sloppy citing has, so it’s far more important than that. Let’s see what I can find.
Randolph Smith dedicates and entire chapter to “Documenting your scholarship” in his _Guide to Publishing in Psychology Journals_. He cites Bruner(1942) as follows:
There are two important ideas encapsulated in the above: “monument” and “future investigators”. Taking them in turn:
I’m establishing a reputation here each time I post (as are you). By adding citations, I’m communicating to readers that I know enough about the topic to be able to cite the literature, and if they’re familiar with the topic themselves the can get a very finely calibrated understanding of the limits of my understanding from my cites.
So when you cite Lewis, this tells me volumes about what you’ve been reading (and haven’t been reading). Folks who don’t cite anything aren’t likely to have read widely or deeply and are probably just expressing an uninformed (though sincerely held) personal opinion.
So that’s the reputation aspect.
Second, it’s unlikely that I’ll ever have anything original to say about foundational mathematics, but what I can do is point readers to people who have said interesting things. I enjoy it when people do this favor for me, and I like returning the favor.
There’s a third reason that only really applies to this kind of forum. When I read something as silly as:
I need a polite way of expressing my skepticism. Saying “you’re wrong” or “that’s silly” isn’t helpful. But if I ask for a citation, one of two things will happen: I’ll get a citation and learn something without losing face, or everyone else reading the exchange will note the lack of citation and conclude that the author was expressing a personal opinion.
I’ve forwarded your question along to the folks at talk.origins. I’m interested to see if they can unearth if science got the practice from the legal profession of if it work the other way ’round.
If you like, I’ll post a summary of the responses here.
As I said yesterday (although it may have been obscured by the missing closing blockquote) look for that to be posted on talk.origins on Monday.
CH@231
Yes, it is a bit disorienting when you realize that there are an infinite number of true statements out there (and an infinite subset of them can’t be proven).
That’s perhaps some of the reason you don’t hear philosophers, mathematicians and scientists describing what they do as “looking for truth”. If truth is universal, we have no common way of gaining access to it. If truth is local, then everybody can have their own truth.
The solution is straightforward. We don’t judge our work based on how many truths we find, we judge it on how many *interesting* truths we find (where “interesting” in on a continuum, not a binary property).
So what’s interesting? Well, starting with G. H. Hardy:
Utility is another test (although not one Hardy would have agreed with>: there has been a huge body of work on how to do arithmetic on a few dozen binary digits, all because we happen to live in a time where that can be done extraordinarily quickly.
Years ago, I summed up my work as “The creation and appreciation of elegance”. Elegance is much harder to come by than truth, and I’ve found it to be far more satisfying.
BarryR,
I mean anything at all being discussed, not research attempting to be published. My point is that you pick and choose which philosophical aspects of StephenB that you’d like to see cited in peer review, but this selection of yours is arbitrary, and you don’t have a peer reviewed citation yourself that guides you in how you make these arbitrary requirements of him needing to provide a citation. It’s really just another evasion, a red herring, something to pull out of the ol box of tricks as an argument maneuver when you do not or cannot take the argument head-on.
So what if he was? It’s your opinion as to what qualifies as needing a citation in a discussion like this. I don’t see a citation that speaks for your opinion either. It’s an evasion tactic.
I can’t wait. 🙂
StephanB@235
Refutation of universals is trivial.
Or, in more words, you have a bad habit of using words like “all” when staking a claim. This tells me you’re not thinking about what you’re saying.
I have next to me Stansifer’s _The Study of Programming Languages_. I’m familiar with the chapters on Lambda calculus, denotational semantics and Hoare’s axiomatic approaches. All of these are methods of reasoning, none of these begin with an enumeration of self-evident truths.
Thus, your statement is false.
(You’ll notice this bit of reasoning also failed to begin with self-evident truths, but there’s no need to pile on.)
Hmmm…. like this?
It works for me…
CH@246
Bother, I’ve dropped another closing blockquote above…. sorry.
Certainly. Some of his mistakes are worth me correcting personally, some are worth me digging up a citation, and some should best be corrected by Stephan realizing he can’t possibly find any support for that claim.
Yes, I’ve run into people who start off conversations by demanding multiple citations. The best way to handle that is to provide them. When they see that tactic isn’t working, they stop asking.
In my case, I actually go off an read the citation I’m given, so just a handful is enough to slow me down.
Certainly. But it’s an opinion shared by many educated people. If Stephan is here to express an opinion, he’s free to disregard mine. If he’s here to change my mind (and I’m here to change his, or at least show him how to argue his point more effectively), then he can take my opinion and learn from it how I can be convinced.
Preview seems to think this is ok, here goes….
BarryR,
That quote reminds me of the Keats line from Ode on a Grecian Urn:
“Beauty is truth, truth beauty, that is all ye know on earth and all ye need to know”
BarryR,
Wow. Just wow. Do you mean Stanifer, the person who wrote on programming languages, is your answer to StephenB that there are not self evident truths? Are you a human being? Are you alive? Do you live in the universe? Do you think? All of these are self evident truths. All the way down to you using a keyboard and typing a sentence. Your thinking is so bizarre to me, you apparently think the world and all of its glorious multiplicity is reducible to programming computers. I would surely hope that a book on programming won’t mention that there is no use in living any longer; if it did, I’m afraid you’d take that to heart too.
#250
Clive I think you will find that the Stanifer example is Barry’s refutation of the statement:
“All reasoning begins with the acknowledgement of self-evident truths”
The Stanifer books includes a lot of reasoning. It does not begin with self-evident truths. QED.
This is different from the statement “There are self-evident truths”.
I am also confused by the statements that you listed as being self-evident:
Are you a human being?
Are you alive?
Do you live in the universe?
Do you think?
These are all obviously true – but self-evidently true? The examples that Stephenb has offered of self-evident truths have been general statements such as “every event has a cause”. These are statements about an individual who may or may not be alive. I would have thought that they are far from self-evident. It requires observation or experience to confirm their truth.
Onlookers:
In Bk I Ch 2 of his famous The Rhetoric {4th C BC, the first major work on the subject), Aristotle aptly summed up how arguments work:
The point is that emotions (the most persuasive appeal) may rest on an accurate judgement, but their mere intensity says nothing about the degree of warrant. Secondly, no authority — and appeal to peer review is appeal to the collective authority of the guild of scholars at a given place and time — is better than his or her facts, assumptions and reasoning.
So, in the end the only appeal that actually successfully warrants claims is the presentation of the material, credible facts, in light of reasonable assumptions [including first principles of right reason], and reasoning. This last may be deductive, inductive or abductive, and may appeal to different degrees of certainty: undeniable and/or self evident, demonstrative, probabilistic, moral certainty.
In the above, what we have been seeing is a persistent evasive refusal to engage the actual issues on the merits [e.g. the original issue on consciousness, the arguents by CSL and GKC, even to some extent the implications of 2 + 2 = 4], by playing at the game of “cite me some recent authorities.” (This, in the teeth of pointing to some serious sources, both classical and modern.)
We are now, sadly, plainly looking at a case of selective hyperskepticism.
Just remember, the same folks raising these arguments, have taken 2 + 2 = 4, and by injecting an arbitrary and contradictory redefinition of the + operator, have tried to justify the notion that axiomatic foundations and associated definitions and concepts are arbitrary, and so 2 + 2 = 4 is not a strictly true claim. You CAN set up axiomatic systems as you please, but as my 6th form math teacher pointed out long ago, if you inject contradictions, the math spits back at you: things fall apart in incoherence. Something that Wikipedia fails to underscore the significance of in the intro-summary for its article on Axioms:
Immediately, we see that this 101 view on conventional, materialism dominated views, is forced to accept the point that logic is a universal basis for reasoning. In going on to tryt to make axioms out to be in effect arbitrary defintitions, it fails to reckon withthe point that mere coherence is a powerful constraint on sets of possible axioms, and that fields of work are therefore constrained by the need for coherence and a related acknowledgement of observable mathematical facts, which may indeed be self-evident [e.g. the matchbook case on 2 + 2 = 4]. If axioms do not point to facts we observe in mathematics, we get suspicious. For good reason: proof by contradiction via reductio ad absurdum, is about reducing a suspect assertion to falsity by showing up an internal contradiction and/or a contradiction to a known mathematical fact.
But, in an era that discounts and dismisses the significance of self-evident principles of right reason, we see ever more and more unacknowledged reduction to absurdity. Wiki gets it right this time:
(And, onlookers, observe how these issues are being studiously ignored. That is not a coincidence.)
GEM of TKI
CH@250
Not unless I really screwed up the formatting. Let’s check:
Nope.
StephanB said this:
That’s trivially false. I explained why to him. I guess you didn’t read that far.
Premise: All foo are bar.
Observation: There exists one foo that is not bar.
Conclusion: The premise is false.
So far so good?
Premise: All reasoning begins with the acknowledgement of self-evident truths.
Observation: There exist at least three reasoning systems that do not rely on self-evident truth.
Conclusion: The premise is false.
In junior high school, when you said something like “All the Red Sox suck”, there should have been a geeky guy with braces and glasses pouncing on you, pointing out that one particular player on the Red Sox was having a career year and thus could not be properly said to suck, and despite the near-universal suckage of the rest of the team, the statement “All the REd Sox suck” was, strictly speaking, incorrect.
This teaches you the value of words like “some”, “most”, “several”, and “the systems of reasoning of which I am aware”.
Depends on who and when you ask. Being a caucasian landowning male in this culture, I haven’t had to worry about the effects of my ancestors being considered three-fifths of a human being. However, in Western China I’m treated very much as a monkey who talks (just not very well).
So no, being human is not self-evident.
If I was undead, how would I know? (Is that why the scary organ music keeps following me around?)
You just don’t put much thought into these exchanges, do you.
Which universe are we speaking of? The geocentric universe of the ancient Hebrews and early Christians? The heliocentric universe of the Greeks and late Christians? The early scientific cosmologies that did not extend past the Milky Way? The universe pre- or post-Hubble? Pre- or post-hubble telescope?
I’d say the universe isn’t self-evident at all.
Descartes figured out “Cogito ergo sum”, and despite several standard criticisms (you can look them up yourself, they’re in wikipedia) he’s justly famous for this.
He’s much less famous for what came after, but I’ll save that for the Lewis essay.
So yes, if you’re enumerating self-evident truths, this is probably the best place to start. It’s also probably the best place to stop.
Had I argued that no self-evident truths exist, this would be sufficient to prove me wrong. Since I’ve read Descartes, I knew enough not to make that argument (although evidently I still don’t know how to communicate my actual argument to you).
Your thinking is quite familiar to me. I used to think exactly the same way.
