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Q: Is Logic simply a matter of axioms at play in an abstract logical world unconnected to external reality? A: Nope

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As we continue to look at the issue of first principles of right reason, one of the key steps being taken by critics of the Law of Non-Contradiction [LNC] is to assert that we are here dealing with axioms unconnected to the real world, at least in relevant cases.

First, let us clip a recent comment to refresh our recollection of the why behind the classical laws of thought, which can here be seen as self-evident and thus “natural,” rather than arbitrary projections unto reality conditioned by genes and memes:


KF, 125: >>Reasoned thought itself is under attack in this ultra-/post- modern era.

So bad is this, that there are ever so many who think that something is wrong if one sticks up for longstanding, self-evidently true and indisputably certain first principles of right reason. (Did you notice how Aristotle described the concept of self-evident first principles of right reason in the clip from last night? [Read above.])

{Let me clip from 119:

[Ari, Metaphysics, defining self evidence and arguing that LNC is such:] >>. . . the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men may be mistaken about things which they do not know), and non-hypothetical. For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms . . . >>

(NB: Aristotle, then, sees self evident truths as real, as certain beyond doubt, as natural, and as first principles that are foundational to thought on particular topics. We can define such as truths we understand, based on our existence and experience of the world as intelligent, conscious communicating, en-conscienced creatures, which we see as true, and as necessarily true on pain of patent absurdity if rejected, without further proof. Such, rather, are start-points for proof.)}

Lest we forget (I know, I know, this cuts across what we have been ever so confidently taught by the professed wise and brilliant, complete with convincing — but misleading — talking points and claimed proof cases), let me again clip the basic summary developed above:

Consider the world:

|| . . . ||

Identify some definite A in it:

|| . . . (A) . . . NOT-A (the rest of the world) . . . ||

{Or, let us use a full diagram:}


Laws of logic in action as glorified common-sense first principles of right reason

Now, let us analyse:

[1] A thing, A, is what it is (the law of identity);

[2] A thing, A, cannot at once be and not-be (the law of non-contradiction). It is worth clipping Wiki’s cites against known interest from Aristotle in Metaphysics, as SB has done above:

1. ontological*: “It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect.” (1005b19-20)

[*NB: Ontology, per Am HD etc, is “The branch of metaphysics that deals with the nature of being,” and the ontological form of the claim is talking about that which really exists or may really exist. Truth is the bridge between the world of thoughts and perceptions and that of external reality: truth says that what is is, and what is not is not.]

2. psychological: “No one can believe that the same thing can (at the same time) be and not be.” (1005b23-24)

3. logical: “The most certain of all basic principles is that contradictory propositions are not true simultaneously.” (1011b13-14)

[3] A thing, A, is or it is not, but not both or neither (the law of the excluded middle).

[4] “to say that what is is, and what is not is not, is true.” (Aristotle, on what truth is)

[5] “Of everything that is, it can be found why it is.” (Principle of sufficient Reason, per Schopenhauer.)

[6] If something has a beginning or may cease from being — i.e. it is contingent — it has a cause.* (Principle of causality, a direct derivative of 5)

*F/N: Principles 5 & 6 point to the possibility of necessary, non contingent beings, e.g. the truth in 2 + 3 = 5 did not have a beginning, cannot come to an end, and is not the product of a cause, it is an eternal reality. The most significant candidate necessary being is an eternal Mind. Indeed, down this road lies a path to inferring and arguably warranting the existence of God as architect, designer and maker — thus, creator — of the cosmos. (Cf Plato’s early argument along such lines, here.)

These six claims, once we reasonably understand them in light of our experience of the world, will patently be seen as true, and necessarily so on pain of absurdity. So soon as we can identify something, A as a definite object, A is itself, not something else at the same time and in the same sense. Similarly, the understanding of what truth is, is the ordinary and reasonable meaning: telling it like it is. And if something is, there is a reasonable question: why, which can be answered. That answer, for something that begins or may cease, is that it has a cause, and this raises the root question of beings that are necessary, and have no cause. (Cf the previous discussion in the ID Foundations series, here.)

This then points to the question, what best explains the contingent cosmos we observe, which turns out to be fine-tuned for C-chemistry, cell based life. Cosmological design thought and theory therefore point to a designer and builder of our observed cosmos . . .  >>


Of course those onward connexions are big issues, but the core question is the bridge between principles of logic and reality.

A good place to look at that is the response in the same thread, to a recent post by Dr Liddle at her blog. It is revealing that she has entitled that post, “The RULES of Right Reason” [Emphasis added], rather than “The FIRST PRINCIPLES of Right Reason,”  which says something very different.

For, we make up rules for games, we start reasoning from first principles that present themselves to us as a good place to begin. And if the first principles in question show themselves to be warranted as self-evidently true, they are natural principles, not artificial rules for a game we may or may not elect to play.