Education is a terrible, awful thing (in the archaic senses of those words).
You use “apparently” in a sense I’m not familiar with.
You’re having so much fun sneering at points I’m not making that I hesitate to ask you to engage with what I’ve actually written.
Eh, you’re having fun. I won’t insist.
MF:
As soon as you make a distinction of meaning by asserting a proposition to describe a true state of affairs, and then proceed to infer from it a conclusion, you are — usually implicitly [that’s where the trick is onlookers] — using the self-evident first principles of right reason, e.g. the law of non-contradiction.
For instance, above, you claim:
In so asserting claimed facts, you are asserting that certain things are so, as opposed to not being so. That a certain book “does not begin with self-evident truths” is an asserted state of affairs about the world, i.e that certain books exist, that they are by a certain author, and that they argue in a particular way that does not begin with self evident truths.
Eachof thsese is as opposed tothe denial of same, and to preserve meaning you imnplicitly assume that if a book exists it does not int he same sense not exist. If it is written by a given author, it is not simultaneously true that they are not written by the said author. If they do not begin with SET’s it is not also just as ture that hey do begin with SET’s.
All of this is a manifestation of the implicit appeal to the law of non contradiction, and leads directly to the conclusion that on the contrary the books DO begin with SET’s, starting with LNC.
Just, it is easy to overlook an implicit appeal.
That’s the trick and trap.
GEM of TKI
Stephenb
As all rational people know, truth is the correspondence of the mind to reality
It’s true if it corresponds to reality. It’s the only rational definition that has ever been offered.
The irrational folks include of Spinoza, Leibniz, G.W.F. Hegel,William James and Dewey. (You only have to go as far as Wikipedia to find that out)
I would also add Kant and Wittgenstein – but that is more debateable.
I am happy to be in this company. To be clear – I would say that a statement is sometimes true because it corresponds to some facts about the world – but other statements are not like this – a pluralist theory.
markf@255
Nice cite! I had no idea that was there.
mark:
I have rather backed out of this debate about consciousness, because frankly I am not much interested in philosophical subtleties.
But just to understand, would you agree on the statement that all logical reasoning is based on some innate rules of the mind? And that, even if you reduce those rules to the minimum (maybe it is the principle of non contradiction, or something even more basic, I leave that to logician), still some fundamental rule of reasoning, universally shared, must be the basis for all logical reasoning?
If it were not so, how could we ever distinguish (in a shared way) logical reasoning from illogical reasoning?
Another point: would you agree that “true” and “false”, at least in the most common sense, are properties of judgements?
So, even if we don’t want to state that “truth is the correspondence of the mind to reality”, which could be a bit methaphysical, would you agree that if a mental judgement (such as “this table is round”) corresponds to reality (the table is really round, and not square), then we can say that such a judgement is true?
That would be an empirical meaning of truth, while there is also a logical meaning: in a logical system, I suppose that some proposition is true if it can be logically derived from the original axioms and assumed procedures. Or not?
Then there is always the metaphysical meaning of truth, like in big questions such as “what is truth?”. But to that question, even very important persons have not given an explicit answer, and remained in silence.
I would appreciate your thoughts on those points.
GP, and Onlookers:
A very long time ago, Aristotle, in Metaphysics 1011B, observed:
Or, in a more morally tinged vein, we may cite the Sermon on the Mount:
And, the prince of the prophets had something to add to this:
In short, there is something both profound and morally significant in seeing thst the truth will say that what is, is, and it will say that what is not, is not; refusing to put light for darkness and bitter for sweet.
For, one’s yes ought to be yes, and one’s no ought to be no.
That is why we recognise the crimes of perjury, slander and libel.
Now, there are of course any number of philosophers, theologians who have proposed alternative statements [most often emphasising clarity and coherence . . . which bespeaks the unity of truth].
But what is interesting is that in so asserting their own statements and arguing for them, they consistently either imply or are dependent on this underlying very simple principle: true claims say of what is that it is, and of what is not, that it is not.
And, that holds even when the philosophers in question dispute the claim that truth is about correspondence of thought or statement or proposition with reality.
Merely listing that certain philosophers have said something diverse from the above is not enough to overturn it.
For instance, if we were to take MF’s claim above and read it as saying that he agreed with Aristotle, he would for good reason think that we have uttered falsehood: we have failed to say of what is that it is, and have instead said that what is not, is.
In short, if we were to ignore and dismiss the principle that truth says of what is that it is,and of what is not that it is not, and that were to become the general rule, verbal communication itself would collapse in a morass of confusion and deception, destroying society.
In short, such fails the test of the Categorical Imperative. Indeed, what goes beyond letting he yes be yes and the no be no, cometh of evil.
And so, to the extent that certain philosophers in recent centuries have indeed denied that truth says of what is, that it is, and of what is not, that it is not, we must therefore not flinch from saying something that is sadly true: to that extent, such have failed at the bar of the duty of truth and reason.
GEM of TKI
—mark: “The irrational folks include of Spinoza, Leibniz, G.W.F. Hegel,William James and Dewey. (You only have to go as far as Wikipedia to find that out.”
Yes, so what? With respect to truth, Hegel was totally irrational; Dewey was eminently irrational; James was monumentally irrational. Do you have anything of substance to say?
—“I am happy to be in this company. To be clear – I would say that a statement is sometimes true because it corresponds to some facts about the world – but other statements are not like this – a pluralist theory.”
Yes, I am sure that you are happy to be in their company, and I agree that you belong there, holding each of their contradictory notions of truth at the same time. I suspect, however, that you have read little of nothing of these men that you identify with. If so, perhaps you would like to argue on behalf of one of these irrational positions. Here is a clue: Popularity among the elitist academians is not a measure of rationality.
F/N: NWE — as opposed to Wikipedia — has a very helpful 101 on truth, for those trying to follow basic ideas and catch a hint of nuances. G
—BarryR: “Oh, I have read Adler. If you’re not very curious about philosophy, he may be better than nothing.”
You provide no evidence of having read a word of Adler, much less his article that I sent you to a few days ago. If you had read that small portion of Adler and comprehended it, you would likely have approached the subject matter the same way that I approached the article that you asked me to read from Edmonds. You would have, as I did, presented the argument you believe to be false, explain why it is false, and offer a better alternative. As it is, you are just going through another round of name dropping [this time with Stanifer].
#225 Gpuccio
I think you were wise to stay out of this debate. However, you are as ever polite and interested in different views so let me do my best to respond. These are quite difficult to explain so please expect false starts and hopefully minor inaccuracies in what I say. I will split this into two comments to try and prevent them becoming too long.
1) Can logic be reduced to some overriding principle and if not how do we tell what is logical?
I think not. Or rather it depends on what you mean by “reduced to”. I see logical principles as descriptive not prescriptive. I don’t think we have to justify valid reasoning by referring to some higher generality. This approach leads to an infinite regress because of any rule we can always ask the proposer of that rule to justify it. You have to stop somewhere – so why not stop at the first level – with the actual statement you are making.
Let me try to be concrete with an example. I think we all recognise that it is valid to argue something on the lines of:
(A) My father was a pilot. All pilots had an eye test. Therefore, he had an eye test.
But if someone was to challenge this line of reasoning it would add little to say it is an example of the general rule:
(B) All As are Bs. x is an A. Therefore x is a B.
It is not the fact that statement A matches rule B that makes it valid. Rather it is the other way round. I would test the validity of the general rule by seeing if it works for specific examples. We might then later on use the rule to remind us that another situation is similar to the first case. But essentially we don’t need criteria or proof of the validity of a statement like A. How we tell it is valid? By imagining the situation, by drawing Venn diagrams, by failing to produce counterexamples.
Gpuccio #225 cont.
Broadly I agree with what you wrote on truth. I prefer to talk about statements rather than judgements – but it comes to much the same thing.
Some statements simply describe some state of affairs in the world and are true if that state of affairs obtains. As you point out, other types of statement are true or false for different reasons. Mathematical statements are true if they follow from a set of explicit or implicit premisses. Logical statements if they correctly describe a type of valid inference.
As I said in #254 I guess I could be described as a pluralist – although I hate “…isms” and “…ists”.
A really important insight comes from Wittgenstein. Often a statement will be true for a combination of different types of criteria and because they always or often coincide we never have to resolve which apply. For example, an arithmetic statement such as 2+2=4 is mathematically true because it follows from the Peano axioms (I think those are the right ones). Now the Peano axioms apply very accurately to a vast range of situations so it is also true that 2+2=4 for a vast range of situations. Unless we are pure mathematicians we are never called upon to decide whether 2+2=4 is true in the mathematical or the descriptive sense. And when challenged as to what makes it true we get confused and end up making up some abstract world of which it is true!
A really powerful example of this ethical statements which are true in virtue of specific facts but also our attitude to those facts but that is a whole new can of worms.
I am sorry, I seem to have practically written a paper here – but these issues are so much subtler than people realise.
#257 Stephenb
I am sorry you found my comment lacking in substance. I hope you will find my comments in response to Gpuccio more substantial. (They do at least go beyond asserting that my theory is correct because it is self-evident or because all rational men believe it.)
—mark: “(They do at least go beyond asserting that my theory is correct because it is self-evident or because all rational men believe it.)”
No, they don’t even go that far. They simply appeal to big names and ask us to believe their doctrines on the grounds that they are famous and, one gathers, smart.
Since each of these smart men posited contradictory notions of truth, and given the fact that you identify with all of them, contradictions and all [“I am happy to be in this company”] I can’t imagine why you would think that your comments were substantive.
#263
I think there is a misunderstanding I was referring to my comments in response to Gpuccio i.e. #261 and #262. The only names mentioned in those comments are Wittgenstein and yours!
Yours – ever trying to be friendly – Mark
—markf: “I think there is a misunderstanding I was referring to my comments in response to Gpuccio i.e. #261 and #262. The only names mentioned in those comments are Wittgenstein and yours!”
I was responding to your comments @254, at which time you listed five authors [later two more] and implied, wrongly, that I didn’t know much about their philosophy, ending with this snippy comment: “you only have to go as far as Wikipedia to find that out.”
To that remark, I responded with a call for less name dropping and more substance.
It was @262 that you made this comment: “I hope you will find my comments in response to Gpuccio more substantial.
So, your recounting of the history is a bit off the mark.
—“Yours – ever trying to be friendly – Mark”
I am always ready to establish and maintain a friendly relationship. I need the practice. [Insert smiley face].
#265 Stephenb
The misunderstandings seem only to get deeper. I wasn’t trying recount any history (I did get a comment number wrong which may be the cause of the confusion). All I intended to say was – look at comments #260 and #261 – you may find them more substantial than #254 (and more substantial than simpy declaring something to be self-evident or rational)
BarryR,
I don’t know why I bother responding to your posts, I find them awful, in the new sense of the word. You change the subject often or intentionally evade the real crux of the subject. All reasoning does rely on self evident truths, fundamentals, what we call first principles. You get rid of these, and you won’t even recognize whether anything else can or cannot “reason.” It would be like taking out your eyes to look at them—it’s impossible. Your thinking is very familiar and bizarre to me, one that needs the treatment of Lewis and Chesterton, which is why you had to defer to your talk.origins buddies to find an argument that wasn’t an ad hominem against the men themselves.
Why?
A few notes on citations, courtesy of Burkhard at talk.origins:
These and other comments may be found in the thread “Citation on citation”.
CH@269
In reverse order:
Because beyond that point Descartes’ argument fell apart, and while a lot of ink has been spilled on the question (including the redoubtable Dr. Adler), nobody has been able to improve on it.
This is exactly the problem Lewis is trying to solve in De Futillitate. He telegraphs it with the phrase “We are always prevented from accepting total skepticism because it can be formulated only by making a tacit exception in favor of the thought we are thinking…”.
This is trivially false, and to me it meas that he either never read Descartes or (more likely) didn’t read deeply. The counterexample that refutes Lewis is “I am skeptical of everything, including the correctness of my own skepticism.” Descartes’ formulation was much stronger: “Cogito ergo sum”.
To move from this point to some certain knowledge of the world, Descartes is forced to postulate a very specific God. While not compelling, it does have the virtue of clarity.
Lewis is far less clear and even less convincing:
1. All knowledge depends on inference.
2. If inference is false, we can know nothing.
3. We know something (his version of “cogito”.
4. Thus inference is true.
To see how this falls apart, let’s substitute “evolution” for “inference”.
1. All knowledge depends on evolution.
2. If evolution is false, we can know nothing.
3. We know something.
4. Thus evolution is true.
You might be motivated to point out that starting with “all knowledge depends on evolution” assumes evolution is true. Likewise, starting with “all knowledge depends on inference” is a statement that can only be reached if inference is true. Once you’ve assumed inference is true, it’s pretty trivial to prove inference is true.
There’s also the small problem that inference has been proved for this single case, not as a general proposition.
I conclude this argument was never presented to an undergraduate philosophy class in the philosophy department. They would have shredded it.
(Anyone know if Lewis ever read Descartes?)
You can use evolutionary epistemology to do an end-run around this problem if you’re willing to give up binary certainty in exchange for a continuum of certainty, but I’ll save that for another time.
The Stanford Encyclopedia of Philosophy has a dense article on Descartes’ epistemology as well as a much more readable article on evolutionary epistemology.
CH@269
Continuing…
Well, I’m certainly willing to be convinced, but all the examples that have been given to me so far (with the exception of the cogito) doesn’t appear to be both self-evident and universal.
But your making an even stronger claim than “self-evident truth exists”. You’re claiming that every reasoning system, no matter how obscure, must use these truths.
Yet when I look at lambda calculus, I see nothing self-evident there.
So let’s say I have an unfortunate brain injury that causes me to be unable to understand the cogito. In fact, this brain injury prevents me from understanding any self-evident truth (although I can perceive them if I can derive them otherwise).
Someone gives me a copy of Stansifer (or I’m pretty sure they did — I could be dreaming) and as I’m working through chapter 7, I use only the material in that chapter, what I’ve derived, and a few self-evident “highly-likelies” (not truths) to reason that lambda calculus can be used to derive the integers. I don’t have absolute certainty that my derivation is correct, but I’ve checked it twice and have a high degree of confidence.
Why is the above impossible? Please be specific.
StephanB@261
Why would any be required beyond the statement that I’ve done so?
The essay was later enlarged into the book “Ten Philosophical Mistakes”, which I read (the 1985 edition) before leaving high school. The memory I have of it, though, was discussing the text with a faculty member of the philosophy department a couple of years later. Its reception among people who did philosophy for a living ranged from disappointed to cringeworthy. As I continued to take philosophy classes I started understanding why.
As I said, if you don’t have any great interest in philosophy, the book might be better than nothing. To the good, it does go over several issues of concern to philosophers. To the bad, philosophers Adler doesn’t agree with come across as making dimwitted mistakes that Adler can explain in just a few paragraphs. These aren’t mistakes, and Adler does a disservice to the discipline by representing them as such.
As you did read the paper I suggested, I glanced at the essay you suggested. Here’s his example of a self-evident truth:
By the time he gets to the end, I’ve been talked out of the idea that this concept is self-evident and instead believe that it follows from the definition of the word “whole”. Is that a mistake? Perhaps, or perhaps it’s just sloppy writing.
To make the error more clear: I describe an object. Is it a whole? How do you know? Well, if its parts were summed and did not result in the whole, then we probably wouldn’t call it a whole in the first place. Do the set of integers form a whole? Does the empty set? The computer I’m using is certainly a whole, and certainly has a number of parts, yet I’d argue that the whole is certainly far greater than the sum of those parts.
So that’s Adler.
(I’m now wondering why you’ve haven’t read him. The “sum of parts” example was quite early on, and far stronger than what you’ve come up with on your own. I’m not encouraging you to read himi, mind — I just find it curious that there’s no, as you say, “evidence” that you’ve read him, and some evidence against.)
Onlookers:
if you want a 101 level look at how first principles of right reason are foundational to reasoning, look at the WCTs here.
Remember, we have already seen how rejecting the law of non-contradiction allowed some above to try to reject the self-evident truth that 2 + 2 = 4. This was done by arbitrarily injecting a contradiction in the definition of the + operator, sot hat one thing did not mean one thing in one context.
That error of descent into self-contradictory absurdity should serve us as a warning of the penalty to be paid for dismissing first principles of right reason that are self-evidently true.
GEM of TKI
PS: Newbie onlookers, Cf above for some of what MF — as usual — refuses to address on the merits.
F/N: The self-evidently true mathematical fact that 2 + 2 = 4 is conceptually prior to Peano’s axioms, which serve more as an explanatory construct than as a foundation for arithmetic. We may then indeed go on to infer interesting theories about arithmetic on said axioms, but had the axioms entailed that 2 + 2 does not equal 4, then they would have been rejected as fatally flawed.
BarryR,
I don’t see how this refutes Lewis’s claim that ““We are always prevented from accepting total skepticism because it can be formulated only by making a tacit exception in favor of the thought we are thinking…”. I see your statement ““I am skeptical of everything, including the correctness of my own skepticism.” as one more removed, that you’re not skeptical of the skepticism of the correctness of your skepticism. You cannot be assured in your skepticism of skepticism without making a contradiction. No matter how many time you may remove the assured-ness behind layers of skepticism, in the end you’re not skeptical of at least one thing. This doesn’t, of course, refute Lewis.
Your argument by substituting evolution for inference never even leaves the ground, because we already know evolution is false :). We cannot say that inference is false in every sense and in every case without contradicting ourselves. It doesn’t matter how trivial it is to point out that inference is true, it is true, and to say otherwise is, as I said, a contradiction. And yes, Lewis mentions Descartes, I’ll have to look up where, but I do remember coming across it. I don’t think you’ve read very deeply Barry. As I said before, Lewis read in 7 different languages, so from everything from Plato to Ptolemy, Dante to Dryden, Aristotle to Aquinas, he read in the original language. Lewis wrote the textbook on 16th Century English literature for Oxford’s English literature series, he had a chair invented for him at Cambridge. You should read his book Studies in Words, and The Discarded Image (which deals with the origination of the scientific method and the mental atmosphere of the medieval and renaissance time period), and Studies in Medieval and Renaissance Literature, and The Allegory of Love, before you would presume to know his reading background.
BarryR,
The years intervening were devoted to what Sayer calls the “immense amount of reading” that Lewis did because (unlike many reviewers) he “refused to give an opinion on a book he had not read.”6 Gene Edward Veith reports that when Charles Huttar was working in the Magdalen College library he saw the register of books Lewis had checked out during the late 1940’s and early 1950’s. It appears that Lewis had “essentially checked out the entire sixteenth-century collection.”7 What was too obscure for either Magdalen or his own personal library to have, he read in the Bodleian’s magnificent Duke Humphrey library—basically what an American library would call its rare book room. Some of it must have been dull going, but he plowed ahead until he had mastered the entire preserved literary output of the century. At the end of some of the books from his own library he marked the date on which he had finished them, and in a few, the added annotation “Never again.”
This is an excerpt of an essay that is a draft of an article for Lion and Logos: The Life and Legacy of C. S. Lewis, ed. Bruce L. Edwards, Jr., 4 vols. (Greenwood/Praeger, 2007)
Onlookers (and MF . . . ):
“Self-evidence” is not a mere arbitrary and subjective declaration rooted in a perception.
(That mistaken notion, itself already shows what C S Lewis so aptly called the poison of subjectivism at work.)
Instead, it is a claim, that, once a particular claim is truly understood, it is at once plain that its denial will directly lead to reductio ad absurdum.
In the case of 2 + 2 = 4, it is plain by simple observation that this is indeed a self-evident claim. And, duly, the attempt to substitute unannounced a new “definition” of + that makes 2 + 2 = 147 instead or something else, immediately lands in hopeless contradictions.
Lesson: one may not blithely disregard the principle of non-contradiction in reasoning, including elementary mathematical reasoning.
And, those who do and then try to stoutly “dance wrong but strong” simply show ever more and more, how absurd the position of rejecting LNC is.
Sad . . .
GEM of TKI
kairosfocus,
Great point, and that is a great essay.
F/N: The live donkey kicking a dead lion ad hominem game above is just a little distateful. Why not summarise CSL’s arguments, then actually show why — on the merits — you think they fail?
(And for instance, CH has brought out the infinite regress implicit in any absolute assertion of skepticism. Practical skepticism is necessarily selective, and when that goes over into an inconsistent standard of warrant for what one wishes to accept vs reject, it then becomes self-refuting. The declaration of universal skepticism is inevitably self-referentially absurd.)
—BarryR: “As I said, if you don’t have any great interest in philosophy, the book might be better than nothing.”
I am formally trained in philosophy at the graduate level, and I am also formally trained in applied communication at the graduate level, and yes, I did graduate with the highest honors. So, your implied ad hominem [that I have no interest in philosophy] simply falls flat. I don’t normally wield my credentials around here because I think it is bad form. You will notice, for example, that I exposed Edmond’s ignorance of syllogisms and I explained the texture of his error without alluding to my own training in logic. (So tacky would that be) If you want to discuss his logical errors in greater detail, let me know.