Ironically, it seems Dr Liddle has made an unwarranted design inference here:


KF, 126: >>I skimmed the thread and OP that Aleta has now repeatedly linked. I can see that from the outset they are making the little error at the beginning that Adler has highlighted, and which is discussed in more details here: failing to recognise the reality of self-evident truths of right reason, and in particular the first principles of right reason.

For instance, in the OP, Dr Liddle remarks:

They are indeed axiomatic – in other words, they are axioms on which a certain form of logic is based. Now I’m no logician, but I am capable of seeing that if we assume those axioms are true, we can construct a logical language in which useful conclusions can be drawn, and useful computations performed.

But there are some propositions that simply are not possible in that language, because those axioms themselves are based on more fundamental assumption: that we know what an “object” is; that we know what “time” is – in other words, that we know what “is” is . . .

Let me clip Wikipedia, speaking against its known ideological interest:

In epistemology (theory of knowledge), a self-evident proposition is one that is known to be true by understanding its meaning without proof.

Some epistemologists deny that any proposition can be self-evident. For most others, the belief that oneself is conscious is offered as an example of self-evidence. However, one’s belief that someone else is conscious is not epistemically self-evident . . . .

A self-evident proposition cannot be denied without knowing that one contradicts oneself (provided one actually understands the proposition). An analytic proposition cannot be denied without a contradiction, but one may fail to know that there is a contradiction because it may be a contradiction that can be found only by a long and abstruse line of logical or mathematical reasoning. Most analytic propositions are very far from self-evident. Similarly, a self-evident proposition need not be analytic: my knowledge that I am conscious is self-evident but not analytic . . . .

For those who admit the existence [i.e. reality] of abstract concepts, the class of non-analytic self-evident truths can be regarded as truths of the understanding–truths revealing connections between the meanings of ideas.

That is, a self-evident truth is one that — providing we understand what is being said in light of our undeniable (and self-referential) experience of the world as intelligent, language-using, knowing and communicating creatures — we see is so, and that it MUST be so, on pain of obvious absurdity if we try to deny it. That is, these are foundational truths that we know or should know are so and must be so. So, to willfully reject such a truth is to implant an absurdity in the heart of our reasoning, and to open ourselves up to that en-darkenment of heart and mind that leads us to reject truth because we have swallowed an error.

The reality of such truths is too often disputed, so let us give a key case, Warranted Credible Truth no 1, per Josiah Royce via Elton Trueblood: error exists.

This is of course an all too familiar and universally accepted truth. That’s why we have arguments over what is correct!

But there is a subtler and highly instructive side to it: it is UNDENIABLY true, on pain of self-referential absurdity. That is, if we try to deny that error exists, as a test, we immediately have a choice of which of two claims is in error: (a) that error exists, or (b) that error does not exist. One of these must be in error, on the common sense understanding that even philosophers must respect.

And obviously, the correct one is (a), as it affirms what we have seen is undeniably so: error exists.

Now, that looks trivial, doesn’t it?


WCT 1 implies that truth exists, and undeniably true truth exists. Warranted credible truth — knowledge — exists. So, those who would dismiss the reality of truth, or the know-ability of truth beyond seeming true to me or you, etc, are in error.

This actually cuts a wide swath across many popular worldview level opinions: radical relativism and its many friends and kissing cousins.

In addition, “error” is not a tangible reality: we cannot touch error as such, though we may see cases of error. Just like we cannot touch two as such though we may touch glyphs that represent it and illustrate with concrete cases. Reality is not to be conflated with [material] physicality; and indeed it is precisely because mathematics often captures logical, abstract facets of reality, that we so often see its awesome power in science, engineering and even day to day life.

Going further, we have in hand a case where we can see for ourselves that axioms are not always arbitrary and merely evaluated on being useful. Some axioms are warranted and credible as self-evident truths. So, the notion that we are free to select whatever axioms we want and then just look to see if it works well enough to be useful, crashes to the ground in flames.

For, there are what Aristotle identified as the most certain of all truths, truths that are certain and know-able to all on pain of patent self-referential absurdity.

It so happens that the first principles of right reason belong to exactly that category of truths.

Now of course, one of the points that are being disputed is that: “we know what an “object” is; that we know what “time” is – in other words, that we know what “is” is . . .”

This actually inadvertently shows what is at stake here: if we reject the first principles of right reason, our ability to communicate itself disintegrates into a chaos. (So, apply Kant’s Categorical Imperative here . . . ) But in fact, we premise our whole structure of knowledge on the undeniable self-referential and in-common common sense facts of human existence, which includes that we can and do communicate using language and keystone concepts such as our ability to answer to who or what [objects], to when [time] and to existence or non existence [is]. Or else, who is speaking, what does s/he say, and about what, when, where, and how accurately, how well warranted, evaporate in a chaos of confusion and contention.

In short, we are patently seeing absurdity piled upon absurdity here.

But of course, the underlying question on the issue being touted is that such words defy precising definitions that state necessary and sufficient conditions that infallibly tell us what they mean and/or operations that we can use to observe or measure them, etc. And, a selectively hyperskeptical voice can have great fun making such efforts at definition seem ridiculous.

The only problem is that the process of making or challenging such definitions alike would depend on the common sense recognition of what these things mean. That is the one pushing such skeptical talking points is being self-referentially incoherent.

So, are we locked into a circle of confusion and begged questions, with knowledge and reason themselves evaporating?

Not at all.

We start from the reality that we exist as intelligent and communicating creatures in a real world, and that we recognise many concepts on the basis of knowing cases, intuiting connexions and using that abstracted pattern to identify further cases on family resemblance. This process obviously can err, but the very fact of error is a case of existence and of truth existing and of knowable truth existing. So, we know well enough what things are, both concrete things and abstract ones of the order of the truth in the statement 2 + 3 = 5.

We know full well that we can recognise cases of such things, and mark them off with labels, like A.

Once that is done, we know full well that A is distinct from NOT-A, just as Dr Liddle is distinct from the rest of the world: her husband, her cat, her car, her workplace, her blog etc etc.

In short, we see the basic laws of thought swinging into action, as has been repeatedly described and explained. And, in a case where to deny such is to end immediately in self-referential absurdity.

What is more, if I were to take what Dr Liddle wrote and say that it means the opposite, she would rightly object that I am distorting what she said.

In short, she full well knows that in relevant cases we know the difference between an assertion and its denial.

She knows or should know that if one stands at the four-state point or the like, one can be “in” four states at once, but only if we take “in” in an inclusive sense. If we take “in” in the exclusive sense, that is not possible, and so the problem being posed turns out to be a case of needing to be clear what we are asking about.

And of course there are things that shade off into one another, indeed Aristotle discussed white and black and grey in the very passage in Metaphysics we have been talking about. Does that mean there is no difference between white and black, or that something can be white and not white in the same sense and time etc?

Patently not.

That stricture on being in the same sense and time etc, is an invitation to be precise enough to mark whether we are equivocating when we say A and NOT-A. As Ari himself observed:

. . . the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men may be mistaken about things which they do not know), and non-hypothetical. For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms . . . .

We did not suddenly see things that Aristotle was blind to, in the past 100 or so years! . . . >>


In short, the first principles of right reason are not merely arbitrary axioms, but in crucial aspects are self-evident truths of right reason. That allows us to bridge the gulf that has been made in modern thought through an error of Kant.

An error of Kant?



KF, 67: >> . . . All of these [cases were given] real world interactions of the intelligent mind rely on the bridge between the world of thought and the world of experienced reality.

But, if you are thinking in light of Kant’s cut, you will still think nope the gap is not bridged. It is un- bridgeable.

Therein lieth the rub: self-referential incoherence. Kant and others are here committing one of those little errors in the beginning that spring up into ugly chasms of error cutting wide swaths across our life of thought and experience alike.

Here is the overlooked problem of self-referentiality: to assert that we know and can know naught of the external world as it is, is to already and inescapably claim to know something about the external world, its alleged un-know-ability. So, which is it, we can know something about the external world (and indeed we can make errors in so claiming to know), or we truly cannot know in which case we could not even know that much.

Or, as William Lane Craig pointed out in his debates with Gerd Ludemann:

insofar as these . . . assumptions include Kant’s strictures on the scope of scientific knowledge, they are deeply, fatally flawed. For Kant must at least be claiming to have knowledge of the way some things (e.g., the mind and its structures and operations) exist in themselves and not merely as they appear; he confidently affirms that the idea of God, for instance, has the property of unknowability. [10] So the theory relies on knowledge that the theory, if it was true, would not — could not — allow. [ Jesus’ Resurrection: Fact or Figment, ed. Paul Copan (Downer’s Grove, IL: IVP, 2000), p. 13. NB: Ref. [10] is to Plantinga’s Warranted Christian Belief, pp. 3 – 30, and is shortly followed by a reference to F. H. Bradley’s gentle but stinging opening salvo in his Appearance and Reality, 2nd Edn.: that “The man who is ready to prove that metaphysical knowledge is impossible has . . . himself . . . perhaps unknowingly, entered the arena [of metaphysics] . . . . To say that reality is such that our knowledge cannot reach it, is to claim to know reality.” (Clarendon Press, 1930), p.1]

Given the self referential absurdity, and the patent confusion, the answer should be plain.

We can and even do in many cases know about the external world.

Indeed, utterly abstract principles like 2 + 3 = 5, routinely and reliably strictly constrain what can be at all in that world. There is no possible world in which we can have heap A, two tokens, and heap B, three tokens, then push together and not get five tokens in the new heap we have so formed. It is only sheer familiarity that blinds us to how astonishing such a finding truly is.