The problem with your earlier readings of Adler, and thank you for sharing your experiences, is that you were not given very good guidance from your philosophy professors, which is quite common. Philosophy has been bitten with the postmodernist bug along with most other disciplines. Where, though, is the substance in your comments. What mistake is it that Adler alludes to that you claim is not a mistake? On this, the really important matter, you remain silent.
—“To make the error more clear:[Adler’s essay, “Little Errors in the Beginning] I describe an object. Is it a whole? How do you know? Well, if its parts were summed and did not result in the whole, then we probably wouldn’t call it a whole in the first place. Do the set of integers form a whole? Does the empty set? The computer I’m using is certainly a whole, and certainly has a number of parts, yet I’d argue that the whole is certainly far greater than the sum of those parts>”
There is no error here at all. [A] Adler is providing an example of a self-evident truth and explaining that self-evident truths comprise an important element in our pursuit of knowledge, arguing rightly, that analytic reasoning and synthetic reasoning are not our only mental tools. Notice how you completely ignore the main point of the argument.
[B] If the whole is greater than any one of the parts, and if no one part can be greater than the whole, this fact ALONE, does not preclude the possibility that the whole could be greater than the sum of all the parts. In only rules out the possibility that one part cannot be greater than the whole. Thus, your final comment is irrelevant and reflects a lack of understanding of the obvious self evident truth. A part cannot be greater than the whole of which it is a part. Everyone understands this as a self evident truth, and that includes you, in spite of your protests.
—“By the time he gets to the end, I’ve been talked out of the idea that this concept is self-evident and instead believe that it follows from the definition of the word “whole”. Is that a mistake?”
It is not a mistake on his part. He has already pointed out that the concepts themselves cannot be defined. It is the relationship between the two that must be understood as a self evident truth independent of any definitions at all.
—“Perhaps, or perhaps it’s just sloppy writing.
No, just inattentive reading. Ask yourself the only real question that matters. Can a part of a whole [of which it is a part] be greater than the whole? You already know, as a self evident truth, that it cannot. On the other hand, you refuse to admit it because your entire materialist/secularist/hyperskepticiirrational framework crumbles with the admission.
As Adler puts it, “We cannot express our understanding of parts without reference to our understanding of wholes and our understanding that a part is less than the whole of which it is a part.”
Again, I stress the significance of this point. Once it is understood that self evident truths exist, Kant’s anti-metphysical skepticism (which was corrected by Reid in his own time) and Hegel’s attempt to correct a problem that didn’t exist, followed by each additional anti-intellectual domino toppling over for the next two hundred years all hearken back to the “Little Error in the Beginning.”
SB:
Excellent.
I only note that I tend to make it a little more specific: a finite whole is greater than any of its proper parts.
Maybe, there is need to cite the key section in Adler in-thread:
____________________
>> The little error in the beginning, made by Locke and Leibniz, perpetuated by Kant, and leading to the repudiation of any non-verbal or non-tautological truth having incorrigible certitude, consists in starting with a dichotomy instead of a trichotomy — a twofold instead of a threefold distinction of types of truth. In addition to merely verbal statements which, as tautologies, are uninstructive and need no support beyond the rules of language, and in addition to instructive statements which need support and certification, either from experience or by reasoning, there is a third class of statements which are non-tautological or instructive, on the one hand, and are also indemonstrable or self-evidently true, on the other. These are the statements that Euclid called “common notions,” that Aristotle called “axioms” or “first principles,” and that mediaeval thinkers called “propositions per se nota.”
One example will suffice to make this clear — the axiom or selfevident truth that a finite whole is greater than any of its parts. This proposition states our understanding of the relation between a finite whole and its parts. It is not a statement about the word “whole” or the word “part” but rather about our understanding of wholes and parts and their relation. All of the operative terms in the proposition are indefinable. We cannot express our understanding of a whole without reference to our understanding of its parts and our understanding that it is greater than any of its parts. We cannot express our understanding of parts without reference to our understanding of wholes and our understanding that a part is less than the whole of which it is a part.
When our understanding of an object that is indefinable (e.g., a whole) involves our understanding of another object that is indefinable (e.g., a part), and of the relation between them, that understanding is expressed in a self-evident proposition which is not trifling, uninstructive, or analytic, in Locke’s sense or Kant’s, for no definitions are involved. Nor is it a synthetic a priori judgment in Kant’s sense, even though it has incorrigible certitude; and it is certainly not synthetic a posteriori since, being intrinsically indemonstrable, it cannot be supported by statements offering empirical evidence or reasons.
The contemporary denial that there are any indisputable statements which are not merely verbal or tautological, together with the contemporary assertion that all non-tautological statements require extrinsic support or certification and that none has incorrigible certitude, is therefore falsified by the existence of a third type of statement, exemplified by the axiom or self-evident truth that a finite whole is greater than any of its parts, or that a part is less than the finite whole to which it belongs. It could as readily be exemplified by the self-evident truth that the good is the desirable, or that the desirable is the good — a statement that is known to be true entirely from an understanding of its terms, both of which are indefinables. One cannot say what the good is except by reference to desire, or what desire is except by reference to the good. The understanding of either involves the understanding of the other, and the understanding of both, each in relation to the other, is expressed in a proposition per se nota, i.e., self-evident or known to be true as soon as its terms are understood.
Such propositions are neither analytic nor synthetic in the modern sense of that dichotomy; for the predicate is neither contained in the definition of the subject, nor does it lie entirely outside the meaning of the subject. Axioms or self-evident truths are, furthermore, truths about objects understood, objects that can have instantiation in reality, and so they are not merely verbal. They are not a priori because they are based on experience, as all our knowledge and understanding is; yet they are not empirical or a posteriori in the sense that they can be falsified by experience or require empirical investigation for their confirmation. The little error in the beginning, which consists in a non-exhaustive dichotomy mistakenly regarded as exhaustive, is corrected when we substitute for it a trichotomy that distinguishes (i) merely verbal tautologies, (ii) statements of fact that require empirical support and can be empirically falsified, (iii) axiomatic statements, expressing indemonstrable truths of understanding which, while based upon experience, do not require empirical support and cannot be empirically falsified.[6] >>
____________________
G
#282
“The whole is greater than the sum of its parts”
This seems to me far from self-evident and very likely false, depending on what exactly it means. Greater in what respect? If we add matter to other matter the result may actually weigh less (that’s one thing that happens in a nuclear reaction). I believe that under extreme conditions it is also possible that the result may take less volume – the additional matter causes the mass to collapse under the additional gravitional pull. In any case it is certainly imaginable that the result would take less volume.
KF,
I must admit that I have to disagree with both examples you listed above of instructive yet tautological statements.
While I agree with your assertion that such statements which can be both tautological and instructive can and probably do exist I see both of your examples as being totally flawed.
Firstly to say that a whole must be greater than the sum of its parts is to make a statement which is not tautologically certain. If there was a substance which was composed of only one part which was objectively indivisible (such as God- or what the Atom was believed to be before its interior was elucidated) then in this case the sum of its part would be equal to whole- which negates the notion of the original statement- because it would still be true to say that the whole has at least some (one) parts.
If however you admit that your statement does in fact presume that at least 2 parts must exist for it to be true- there are in fact examples in cosmology and non-euclidean geometry where the parts of an object could be greater than the whole which they comprise- though I admit my understanding is that these presupposed phenomena are purely speculative.
However, the second example is totally false on its face as many people desire things which are not good. I surmise you are using a definition of “desire” which is loaded as meaning all but the same thing as “good”- or a definition of good which somehow implies that which is desireable- but in that case the value of the example is really not that instructive at all. A value of a desire is independent of object. Certainly in theology (which many people myself included see as the highest form of understanding) there exists desires which are not good but in fact its opposite- evil.
However, we probably agree on the principle which your examples are directed at.
^Pardon me- a correction above-
“The value of a desire is independent of ITS object”
–DOUBLE correction above.. please remove post 286 if possible.
What I meant is:
“The value of a desire is DEPENDENT on its object.”
That is, a desire is ONLY good if its object is warrented.
Pardon the double mistake above.
—Markf:“The whole is greater than the sum of its parts”
—“This seems to me far from self-evident and very likely false, depending on what exactly it means.”
Of course it is far from self evident and, of course, it may well be false. The self evident truth is NOT that the whole is greater than the sum of its parts. [That’s BarryR’s gig. Didn’t you read the comment that I was responding to?]
The self evident truth is that the finite whole is greater than any one of its parts. Please read for context.
Frosty:
Hi mon. I am citing actually, Adler.
But, he is right.
He is talking about — note the context — complex entities and saying that once something is made of or has parts in it, the whole is more than any one of the individual parts; and that parts and wholes can only be understood on our experience of such complex entities and their complementarity. Of course, if you take him out of the context of complex unities, you may will THINK you have a counter-example, but you don’t.
As to the others, we are dealing with people who tried to deny that 2 + 2 = 4 is something that you can deny without tying yourself up in absurdities. To do so, they argued above that by changing he definition of + in midstream, we could also argue that 2 + 2 = 147.
EEP!
The absurdity here is injecting an equivocation that embeds a contradiction.
G
—Frost: “Firstly to say that a whole must be greater than the sum of its parts is to make a statement which is not tautologically certain.”
I don’t understand why this continues to be misread. The self-evident truth is that the finite whole is greater than ANY ONE OF IS PARTS.
PS: You will see how I modified the sort of remark Adler made: a FINITE whole is greater than any of its PROPER parts.
Steve:
You are right to spot that point.
I think many people are thinking of a common saying about systems, a reflection on synergies whereby the whole as a complex functional entitiy depends on the particular organisation of the parts.
So the systemic whole is indeed greater than the MERE sum of the parts. (A pil4e of bricks, timbers, glass and cement a house do not make, nor will one get a house by stirring all with a tornado!)
G
—kairosfocus: “I think many people are thinking of a common saying about systems, a reflection on synergies whereby the whole as a complex functional entitiy depends on the particular organisation of the parts.”
Precisely. The same phenomenon is often referred to in communication as the “assembly affect bonus” or “synergy,” especially with respect to the creative faculty inherent in “brainstorming.” Some appear to be reading that common understanding into Adler’s words rather than extracting the intended meaning.
This practice, by the way, is not unusual for postmodernist deconstructionists, who believe that readers can and should change [deconstruct] an author’s intended meaning into something more congenial with their inclinations. One self-evident truths are denied, all things are possible–or rather, deemed to be possible.
[Once] self evident truths are denied, all things are possible–or rather, deemed to be possible.
Frosty:
One last point, pardon: a self evident truth is NOT a tautology.