Thence, with elaboration, the so-called “unreasonable” effectiveness of mathematics in science, engineering and day to day life.

There are using abstract, conceptual realities that do control what can be in this or any other possible world.

And, as one of these, it so happens that once we can identify an item A, and distinguish it by whatever means from the rest of the world, under the usual rules of consistency in meaning etc:

(a) the part labelled A will be A (symbolically, [A => A] = 1),
(b) A will not be the same as NOT-A ( [A AND NOT-A] = 0); and
(c) there is no third option to being A or NOT-A ( [A OR NOT-A] = 1).

Such holds whenever an A exists. It is a necessary constraint on what is possible, once A exists as a distinct thing, even if it may have fuzzy borders. try this one: where does your arm end and the trunk of your body begin? Your nose? Your leg? sure, you can identify ever so many border zone points that you could debate what they are till the cows come home, but that has not changed the realities that we have arms, noses and legs etc. A nose is a nose and not also a non-nose. Something is nose or not nose but not both or neither. Regardless of fuzziness of the border.

This point will hold even where we struggle to decide if this is indeed A.

If it IS A in truth, the three principles apply. Our limitations as finite and fallible do not stop those consequences from actually following, they are just our limitations.>>


So, it is plain that the issues at stake are truly foundational.

If we cannot come to agreement here, agreement later on will be a matter of accident, and attempted discussions will face the fatal flaw of playing games based on arbitrary rules. And, if someone is losing based on the rules in play, the temptation will be to challenge the rules. Consequently, if one sees logic as little more than a mental game played by rules that are essentially arbitrary, one will be temped to try to switch rules in mid-game if one seems to be losing.

Moreover, one who thinks like that will see the “game” as a game, without serious import, so gaming the game will seem a reasonable thing to do.

Suddenly, a lot of the features of exchanges on design theory and related areas make a lot of twisted sense: one side has been operating based on a rules for games model, where the rules are open to being pushed to one’s advantage.

And, if logic is a matter of a game, so is morality, hence the slide to nihilism we have been so frequently forced to comment on. That is, the “logic is a game” view multiplied by evolutionary materialism’s want of a foundational IS that can ground OUGHT leads to the playing out of the consequences of the agenda that thinks that might and manipulation make ‘right.’

Some pretty serious things are at stake here, things that explain how frequently post-/ultra- modern evolutionary materialist advocates become disruptive and uncivil.

So, we can easily see why in the end authorities may well need to restrain the disruptive, or at length remove them. For, if there are some who reject the basis for reasoned discussion and responsible debate, they cannot be reasoned with, they can only be removed if they become too disruptive and distractive in the teeth of repeated warning. To use the classroom metaphor, why should we allow those who have no intention to learn, to stop the learning process for those who do want to learn?

But also, we see here the diagnosis that allows us to identify and possibly fix the problem.

So, we really do need to settle the question of the first principles of right reason and the linked bridge between the world of thought and the world of external reality.

The argument here is that this bridge from mind to external reality is made up from self-evident first principles of right reason; which are thus natural, not arbitrary rules that can be changed at will.

If you reject that claim, why? What would you put in its place, why?

As for me, I am ever more led back to seeing the wisdom in this bit of classical literature that is so often despised and derided today:

Prov. 16:22 Understanding is a fountain of life to those who have it,
but folly brings punishment to fools.

23 A wise man’s heart guides his mouth,
and his lips promote instruction.[b]

24 Pleasant words are a honeycomb,
sweet to the soul and healing to the bones.

25 There is a way that seems right to a man,
but in the end it leads to death.

Isa 5:18 Woe to those who draw sin along with cords of deceit,
and wickedness as with cart ropes . . .
20 Woe to those who call evil good
and good evil,
who put darkness for light
and light for darkness,
who put bitter for sweet
and sweet for bitter.

21 Woe to those who are wise in their own eyes
and clever in their own sight.

Eph 4:17 So I tell you this, and insist on it in the Lord, that you must no longer live as the Gentiles do, in the futility of their thinking. 18 They are darkened in their understanding and separated from the life of God because of the ignorance that is in them due to the hardening of their hearts. 19 Having lost all sensitivity, they have given themselves over to sensuality so as to indulge in every kind of impurity, with a continual lust for more. [cf Rom 1:18 – 32]

So, which way will it be, for us and our civilisation? END

PS: Those who want to raise objections on quantum theory issues are asked to first see here (and, do, watch the Dr Quantum video). For more, cf. the comments and video here, the online exchange here (to see how such things play out in debates), and the papers here and here to see how the issues can be addressed at the next level. The famous exchange of Ravi Zacharias with an un-named professor over either-or vs both-and, is also helpful.

Hey Kairosfocus. I have a question. Not to beat a dead horse, but how does quantum computing square with the laws of logic, especially the law of noncontradiction? The whole apeal of a quantum computer is that it would be much faster since it could exist in all possible states simultaneously. kuartus
WJ Murray: Thanks for the kind words. TGPeeler: Yes, excellent! Aquinas said, "Reason in man is rather like God in the world." With respect to the origins of intellectual depravity, I would add this: He who fails to live what he believes will soon believe what he lives. StephenB
Folks: Here's where I am coming out on this topic. I think Ari et al saw something, something that is connected to how reasoning works and to how assigning items to sets works. For instance, we can view the syllogisms as assertions about sets and membership in intersections of sets: Socrates is a Man --> s is in set M Men are Mortal --> M is a subset of R ______________________________________ Socrates is Mortal --> s is in M, in turn in R Identifying that something is there and is in a set are fairly basic and uncontroversial operations, especially when we for the moment deal with sets that do have members. (We can do adjustments for sets that may be empty, which do have significant results, but they don't change the force of the above.) Law of identity is really saying that if we have in hand an element, s, that is what we have and not something else. Since we have identified s, we are excluding NOT-S, and the act of specificity locks out something between these two options. The cut is a clean, sharp one. Of course there are things that shade off from one end to another of a spectrum, or are non-exclusive. Those cases will have specific properties for that aspect, but as a general rule, to deal with the cases all the way along we are dealing with other aspects that do follow the patterns just identified. For instance, consider the four state border point. Stand on it and you are -- non-exclusive sense -- IN four states. But, there you [and not NOT-You, and most definitely you are something . . . .] are [and this is a case of what is is! and when is is too!], standing [and not NOT-standing] there. So the wise thing is to see that we cannot get away from the either or side of things. To try to use t6he four borders point to dismiss the principles we have discussed is to saw off the branch on which we all must sit as we engage the real world Oops, there goes that metaphysical bridge from the world of thought to the world of reality. Yup, just like standing on the side of the road and jumping out of the way when we perceive a car brushing by too close too fast. No-one is going to play fancy phil games there! The very concept, as SB stresses, of distinguishing a sound argument from a merely valid one, brings a lot to bear. There is a bridge, truth understood as that which accurately refers, which we can warrant by all sorts of ways and means, not least in many cases good old fashioned common sense. In other words truth is real and knowable truth is real. What about the grey horse, as opposed to a black or a white one? It's standing there isn't it? It is grey and not NOT-grey isn't it? Grey is distinct from both black and white in a particular case that we can see isn't it? So, let's get it: grey is a blend -- a superposition of black and white. Yup, x% B + (100 - x)% W --> Gx. Each of those terms is riddled with specificity of identity and distinctions, and the relationships are similarly riddled. We could do a pink too, as W + Red. (Ever made cherry or strawberry milk using syrup or pulp?) Even in the vaunted q-mech cases, the relationships and analysis are simply riddled with the same patterns. And if we are looking at the electron beams hitting as double slit, even one at a time, we plainly are dealing with a phenomenon that is joining wave and particle properties in a way we do not fully understand. yes, it is mysterious, and that we could add up one electron at a time and end up with a classic interference pattern is amazing, but that is telling us that the thing we call and electron is not just like the marbles and cricket balls or baseballs we are familiar with. Even when you monitor to see which slit it goes through, you have changed the circumstances and trigger collapse of the wave effect. Does that mean the electron is and is not, or is in different places at once or whatever, or does it just mean that we are observing a different kind of phenomenon and are trying to analyse it using models that form maps, not the reality of the territory? As for superposition, classically a wave interference pattern is from just such a superposition. So, if an electron has wave properties, why shouldn't it superpose them, and why should that not have effect on the statistical distribution of possible impact points on a screen? Let's hear Wiki, to get a feel for the observable facts:
When Thomas Young first demonstrated this phenomenon, it indicated that light consists of waves, as the distribution of brightness can be explained by the alternately additive and subtractive interference of wavefronts.[3] Young's experiment played a vital part in the acceptance of the wave theory of light in the early 1800s, vanquishing the corpuscular theory of light proposed by Isaac Newton, which had been the accepted model of light propagation in the 17th and 18th centuries. However, the later discovery of the photoelectric effect demonstrated that under different circumstances, light can behave as if it is composed of discrete particles. These seemingly contradictory discoveries made it necessary to go beyond classical physics and take the quantum nature of light into account. A double-slit experiment was not performed with anything other than light until 1961, when Clauss Jönsson of the University of Tübingen performed it with electrons.[4][5] In 2002, Jönsson's double-slit experiment was voted "the most beautiful experiment" by readers of Physics World.[6] In 1999, objects large enough to be seen under a microscope — buckyball molecules (diameter about 0.7 nm, nearly half a million times larger than a proton) — were found to exhibit wave-like interference.