That is, it is not merely analytically true, simply restating the same thing in different terms.
Adler rightly points out that there are statements whose truth is contingent on observation, e.g. that I am a Caribbean, male person. others are true by the sort of reiteration just described. But others are true on our understanding based on experience, where we also see that on pain of immediate reductio ad absurdum, they MUST be true.
As you will recall, my favourite example of this is “Error exists,” following Josiah Royce. [Onlookers, try the experiment of an attempted denial and you will immediately see why it is undeniably true.]
G
Steve:
Strangely, in my own studies on organisations as sociotechnical systems, teamwork based synergies that give rise to unique competitive advantages that cannot be duplicated play a key role.
(BTW, when the environment undergoes a catastrophic, butterfly-effect type change, that can come back to haunt. Hence issues on robustness and agility as opposed to optimisation for a given environment. And this is also one reason why I do not take the notion of thinking that sub-optimal designs are inferior, seriously. If you are over specialised and the world changes, you are dead, Fred.)
Synergy is a powerful concept, and this is one way that we can get the magic of more out than was put in; thence one ground of profit making as a morally defensible activity.
But, the misreadings that you describe falls under the head of strawman fallacies; which may be inadvertent, but lead to profound misunderstanding.
Which is precisely one of the things Adler implicitly warned against; by stressing understanding rooted in our reflective experience of the world.
G
#288
I apologise for misreading the quote, but I think my argument applies equally to the statement
“the finite whole is greater than any one of its parts”
The same objections arise. What kind of whole? What kind of parts? Greater in what respect? Are we talking about physical objects and mass or volume? I believe a nuclear reaction could mean that the whole had a mass less than any of the contributing components. Even if that is not possible it is not obviously absurd. Similarly for volume.
Or perhaps the whole is not a physical object but say a sound? A combination of sounds may be less pleasant to the ear and under certain conditions less loud than any of the single elements.
—Markf: “The same objections arise.
So, it isn’t clear to you that an automobile is greater than its crankcase, and that the automobile’s crankcase cannot be greater than the automobile?”
—“I believe a nuclear reaction could mean that the whole had a mass less than any of the contributing components.”
You are confusing a process with an entity or thing.
—“Or perhaps the whole is not a physical object but say a sound? A combination of sounds may be less pleasant to the ear and under certain conditions less loud than any of the single elements.”
First you describe the sound as a whole and then try to apply it as parts of a larger whole.
StephanB@282
My, but that was worded carefully.
I’m not quite sure what you meant to communicate, but what came across was:
1. No undergraduate philosophy classes,
2. No graduate philosophy classes, and
3. No graduate degree.
In the interests of unambiguous communication, by classes I mean seat-of-the-pants-applied-to-the-seat-of-the-chair in an accredited university within a philosophy department.
If you meant to communicate something else, please clarify if you think it’s important.
One of the many nice things about expertise is that it allows you to judge competence using criteria other than credentials. You’re not making a competent argument, regardless of your credentials (and regardless of whether or not I agree with you). You don’t qualify your statements, you don’t handle counterexamples, you don’t cite the literature, and you’re not learning from your mistakes as they’re pointed out. These are the kinds of things that students learn in the give-and-take of university philosophy classes.
Perhaps you had a run of back luck and only experienced classes where this give and take wasn’t encouraged. If so, you’ve been very ill-served by your “training”.
MarkF in 297 has the good sense to ask what you (and Adler) mean by a whole and a part. The fact that he has to ask is an excellent indication that the definitions are not self-evident.
Your rejoinders are frankly childish.
StephanB
I’d much prefer to formalize this conversation; no doubt I’m going to have some difficulty keeping up, but I promise to do my best.
Just so I know we’re on the same page, could I trouble you to solve this problem?
Give the following in standard form:
(Ex)(Ay)(Az)(Eu)(Av)(Ew)P(x,y,z,u,v,w)
This is given as an example in the textbook I used for my first logic class. It’s perfectly straightforward with the answer given after a short paragraph of discussion.
Given your training in philosophy, I expect this will be trivial for you. But it will assure me you didn’t google the answer.
With that bit of administrivia out of the way, I’d like you to propose a solution to Edmonds’s proof given in section 4 that does not rely on assuming the existence of universal truth. Please use formal notation.
I look forward to your reply.
CH
I posed a direct question, and if you would answer it I think it would help me to understand your point of view.
Please search the above for:
“Why is the above impossible? Please be specific.”
Thanks.
#298
So, it isn’t clear to you that an automobile is greater than its crankcase, and that the automobile’s crankcase cannot be greater than the automobile?”
By “greater than” do you mean “larger than”? The purpose of automobiles is such that I couldn’t see how to make a working automobile that did not have some parts extraneous to the crankshaft – but I thought this was a necessary truth that applied to all “wholes”. There are plenty of physical objects where one part is the outer casing and thus the size of that part is the same as the size of the object. The system unit on my PC for example. If you allow imaginary objects (after all we talking necessary truths which should be true in all conceivable universes) consider the Tardis in Doctor Who – open the door and inside it is full of components much larger than police box which contains them.
—”I believe a nuclear reaction could mean that the whole had a mass less than any of the contributing components.”
You are confusing a process with an entity or thing.
—”Or perhaps the whole is not a physical object but say a sound? A combination of sounds may be less pleasant to the ear and under certain conditions less loud than any of the single elements.”
First you describe the sound as a whole and then try to apply it as parts of a larger whole.
I am confused as to what is meant by “whole” , “part” and “greater than”. They are such vague generic words. So I am throwing out some examples to check my understanding. I can’t say I am much the wiser yet.
All this is to establish the existence of self-evident truths that are not true by definition. Perhaps you could propose a clearer example?
MarkF (and onlookers):
RE: . . . All this is to establish the existence of self-evident truths that are not true by definition. Perhaps you could propose a clearer example?
First, there has been a very simple case all along in this thread, on matchsticks and symbolisations of what is going on with cardinalities:
Second, for many months, you have known or should have known of the simple but potent — indeed, pivotal — case of an undeniably true and self-evident claim from Josiah Royce, that I have repeatedly linked or cited [cf 6 – 7 here, and the following discussion here:
This last is obviously not a tautology, nor a definition, and you cannot define the underlying concepts in isolation. It is undeniably true as to try a denial exemplifies its truth. And it immediately implies that truth exists, warranted credible truth — i.e. knowledge exists — and that we would be wise to have a humble epistemic stance.
[ . . . ]
Third, on looking at your remarks just above, especially the crank-case example: pardon, but I must shake my head.
A crank case is a proper part of an engine, and it is indeed less than the whole: a crank case by itself is nowhere near an engine.
The case for an item of lab equipment will again be less than the whole, i.e the “guts” have to be added to get the whole. That is in both cases you have ignored the part-whole context and have in fact descended into precisely the sort of obvious absurdity that rejecting a self-evident truth will immediately precipitate.
And so, the part-whole, less than- greater than distinctions make sense once one recognises that they are going to be generic because of that generality, and will have to be be fleshed out in various particular ways in particular cases, once one accepts that one is dealing with composite wholes. (Such experience is abundantly accessible for anyone with significant experience of a world that is full of composite wholes, starting with the letters, words, sentences and paragraphs used to make posts here.)
So, sadly, the above objections come across as utterly strained and driven by what you wish to reject rather than by any truly substantial point. By selective hyperskepticism, in short. And, they land you in precisely the sort of absurdities that such an incoherent rhetorical pattern leads to.
I must therefore ask: have you seriously tried to understand instead of to object on any and every convenient excuse? [Do you not realise that Mortimer Adler was not exactly a philosophical novice who would make elementary mistakes?]
I know your usual claim is that you refuse to look at what I write (which comes across more and more as a convenient evasion), but this one went utterly beyond the pale.
You need to revise your “policy” — which rather sounds like Wilson’s cynical advice to evade inconvenient points, in his Arte of Rhetorique — and you need to stop and re-examine what you have said many times above in this thread [starting with on 2 + 2 = 4], and what it is pointing to.
GEM of TKI
—markf: “I am confused as to what is meant by “whole” , “part” and “greater than”.
From the dictionary:
Whole
1. comprising the full quantity, amount, extent, number, etc., without diminution or exception; entire, full, or total: He ate the whole pie. They ran the whole distance.
2. containing all the elements properly belonging; complete: We have a whole set of antique china.
Part
1. A portion, division, piece, or segment of a whole.
2. Any of several equal portions or fractions that can constitute a whole or into which a whole can be divided: a mixture of two parts flour to one part sugar.
—“All this is to establish the existence of self-evident truths that are not true by definition. Perhaps you could propose a clearer example?”
If you don’t understand that an automobile is more than its crankcase, or its axles, or its frame, or its wheels, or its engine etc, I don’t think I can help you.
—“There are plenty of physical objects where one part is the outer casing and thus the size of that part is the same as the size of the object. The system unit on my PC for example.”
If you don’t understand that there is more to your computer than its system unit, I don’t think I can help you.
StephanB@305
If you need a dictionary to explain a concept, I think that’s a pretty strong hint that it’s not a universal self-evident truth.
#302 Stephenb
Of course I understand the meaning of the English words “whole” and “part”. I am trying to understand what they mean in this context. They are very broad words that can be used all sorts of ways and this is a most unusual statement. Does the statement apply to anything which can have components of any kind? e.g. musical chords, poems, business processes, supernovae?
You don’t clarify what is meant by “greater than” – although I think the sentence:
If you don’t understand that an automobile is more than its crankcase, or its axles, or its frame, or its wheels, or its engine etc, I don’t think I can help you.
is meant to throw some light on this. I do understand that an automobile comprises many components in addition to a crankshaft. If by “greater than” you simply mean “comprises more than” then “X is greater than one of its parts” simply follows from the definition of “part”.
Normally if you say X is greater than Y there is some implicit or explicit dimension in which it is greater – mass, volume, artistic merit, decibels whatever. But the dimension is not clear to me in this case.
In the example of the system unit I was treating the system unit as the whole and trying to point out that it was no larger than its case which is one of its parts (others being things such as motherboard). I should have made myself clearer.
But why not choose a different, clearer, example of a self-evident truth?
BarryR,
Are there no universal truths? Is that statement itself universal and true? Please answer me directly, with a yes or a no, and explain how it isn’t (if you claim it’s not), and explain how your affirmation or negation is not itself a universal truth if there are no universal truths.
BarryR,
My point of view is in my last comment to you, articulated by pointing out your confusion pertaining to skepticism and how you think it can be absolute and yet not. I noticed that you haven’t responded to Chesterton, and your response to Lewis was short (but thank you for responding nevertheless), but answered by me, and I’ve yet to see any more response.
BarryR,
Why? No truth can be written down? Because things are self evident doesn’t mean that everyone realizes them just yet, just as counting numbers up to twenty aren’t always realized by tribes people, that doesn’t mean they are nothing.
CH@308
The direct answer to the question: “Are there no universal truths? Is that statement itself universal and true.?”
For the fourth time, I think.
“We don’t know any universal truths” is simply an observation.
“We can’t know any universal truths” is an epistemic argument that can be made from observations.
I see nothing controversial with either statement.
“There are no universal truths” is an ontological statement that, as Edmonds discusses, requires assuming universal truth exist in order to prove. (He makes this argument using formal notation; if you disagree, please point out which step you disagree with.)
I don’t see where that statement can be justified.
Likewise, “There are universal truths” also requires assuming universal truths exist in order to prove that it’s the case.
I don’t find this justified either.
(The universal and existential qualifiers in logic are usually limited to a well-defined context, and as such are perfectly fine. The trouble comes in when trying to map that system onto a poorly-defined concept like “everything”.)
Onlookers:
Observe again, how MF, with his attention already drawn to an example he has been corrected on above [2 + 2 = 4], and one he has ignored for months [“error exists”], proceeds — predictably — to ignore inconvenient evidence yet again.
In addition, he now wishes to belabour the concepts whole-part and greater-lesser, as though he has no experience of whole-part relationships (which BTW play a very important role in information systems, e.g. the structure of a program).
The precise ways in which parts and wholes interact or relate differ from one case to the other, but there is a common conceptual core that we may legitimately extract and address: the part-whole relationship, and the part is always a component, making it less than the complex whole. In turn, that complex whole is made up from the parts, their specific organisation/ relationships, and the interactions that are associated with that organisation.
One feature of such is of course that we come to understand that a part is a component of a whole. Consequently, the whole not only is, but must be, more than the part. On pain of absurdity; which may of course be disguised by the claim that one does not understand. (But if you have worked with software systems as a career, as MF acknowledges, then such a plea looks very suspiciously evasive indeed.)
In the case of a star undergoing supernova [cf section a esp point 17 on here], the Iron core that forms and stops fusion from releasing further energy (as Fe is at the peak of the binding energy per nucleon curve), and the imploding and bouncing envelope (for want of radiation pressure etc to keep it from imploding) are both parts, and the star is a whole. In the case of a sentence or a poem, the letter is a part and the composition is a whole. In the case of say a 4G63 Mitsubishi automobile engine, the pistons, the engine blocks, and the crank case are parts.
And so on.
Reductio ad absurdum, right before our eyes.
If this were not so saddening, it would be funny.
GEM of TKI
—Markf: “You don’t clarify what is meant by “greater than”
Although I provided dictionary definitions of the words “part” and “whole,” the terms [insofar as they refer to the self-evident nature of the fact] cannot be defined.
From Adler:
“One example will suffice to make this clear — the axiom or selfevident truth that a finite whole is greater than any of its parts. This proposition states our understanding of the relation between a finite whole and its parts. It is not a statement about the word “whole” or the word “part” but rather about our understanding of wholes and parts and their relation. All of the operative terms in the proposition are indefinable. We cannot express our understanding of a whole without reference to our understanding of its parts and our understanding that it is greater than any of its parts. We cannot express our understanding of parts without reference to our understanding of wholes and our understanding that a part is less than the whole of which it is a part.
When our understanding of an object that is indefinable (e.g., a whole) involves our understanding of another object that is indefinable (e.g., a part), and of the relation between them, that understanding is expressed in a self-evident proposition which is not trifling, uninstructive, or analytic, in Locke’s sense or Kant’s, for no definitions are involved. Nor is it a synthetic a priori judgment in Kant’s sense, even though it has incorrigible certitude; and it is certainly not synthetic a posteriori since, being intrinsically indemonstrable, it cannot be supported by statements offering empirical evidence or reasons.
The contemporary denial that there are any indisputable statements which are not merely verbal or tautological, together with the contemporary assertion that all non-tautological statements require extrinsic support or certification and that none has incorrigible certitude, is therefore falsified by the existence of a third type of statement, exemplified by the axiom or self-evident truth that a finite whole is greater than any of its parts, or that a part is less than the finite whole to which it belongs. It could as readily be exemplified by the self-evident truth that the good is the desirable, or that the desirable is the good — a statement that is known to be true entirely from an understanding of its terms, both of which are indefinables. One cannot say what the good is except by reference to desire, or what desire is except by reference to the good. The understanding of either involves the understanding of the other, and the understanding of both, each in relation to the other, is expressed in a proposition per se nota, i.e., self-evident or known to be true as soon as its terms are understood.”
Thus, you understand as a self evident truth, that any finite whole is greater than any one of its parts–just as you understood that an automobile is greater than its crankcase. In this case, greater means more parts, greater volume, weight etc. In other cases, it could mean more of something else. Thus, the word “greater” cannot be defined the way you are asking except to say that there is “more to” the whole than any one of its parts. To the question more “what,” the answer depends on which “whole” is in question. A paragraph may not weigh more than one of its sentences, but it contains more words.
markf
“But why not choose a different, clearer, example of a self-evident truth?”
It appears you completely ignored KFs responses at 300 and 301.
Why are you trying to make this more complicated than it is? I think KF and StephenB have been quite clear on the issue of “a whole is greater than any of its parts.”
Your feigned incomprehension of this (causing KF to shake his head) is nothing short of absurd. However, your evasive maneuvers are quite entertaining at times. Of course I am often amused by bizarre things, like this:
“There are plenty of physical objects where one part is the outer casing and thus the size of that part is the same as the size of the object.”
In that you have created a miracle. Let’s see, the outer body of a car is pretty much the same size as the car itself, so it must be equal to the car. Right?
The miracle is that we can now drive around in the bodies of our cars without the engine and few other important parts like whieels and such. Right?
The body is not equal to the whole car. The body is a part of the whole. The whole is greater than the parts.
The outer casing of a computer is not equal to the computer itself. The whole is greater than the parts.
A banana peel is not equal to a banana. The whole is greater than the parts.
A facade is not equal to the whole building. The whole is greater than the parts.
Do you require any more examples?
CY:
Thanks.
Maybe MF will wake up now that his gambit of persistently ignoring what I have said — on the pretence that what I say is garbled, or incomprehensible or takes too long to process, etc — is plainly getting threadbare.
G
—BarryR: “If you need a dictionary to explain a concept, I think that’s a pretty strong hint that it’s not a universal self-evident truth.”
As it turns out, the terms, whole, part, and greater cannot be defined as elemts of a self evident truth–which is the whole point under discussion. However, as a tribute to those pretend not to know what I mean when I say that the “whole” of an automobile is “greater” than its crankcase, the dictionary is a handy tool for such low level responses.
CY @13, you would have been entertained by a recent blogger who insisted that a crankcase could, indeed, be greater than an automobile, asking us to conceive of an artist’s conception in which an automobile was situated inside a giant crankcase. I am not joking. Obviously, he missed the point about the finte whole being greater than any one of ITS parts, but it was a wild ride which featured a number of Darwinists taking up for the irrational side of the argument.
KF,
I always look forward to reading you posts, because you could not be more clear. I admit that I had trouble with your unique use of the English language when I first encountered your writing several years ago, but it’s something I’ve become accostomed to now. Your use of the best examples, references and input are quite compelling. I don’t know why anyone would not want to gain someting from your insight.
I look forward to getting to the end of this debate, however, as it’s getting tiresome.
We know of parts only in reference to wholes, and we know of wholes only in reference to parts. wholes are not equal to but are greater than the parts.
Attempts to object that this is self-evident is simply an exercise in evasion in order to maintain a relativistic outlook on truth.
What’s interesting here is that if you hold to truth as relative, you are then not committed to being truthful. You can evade, change the subject, equivocate, supplant and use all kinds of other trickery in order to avoid what is inconvenient, because your morals and values are relative to your need to please the self, rather than to make commitments to love and to serve others.
The Darwinist does not believe that truth has anything to do with morality. This is a huge mistake.
KF, others
Another observation here is that Darwinists are fond of the argument that modern medicine owes it’s development to methodological naturalism in science, and that it would not have advanced apart from it.
What they fail to understand is that modern medicine is founded upon the value of human life – that it developed because people understood that they “ought” to care for people. Methodological naturalism had nothing to do with it. If you study the history of the care and treatment of various disorders, and the institution of hospitals, nursing homes, clinics, etc., there exists a trend towards more humane treatment based on the philosophy that humans are valuable. Darwinism does not offer this kind of insight.
If we founded our values on a faulty understanding of truth; i.e., if relative truth were the only operating paradigm in this world among humans, we would not have developed an understanding that morality and values are intrinsic to certain absolutes.
In other words, it matters that there are self-evident truths in establishing that there are absolutes. Without absolutes there can be no morality, because we could not distinguish what is good from what is evil. These concepts would be meaningless.
Consciousness must therefore be something that is separate from the “is” of our physical makeup; for it is through consciousness that we distinguish what is an “ought.” Of course there are other arguments for why consciousness is of this nature.
#313
It appears you completely ignored KFs responses at 300 and 301.
I can’t read everyone’s response to everything. It is nothing personal against KF – I just think we have so little in common that there is no basis for an interesting discussion. However, you asked me to look at them so I have. I have to say paragraphs such as:
And so the part-whole, less than- greater than distinctions make sense once one recognises that they are going to be generic because of that generality, and will have to be be fleshed out in various particular ways in particular cases, once one accepts that one is dealing with composite wholes. (Such experience is abundantly accessible for anyone with significant experience of a world that is full of composite wholes, starting with the letters, words, sentences and paragraphs used to make posts here.)
confirm to me that my decision is the best for both of us.
KF does offer 2+2=4 as another example of a self-evident truth. I thought we dealt with that but this is what I said above in a response to Gpuccio – I stick by it.
A really important insight comes from Wittgenstein. Often a statement will be true for a combination of different types of criteria and because they always or often coincide we never have to resolve which apply. For example, an arithmetic statement such as 2+2=4 is mathematically true because it follows from the Peano axioms (I think those are the right ones). Now the Peano axioms apply very accurately to a vast range of situations so it is also true that 2+2=4 for a vast range of situations. Unless we are pure mathematicians we are never called upon to decide whether 2+2=4 is true in the mathematical or the descriptive sense. And when challenged as to what makes it true we get confused and end up making up some abstract world of which it is true!