[7][8] The double-slit experiment (and its variations) has become a classic thought experiment for its clarity in expressing the central puzzles of quantum mechanics . . . . Sending particles through a double-slit apparatus one at a time results in single particles appearing on the screen, as expected. Remarkably, however, an interference pattern emerges when these particles are allowed to build up one by one (see the image to the right). For example, when a laboratory apparatus was developed that could reliably fire one electron at a time through the double slit,[10] the emergence of an interference pattern suggested that each electron was interfering with itself, and therefore in some sense the electron had to be going through both slits at once[11] — an idea that contradicts our everyday experience of discrete objects. This phenomenon has also been shown to occur with atoms and even some molecules, including buckyballs.[7][12][13] So experiments with electrons add confirmatory evidence to the view of Dirac that electrons, protons, neutrons, and even larger entities that are ordinarily called particles nevertheless have their own wave nature and even their own specific frequencies . . . . However, the electrons do not arrive at the screen in any predictable order. In other words, knowing where all the previous electrons appeared on the screen and in what order tells us nothing about where any future electron will hit, even though the probabilities at specific points can be calculated . . . . A low-intensity double-slit experiment was first performed by Taylor in 1909,[16] by reducing the level of incident light until photon emission/absorption events were mostly nonoverlapping. The appearance of interference built up from individual photons could be explained by understanding that a single photon has its own wavefront that passes through both slits, and that the single photon will show up on the detector screen according to the net probability values resulting from the co-incidence of the two probability waves coming by way of the two slits.[17] Note that it is not the probabilities of photons appearing at various points along the detection screen that add or cancel, but the amplitudes. If there is a cancellation of waves at some point, that does not mean that a photon disappears; it only means that the probability of a photon's appearing at that point will decrease, and the probability that it will appear somewhere else increases . . . . The double-slit apparatus can be modified by adding particle detectors positioned at the slits. This enables the experimenter to find the position of a particle not when it impacts the screen, but rather, when it passes through the double-slit — did it go through only one of the slits, as a particle would be expected to do, or through both, as a wave would be expected to do? Numerous experiments have shown, however, that any modification of the apparatus that can determine which slit a particle passes through reduces the visibility of interference at the screen,[3] thereby illustrating the complementarity principle: that light (and electrons, etc.) can behave as either particles or waves, but not both at the same time.[18][19][20] An experiment performed in 1987[21] produced results that demonstrated that information could be obtained regarding which path a particle had taken, without destroying the interference altogether. This showed the effect of measurements that disturbed the particles in transit to a lesser degree and thereby influenced the interference pattern only to a comparable extent . . . . The delayed-choice experiment and the quantum eraser are sophisticated variations of the double-slit with particle detectors placed not at the slits but elsewhere in the apparatus. The first demonstrates that extracting "which path" information after a particle passes through the slits can seem to retroactively alter its previous behavior at the slits. The second demonstrates that wave behavior can be restored by erasing or otherwise making permanently unavailable the "which path" information . . .
What about Copenhagen? (The view said to most give problems.)
One of the mathematical constructs that enables experimenters to predict very accurately certain experimental results is sometimes called a probability wave. In its mathematical form it is analogous to the description of a physical wave, but its "crests" and "troughs" indicate levels of probability for the occurrence of certain phenomena (e.g., a spark of light at a certain point on a detector screen) that can be observed in the macro world of ordinary human experience. The probability "wave" can be said to "pass through space" because the probability values that one can compute from its mathematical representation are dependent on time. One cannot speak of the location of any particle such as a photon between the time it is emitted and the time it is detected simply because in order to say that something is located somewhere at a certain time one has to detect it. The requirement for the eventual appearance of an interference pattern is that particles be emitted, and that there be a screen with at least two distinct paths for the particle to take from the emitter to the detection screen. Experiments observe nothing whatsoever between the time of emission of the particle and its arrival at the detection screen. If a ray tracing is then made as if a light wave (as understood in classical physics) is wide enough to take both paths, then that ray tracing will accurately predict the appearance of maxima and minima on the detector screen when many particles pass through the apparatus and gradually "paint" the expected interference pattern . . .