StephenB,
One of my favorite movies is “The Adventures of Baron Munschausen,” in which all kinds of bizarre explanations end up being true. I also like Mel Gibson’s “Conspiracy Theory,” in which a paranoid delusion ends up being true. I was also a big fan of “The X-Files.” Chris Carter’s scepticism of conspiracy theories was what inspired the show.
Of course, these are all works of fiction, intended to poke fun at bizarre beliefs. None of them are serious. But the Darwinists making arguments here are DEAD serious; which is scary.
#312 Stephenb
Thanks for the Adler passage. I had already read it but you weren’t to know that. I think you (and Adler) are saying that the sense in which a whole is greater than its parts is indefinable. This is surprising – because in any other context I can think of the phrase “greater than” is definable. There is the rather obvious sense that a whole object like a car is comprised of one or more parts. But this follows from the definition of “part” that you give:
1. A portion, division, piece, or segment of a whole
and is just an analytic statement.
I think we have to give up on the whole and parts bit. I promise you I am not being deliberately obtuse. I really think that if you break down the loose phrase “a whole is greater than its parts” into all the things it might mean they will either be analytic or not necessarily true.
markf,
I perceive that your difficulty is that you equate our perception and explanation of truth as the truth itself. The problem is that we have to perceive and explain in order to understand truth, but the truth exists apart from our perception or explanation of it.
Therefore 2+2=4 is merely our way of quantifying a truth. The truth expressed by the equation lies outside the equation itself. This is why the argument that if you change the value and meaning of the +, you can change the truth represented by the equation. This is bizarre. It’s like saying that if I multiply the figure representing the balance of my bank account by two, this increases the amount of money I have in my bank account (I think this example has been used before).
The self evident truth that the whole is greater than the parts lies outside the physical examples we use – such as crank shafts and automobiles; however it applies to them, in the same way that two apples added to two apples gives us 4 apples. It’s true that our perception and quantifying representations of truth are limited, but our inadequacies in this regard do not affect the truth itself. 2+2=4 represents an abstract that is true. That abstract is applied to physicality, demonstrating that it is true. However, we don’t require the physicality for it to be true. This is why mathematics works.
Allow me to repeat then what has in my view been sufficiently explained by KF and StephenB:
We know of wholes only in reference to parts, and we know of parts only in reference to wholes. A whole is not equal to, but is greater than its parts, and a part is not equal to but is less than the whole.
To say that you have a crank shaft does not mean that you have an automobile. However, to say that you have an automobile IS to say that you have a crank shaft and all the other component parts that make up an automobile – given that a crank shaft is a part of an automobile. While this perception of the truth is limited, it does not limit the truth itself. That I can draw a complete automobile as part of a crank shaft does not change the truth; it only changes the perception to a false representation of the reality of automobiles.
—BarryR: “With that bit of administrivia out of the way, I’d like you to propose a solution to Edmonds’s proof given in section 4 that does not rely on assuming the existence of universal truth. Please use formal notation.”
I appreciate the creativity involved in your latest attempt at a distraction, I really do. However, this is the umpteenth time that you have ignored a refutation, changed the subject, and asked me to solve an irrelevant riddle. As I pointed out earlier, you will be more persuasive if you advance cogent arguments and ask/answer relevant questions.
Here are a few items of unfinished business:
[A] First, you claimed that there are no mathematical laws, followed by an acknowledgement that there are, indeed, mathematical laws. I asked you to take one position or the other. You remained silent.
[B] Next, Edmond’s presented no definition of truth. That point still stands and you have not addressed it.
[C] Further, Edmonds used an inappropriate example in order to argue, wrongly, that syllogisms are unreliable and may produce conclusions at variance with their major and minor premises. You did not respond.
[D] Further, you have yet to tell me which philosophical errors that Adler alluded to are not really errors and why you think so.
[E] Further, you have not addressed the current theme about the self evident truth concerning the relationship between the whole and its parts.
[F] Further, I argued that truth must be unified in order to be truth, and I explained why. You have not explained how a contextual truth, which could conflict with other contextual truths, could be true in any case. How, for example, can a mathematical “truth” be true if it contradicts a scientific “truth?”
[G] Further, I argued that it is impossible to do science without acknowledging the law of causation. Given that all evidence must be interpreted through the first principles of right reason, how does one track down causes if some effects can occur without them?
StephanB@323
Thank you for settling the issue of your qualifications.
The textbook I used is _Symbolic Logic and Automated Theorem Proving_, although any standard textbook should cover Skolem normal form.
Thank you for providing the list of topics you’re still unsure about.
[A] Mathematical laws exist and depend on context, specifically the initial selection of axioms. No context-free laws have been observed, and we know of no way to accurately perceive any that may exist. When speaking informally, I shorten the above to “mathematical laws do not exist”.
[B] Peer-reviewed literature relies on a shared body of knowledge between the author and the reader. Edmonds’ idea of truth is clear enough to his intended audience: those who are [actually] trained in philosophy. I can understand your frustration — I go through the same thing when I start reading up in a new field — but it’s usually safe to assume the fault is your lack of knowledge, not the author’s lack of clarity.
[C] Syllogisms haven’t been relevant in philosophy for, oh, 150 years? No, that’s an overestimate:
fide wikipedia.
That’s probably why I kept running into first-order predicate logic in philosophy classes. Syllogisms were mentioned as an historical artifact, if that. There’s just no way to make them rigorous.
[D] As I said before, Adler errs in identifying legitimate differences as errors. That makes for a very marketable book that’s easy to read. It also makes for lousy philosophy.
[E] Repeating my earlier comments, Adler defines a whole in terms of parts and then calls his definition self-evident. To get around this problem, you’ve had to introduce qualifiers like “finite” wholes and disambiguating dictionary definitions — that wouldn’t be necessary for something universal and self-evident.
[F] You did not argue that truth must be unified to be truth. You stated it, without defining truth, no less. I can just as easily say that truth must be contextual. I have the advantage of a citation from someone who does philosophy for a living.
[G] You did not argue that it is impossible to do science without the law of causation. You stated it (without stating the law). I get paid to do science. I somehow manage to do it pretty well without any such universal law.
Your opinion as to how science is done carries even less weight with me than your philosophical opinions. You can improve this defect by providing a citation to the peer-reviewed literature for someone else who thinks this way. Then, I’m not only disagreeing with you, I’m also disagreeing with someone who has a presumption of competence.
But around here, asking for citations is seen as an evasive tactic. It doesn’t have to be that way — assuming you knew how to do a literature search and that your opinion was sane enough to be held by someone who published. I don’t have a great deal of confidence that either of those conditions hold.
So I think that’s where things will remain. My expertise in science and philosophy exceeds yours; I can buttress my opinions from the professional literature and you either cannot or will not.
CH@310
I think you’re starting to see the morass that “self-evident” becomes.
Is the integer 20 self-evident? I think you’d say yes, even though many native societies never ran across the concept.
Is zero also self-evident? Here we have many European societies not figuring this out until relatively recently (9th Century India).
Is infinity self-evident? The mathematical world’s reaction to Cantor’s formulation of it ranged from skeptical to hostile.
Are quarternions self-evident? Tensors? Lie groups?
They don’t appear to be.
But mathematically, there’s nothing that distinguishes some of these concepts as being self-evident and others not. Given the right selection of (non-obvious) axioms, I can derive any of these ideas.
As a term of art, I just don’t see where “self-evident” adds anything.
CH@309
As to absolute skepticism — this simply isn’t a problem.
[At this point my posting here has been reduced to trying to find ways of restating the same five or six points over and over again. It becomes tedious.]
A naive formulation of absolute skepticism (like that used by Lewis) might lead to a logical impossibility. This is naive because Lewis only admits true and false. This makes for easy but not very convincing philosophizing.
My personal skepticism is of the more useful scientific variety. I don’t have any certainty about truth or falsity, and this easily extends to “the idea that I don’t have any certainty about truth and falsity”.
However, I do have a continuum of certainty, and it’s no great loss that the extremes aren’t available to me. I can have near-certainty about the truth of some proposition and near-certainty about the falsity of others, but I spend most of my time somewhere closer to the middle where I’m constantly revising what I believe as I continue to experience new things.
Could this approach be wrong? Sure. And with that admission I remove the possibility of contradiction.
All I’ve given up is certainty, and that’s made me a much nicer person (as well as a better scientist).
CH
Backing up a bit and reading Chesterton in context, I now realize that he’s writing polemic, not philosophy, and the style he has chosen in a perfectly reasonable one for polemic.
Here’s the nub:
That’s a textbook argument from incredulity. I have no difficulty imagining either (and I work with expensive machines where the arithmetic is far stranger than 1+1=3).
This passage may be more telling:
I don’t believe he’s intending either passage to be read literally, or, perhaps I should say that I don’t think either passage reflects what he actually believes. This is emphatically written for an audience, an audience who wants to be reassured.
But no, I don’t think there’s an English professor or philosopher who would mistake this for philosophy.
CH
The more I think about it, the more I think that I’m more Chestertonian than Chesterton.
That’s a tolerably good definition of mathematics, and I regret that Chesterton didn’t know any or he might have written a much more interesting essay.
I’m glad that 1+1=2 because I understand that 1+1 could have been 147, and the decision is not one that can be appealed to the real world, only to the storyteller (the mathematician). If the internal logic of the story (theorem) is sound, the story rings true, and it doesn’t matter if the (real or metaphorical) snow is black or white or plaid.
Thank you for reminding me to revisit that.
Onlookers (and MarkF):
I must shake my head as I see the likes of:
This is getting even more and more sadly threadbare.
Evidently, MF — a trained philosopher — is unwilling to engage in comparative difficulties analysis on the issues that are at stake; which automatically locks him into worldview-level question-begging. (And the gobbet he snipped out of context shows why: he refused to address the point that the SET on whole-part relationships is an in-common claim, which is instantiated in particular cases in diverse ways, simply citing it as though that were enough to set it aside. But, any intelligent 6 year old will know that once we have a composite whole, the part is a component, not the whole. As we may see/understand in light of abundant experience from early childhood on.)
Now, above, MF has had three cases of self-evident truths to deal with explicitly, and a fourth mentioned more or less in passing, of which he picks what he wants to deal with (and ducks the most directly evident one, of course):
Now, in MF cites a rebuttal to GP on case 2, which I will remark on with arrow-points:
___________________
>>A really important insight comes from Wittgenstein. Often a statement will be true for a combination of different types of criteria and because they always or often coincide we never have to resolve which apply.
For example, an arithmetic statement such as 2+2=4 is mathematically true because it follows from the Peano axioms (I think those are the right ones).
Now the Peano axioms apply very accurately to a vast range of situations so it is also true that 2+2=4 for a vast range of situations.