See the pivot of the problem? What we can observe is different from what we cannot observe. The map is not the territory. In that context, I suspect that the perceived contradictions are really the shadows of projecting from our everyday world into the world of the quantum, like how at first we may think it a contradiction to say one can stand on a single point on the earth's surface [providing the ice is still there!] and be due north of London, New York and Tokyo. Simple: stand at the north pole and forget the shadow of the two-dimensional maps we usually use, they are not the actual territory, which is a sphere. So if there is a sort of wave-based model that use3s a superposition effect and maps to a pattern of observables with a statistical distribution in it (and where intervening will change what is happening so to see the waves we really have to not try to peek in . . . ), and it covers what we can see, is there a real contradiction, apart from to the mental maps we would like to have? Or is it that we are thinking that chance statistical distributions are effects without causes? I would suggest that we have all sorts of causal constraints at work, without which we don't see the effects. And why on earth should a chance-distribution phenomenon be seen as "causeless," even if we cannot trace the sources to the nth degree? Just asking . . . GEM of TKI kairosfocus
tgpeeler and StephenB, Beautiful, truthful messages. William J Murray
tgpeeler, If that's two cents' worth I don't think we need to worry about inflation just now. Very nice! Brent
Spot on, tg. Insightful and lucid. Axel
I think the problem ultimately boils down to rebellion. If God is Reason, and He is (I AM WHO I AM - an expression of the Law of Identity and the basis for all thought, rational or otherwise, because it is the basis for all language) then to reject Reason is to reject God. We are not dealing with intellectual problems here, we are dealing with willfully disobedient (to the First Principles of rational thought) fools (Psalm 14:1). It's a hard thing to say but there it is. I hope lurkers are being reached because I've never had one acknowledgement of undeniable truth "out here" in years of posting with the ELs and their ilk. At bottom, this is moral degeneracy because it is willful and obstinate rebellion against undeniable Truths. Isaiah warned against this when he said "woe to those who call evil good and good evil." This is a violation of the law of identity. And woe to those who do it. $0.02 tgpeeler
KF: Oh yes, I agree. The problem, as I have always indicated, is postmodernist/subjectivism. Keep in mind that Atheist/Darwinists/materialists do not typically analyze, indeed, seldom even know about, the epistemological foundations that drive their ideology. In fact, [a] the postmodernist lie in philosophy (the mind does not correspond to reality) prepares the mind to accept [b] the pseudo-scientific lie about origins (Darwinism). Our adversaries do not consciously make the connection because they seldom know that any such connection exists. Naturally, if our intellect is powerless to apprehend the essences of existing things [metaphysics], then there can be no link between logic and reality [deducing truth] and, therefore, no reasonable standard for interpreting evidence [pseudo science]. If there is no reasonable standard for interpreting evidence, then we must interpret evidence according to the irrational whims of the Darwinist establishment [no Divine foot in the door]. Predictably, atheist/Darwinists are aware of none of these distinctions. One reason that they do not deny the rules of right reason outright is because, in most cases, they have never even heard of them until we introduce the subject to them. Unwilling to admit that they have not been trained to think, they respond by writing long, incoherent posts in an attempt to argue against a subject they know nothing about. No one with even the slightest familiarity with logic would dare to argue that it has no application to the real world. It's all part of the Darwinist bluff. I believe that we should aim our rhetorical weapons at this intellectual deficiency (coupled with their denial of causality) because it informs all their other objections. Why argue calculus with someone who cannot do basic arithmetic? StephenB
SB: This is a hard one. It is very hard to see anyone who dismisses the idea of a sound, well warranted argument as rational. That's part of why I have said that since we obviously have a large number of people who have been taught -- and yes, they have been TAUGHT by their profs and those who repeat what the avant garde profs are saying in the media news and views talking heads shows and novels and pop sci shows and textbooks etc etc as the latest and greatest in wisdom . . . -- there is widespread need for therapy for a very sick civilisation. And indeed, it is fair (but perhaps harsh and alienating . . . ) comment to say that such irrationality is folly. When we see something like the current breathless vapours and storm in a teacup over Sen Santorum saying that there is evil -- even, personified evil -- on the loose in our civilisation, and that it will tempt people and damage institutions through pride and vanity, lust, envy and more into folly, that too is a warning sign. My thought, though, is that darwinism and even atheism are not inherently wedded to denial of the law of non-contradiction. I don't doubt that there are darwinists and atheists out there who would affirm the laws of thought, indeed the debate on the principle of sufficient reason (thus causality) in part has to do with those who want to take it captive to naturalism and determinism. What I am thinking is that what is really going on here is that we are in an era where ultra-modernism, aka post- modernism, is the conventional wisdom of the day in circles influenced by the sort of elites Santorum was fingering as dupes of the prince of darkness grim. You know how hard I have come down on the point that if we can be got to swallow an absurdity, a necessarily false notion, it then corrupts our ability to discern truth and falsity, as it leads us to reject the truth that will obviously not conform to such error. So, what happens when his lowness and the lowerarchy --C S Lewis got that part dead right -- get our civilisation to drink deep and long at the well-springs of absurdity? Oh yes, I know I know, it is seen as utterly dummy fundy or the like to suggest that -- horrors -- there actually might be such a thing as the prince of darkness grim. Well, let me cite the Catholic -- yes, they were Roman Catholics, and were standing in the name of the principles they had been taught through the Catholic church [and I say that as an Evangelical Protestant] -- martyrs of the White Rose movement on the subject, in exposing and explaining one of the chief, willing disciples of that dark prince in recent years, herr Schicklegruber the foam- at- the- mouth carpet-chewer:
WR, Tract IV: Every word that comes from Hitler's mouth is a lie. When he says peace, he means war, and when he blasphemously uses the name of the Almighty, he means the power of evil, the fallen angel, Satan. His mouth is the foul-smelling maw of Hell, and his might is at bottom accursed. True, we must conduct a struggle against the National Socialist terrorist state with rational means; but whoever today still doubts the reality, the existence of demonic powers, has failed by a wide margin to understand the metaphysical background of this war.
I trust that is clear enough. GEM of TKI kairosfocus
The link between logic and the real world is INHERENT in the law of non-contradiction, which entails a logical, psychological, and ONTOLOGICAL component. No one element can be separated from the other two. That is why we can distinguish a "sound" argument, which speaks to the relationship between logic and the real world, and a "valid" argument, which does not. Without exception, and in spite of their disingenous attempts to redefine it, atheist/Darwinists who visit this site reject the law of non-contradiction. We have empirical evidence of that fact. The question we must ask, though, is this: Does any atheist/Darwinist anywhere accept the law of non-contradiction? StephenB
The craziest thing about the logic-deniers is, if not for the fact that the rules of logic are connected to external reality and lead us to objective truth about it, then nothing can be evidence of anything! Consider the fact that the earth is round rather than flat. We have multiple lines of evidence for this, from the mathematical measurements that the ancients performed, to photos of the earth from space. But what makes that evidence evidence? How do we conclude one thing from it and not another? Well, using the data we gather through our senses, we are able to grasp something about the Earth's form: that it is spherical. By the Law Of Identity, we know that sphericity is different from flatness, and by the Law Of Non-contradiction, we can perceive that it is impossible for something spherical to be flat (or otherwise not spherical) at the same time. If the laws of rational thought are not universal laws of reality, then all the data we've collected about the earth actually tells us nothing about whether it's one shape or another. The same goes for everything else, including whatever evidence Liddle believes she has for materialism and for her rejection of logic. Btw, I wonder how many of Mrs Liddle's like-minded will be at the "Reason Rally"? Deuce
"anyone who denies the law of non-contradiction doesn’t need an argument..." Well that's just it, isn't it? They don't need an argument because they have rhetoric masquerading as whatever behind them. Masquerading as science. Masquerading as "correctness" as in political correctness. Masquerading as journalism. Masquerading as entertainment. Masquerading as common sense. Etc.................................................. At least Santorum knows about the "angel of light." CannuckianYankee
Liddle denies the universal applicability of the three laws of thought. And people wonder why I refuse to countenance her self-repudiating incoherence masquerading as rational argument on this site. Why? As has been said, anyone who denies the law of non-contradiction doesn’t need an argument; they need therapy. Someone else said, “Do not answer a fool according to her foolishness lest you be like her.” Liddle is a fool. She will no longer be spewing her folly on this site. Barry Arrington
H'mm: Went online and took a gander at the news just now, and I see that there is a hot and heavy topic tied to Sen Santorum. Looks like some of the themes in the above pretty directly echo Santorum's 2008 Ave Maria U "Satan at work" speech, which seems just now to be stirring controversy in the usual talking heads news and views shows:
SANTORUM: The Father of Lies has his sights on what you would think the Father of Lies, Satan, would have his sights on: a good, decent, powerful, influential country -- the United States of America. If you were Satan, who would you attack in this day and age? There is no one else to go after other than the United States, and that's been the case for now almost 200 years, once America's preeminence was sown by our great Founding Fathers . . . . Satan has done so by attacking the great institutions of America, using those great vices of pride, vanity, and sensuality as the root to attack all of these strong plants that have so deeply rooted in American tradition. He was successful. The place where he was, in my mind, the most successful and first successful was in academia. He understood pride of "smart" people. He attacked them at their weakest, that they were in fact smarter than everybody else and could come up with something new and different, pursue new truths, deny the existence of truth, play with it, "because we're smart;" and so academia a long time ago fell . . . . The next was the church. Now, you say, "Well, wait. The Catholic Church?" No. We all know that this country was founded on a Judeo-Christian ethic, but the Judeo-Christian ethic was a Protestant Judeo-Christian ethic. Sure, the Catholics had some influence, but this was a Protestant country, and the Protestant ethic. Mainstream, mainline Protestantism. And of course we look at the shape of mainline Protestantism in this country, and it is a shambles . . .
Let's ask: in light of how reason and logic and truth as understood above are now evidently deeply suspect among our intelligentsia in our civilisation -- not just the USA -- is the former Senator right in any material respects, or is his concern over the top, based on outrageous rhetoric? Or, is all of the above stuff on first principles of right reason and definitions of truth etc just rhetorical smoke that can easily be exposed and dismissed? Let's see . . . (and BTW, you may want to look here on in context) KF kairosfocus

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