Unless we are pure mathematicians we are never called upon to decide whether 2+2=4 is true in the mathematical or the descriptive sense.
And when challenged as to what makes it true we get confused
and end up making up some abstract world of which it is true!
>>
______________________
So, it becomes ever more plain how rejection of self-evident first principles of right reason leads us ever deeper into a morass of error. And, we then see the turnabout, where plunging into the morass of ever deepening errors, is held to be the epitome of intelligence, knowledge and wisdom. [The inadvertent echo of Rom 1 is ever so richly ironic.)
It is time to cut the Gordian knot with one clean stroke.
And Adler shows us just how: identify and correct the little error at the beginning.
GEM of TKI
CY:
Thanks, your input above was both helpful (cf how MF responded, however reluctantly) and encouraging.
You are right that he seems to conflate perception [on evolutionary materialistic premises] and reality. Thus, he needs to appreciate that there are diverse worldviews held by intelligent, educated, thoughtful people, and that they are worthy of sitting down to the same serious table of comparative difficulties.
Those who adhere to evolutionary materialism also need to realise that their own view is not privileged. For instance, observe MF’s closing remark in his excerpt above: “. . . end up making up some abstract world of which it is true.”
These words reflect an extreme view, whereby the only “real” things are/”must be” physical/ natural (NB: to try to fully and exactly define those will land you in the most horrendous morass of complexities that make the objections on parts and wholes pale into insignificance . . .), and the meaning of abstractions lies in operations and observations on those things. But in fact, that begs the question of the central experience of the world we all have: our self-aware, conscious, thinking, enconscienced, unified selves. It is through that central fact that we interact with the external world and reflect in turn on it.
In short, we are minded, indeed ensouled creatures. And to such creatures, love, good and evil, number, truth and the like are as much experiences as are the redness of a ball, or the velocity of the car in which we may be travelling. The issue is to coherently account for these, and that brings us tot he reality of self-evident truths starting with first principles of right reason.
We may indeed understand and perceive such things as true, but their truth is not he product of our perception. Self evident first principles of right reason are true in the context that once we understand them, to try to reject them at once lands us in the shipwreck on the reefs of absurdities. (For instance, so soon as you utter a claim that something is the case, you entail that it cannot be not the case as well, in the same sense and at the same time and place. When someone tries that, as was done with the meaning of + above, the anchors start and we end on the reefs of absurdity in a moment.)
Looking at remarks above on parts and wholes, one is left with the very strong impression of an utterly strained objection, one made in the teeth of commonplace concrete experience and concepts formed on such experience. Of course, it is probably felt that there must be some exceptions out there that allow us to doubt the specific and broader claims, so freighted with implications that seem to be unwelcome to materialists.
But, we can unpack the claim that “a finite whole is greater than any of its parts.” In context, we are talking of composite unities, things that have a unified identity, but which are made up from components. In such a case, it is — or should be — obvious that the part/component is not the same as the unified whole, and that as there must be at least two parts, no one part will be equivalent to, the same as, or as great as the whole. For components have to be joined together in organised ways and/or relationships to get to the whole. Letters are joined to make words, parts are joined to make engines, varieties of animals are organised in hierarchies to compose the Animal Kingdom, and lines of code are organised to yield a functioning program.
But, if one is sufficiently determined not to acknowledge that, one can doubtless find and make objections that one would not ever have come to mind if one were open to the idea.
Only to land in absurdities.
GEM of TKI
Kairosfocus:
And, we see why 2 + 2 = 4 is self-evident: once we understand the symbols, the operation of addition and the relationship of equality [typically, age 5 or so] we see that 2 + 2 = 4 [however we may label or symbolise] as a matter of brute fact, AND that it could not have been otherwise, on pain of confusion and gross error.
I may just be a dumb high schooler, but I can see a situation where 2 + 2 = 11 and a situation where 2x + 2x = 0 for a non-zero value of x. Which I think is Mark’s point about context.
SAR:
Pardon, but the points you are making were discussed long since above, e.g. cf 187 – 191 for about the fourth round of such explanation: 65, 74, 111, etc.
Again, the precise point is that we are to understand the situation we deal with.
As the simple illustration below suffices to show [try it with some matchsticks], 2 + 2 = 4 is not a mystery, nor is it to be dismissed by arbitrarily and contradictorily redefining + to make a point:
{||} + {||} –> {||||}
And that thus, with the usual symbols and meanings, we can see that:
2 + 2 –> 4
Thus, we can then go on to see that in that context, 2 + 2 = 4 is not only true in fact but must be so; given what 2, +, + and 4 normally mean.
To come up with claims that 2 + 2 = 11 or that 2 + 2 = 147 etc, and assert that they are “just as true” requires unannounced injection of a contradiction into the system.
Of course, I know of a very common situation where we use very similar symbols thusly:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1
But of course, how that comes to be underscores the point: + here symbolises a boolean operation of INCLUSIVE OR, and 1 is here a boolean variable that takes the values 1 or 0. [And BTW, the boolean algebra relationship here is self evident, once its symbols, meanings and relationships are understood. Self-evident is not the same as simplistic.]
The issue is not that we must appreciate context. That, is a distractive red herring led away to a strawman.
The point is that once we do properly understand the relevant symbols, 2 + 2 = 4 is SELF EVIDENTLY TRUE.
That is:
1 –> we understand based on our experience of the world as minded creatures, i.e. this is not a definition we are making up out of the air.
2 –> on understanding, we see that the claim is true, and MUST be true, on pain of absurdity.
And so it illustrates how self-evident truths are real.
As does: “Error exists.”
As does: “a finite whole is greater than any of its parts.”
As does: “a given thing cannot both be and not be.”
The problem is not contexts of discussion — any use of symbols to express meaning is inherently about contexts, conventions, and the like — but about a reality that ever so many are loath to acknowledge: there are truths which on understanding what is being said we can see are so and must be so on pain of absurdity.
GEM of TKI
PS: Interpreting the Inclusive Or function: 1 –> true, and + means AND/OR. So, a compound statemment p + q means “P is true and/or q is true.” the truth value of the composite statement will be true if at least one of p and q are so. For instance, “A guava is a fruit AND/OR the moon is made of green cheese” is true, as the first of these is true. Does not matter that the second is false, even ridiculously false.
Pardon, but the points you are making were discussed long since above,
Is that your way of saying “run along little girl, the adults are talking?”. I’ve read those comments and you are wrong. I can make 2 + 2 = 11 without changing the meaning of 2 or + or =.
The point is that once we do properly understand the relevant symbols, 2 + 2 = 4 is SELF EVIDENTLY TRUE.
It is not self evidently true to an alien that is unfamiliar with your unstated assumption of a base 10 system. If an alien used a base 3 system, it would be self-evidently true to him that 2 + 2 = 11.
Furthermore, 2x + 2x = 0 (for a non-zero value of x) is self evidently true when talking to an alien only familiar with geometry about right angles.
The issue is not that we must appreciate context. That, is a distractive red herring led away to a strawman.
Yes, we must appreciate context, Mr. Smartypants. LOL.
Whoopsie! That should have read “self evidently true when talking to an alien (who is only familiar with geometry) about right angles.”
SAR:
Again, one last time for now: once we use the relevant symbols in their usual ways [and as not one of those reading misunderstands!], the claim 2 + 2 = 4 is both true and necessarily true, on pain of absurdity. (And I provided other cases where on different interpretations of the glyphs we do get different results, but that is about a different context. Which is strictly irrelevant to the self-evident nature of the truth that 2 + 2 = 4.)
The willful injection of distractive red herrings and strawmen to try to undermine a simple and well-warranted point, is therefore not a sign of good intellectual health on the part of evolutionary materialists, radical relativists and fellow travelers, as may be seen above.
Pardon, finally, but I must object to your taking unwarranted offense at my pointing out a simple matter. At no point have I said or implied anything denigratory. To correct is not to denigrate.
G’day
GEM of TKI
once we use the relevant symbols in their usual ways [and as not one of those reading misunderstands!], the claim 2 + 2 = 4 is both true and necessarily true, on pain of absurdity.
Nope. I have not changed the meaning of 2 or + or =.
And I provided other cases where on different interpretations of the glyphs we do get different results, but that is about a different context. Which is strictly irrelevant to the self-evident nature of the truth that 2 + 2 = 4.
If you fail to completely state the context, then the truth is hardly self-evident. Just think of the alien who only understands base 3. If the first thing he heard when he got off his spaceship was you saying “2 + 2 = 4 is self-evidently true,” he would think you were the one laboring under the pain of absurdity. So, until you fully explain your context, you aren’t being nearly as self evident as you seem to think.
The willful injection of distractive red herrings and strawmen to try to undermine a simple and well-warranted point, is therefore not a sign of good intellectual health
Is that your way of saying you think I am not smart enough to comment?
Pardon, finally, but I must object to your taking unwarranted offense at my pointing out a simple matter.
You came across as haughty in your comment to me at 327. If that wasn’t your intent, then I accept your apology.
—San Antonio Rose: “If you fail to completely state the context, then the truth is hardly self-evident.”
So, tell me SAR, is the law of non-contradiction self evident or not? Your friends on this thread say that it is not self evident. They believe that, in principle, the planet Jupiter could exist and not exist at the same time and under the same formal circumstances. For them, there is no logical law to prevent us from saying otherwise. Do you agree with them?
SAR:
Not at all.
The point of a self evident truth is that we are intelligent, experienced minded creatures who routinely UNDERSTAND meanings and contexts.
Which is a basic fact of life you imply every time you post a message here: you expect to be understood without giving the full context of your remarks — from the definition of alphabetic glyphs and English words and grammar on up — without text in the first intance.
In short, the objection is based on an exercise in self-referentially inconsistent selective hyperskepticism.
And, in the case in view, 2 + 2 = 4, that meaning and context is the property of just about every 5 year old who has had the privilege of schooling.
So, the objection is specious and self-defeating.
Indeed, it aptly illustrates how those who choose to object to a self-evident truth are forced to resort to absurdity.
GEM of TKI
PS: I will ignore the personalities, and simply point out that to substitute that 2 + 2 = 11, you have redefined symbols.
—BarryR: “I’m not quite sure what you meant to communicate, but what came across was:
1. No undergraduate philosophy classes,
2. No graduate philosophy classes, and
3. No graduate degree.”
Yes, I have a graduate degree. It is a bit difficult to graduate with high honors without actually graduating. There is that law of non-contradiction rearing its ugly head again. Yes, I have taken numerous philosophy courses both at the undergraduate and graduate level.
On the other hand, credential checking is your gig, not mine. I would prefer to address substantive points on the table, such as all those unattended hanging chads of yours that I listed @323.