Mathematicians debate the war on math

_{Denyse O'Leary

September 23, 2020

Culture, Intelligent Design, Mathematics, Naturalism}

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Surprising numbers seem okay with it. A teenager’s question at Tik Tok ended up triggering an academic debate:

“I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science recently retired from the University of Toronto. “Working mathematicians overwhelmingly are Platonists. They don’t always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”
Other scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago …
Rovelli goes further, calling into question the universality of the natural numbers: 1, 2, 3, 4… To most of us, and certainly to a Platonist, the natural numbers seem, well, natural. Were we to meet those intelligent aliens, they would know exactly what we meant when we said that 2 + 2 = 4 (once the statement was translated into their language). Not so fast, says Rovelli. Counting “only exists where you have stones, trees, people—individual, countable things,” he says. “Why should that be any more fundamental than, say, the mathematics of fluids?” If intelligent creatures were found living within, say, the clouds of Jupiter’s atmosphere, they might have no intuition at all for counting, or for the natural numbers, Rovelli says.
Dan Falk, “What is math?” at Smithsonian Magazine

That’s pretty deceptive, isn’t it? The natural numbers are what they are whether the intelligent aliens have a use for them or not. Carlo Rovelli stops short of saying that 2+2=5 but the article gives every sense that many would love to go there if only they could get some kind of a nudge.

Indeed, if that’s the best he can come up with, it is far to say that the war on Platonism is just the war on math, PhD version.

See also: One of Boghossian’s hoaxers started the Woke on the 2 + 2 + 5 drive.

Comments

Hmmm. I see that the recent comments section of this site doesn't work. I think I'll write this off as a lost cause.Viola Lee_{September 28, 2020
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It took some time for my first post here to be allowed through moderation, although I'm assuming that now my posts will show up promptly. This is probably not an important topic here (as it seems all the main topics of discussion are political), but I'll post this one more time to see if anyone else is interested in the post on Rovelli.Viola Lee_{September 28, 2020
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I think Rovelli is right, and I see that polistra agrees with me: I like his examples. The counting numbers are natural, and seem inevitable, because we are the kind of being that experiences discrete objects with clear distinctions from other objects. It may very well be that the universe is fundamentally fluid, and that discrete objects are an emergent property related to the kind of being we are. In such a case, the mathematics that is truly embedded in the universe is something that is not fundamentally related to the counting numbers. As the article says about Rovelli's views, math “works” because we crafted it for its usefulness. (Wigner said some similar things.) We are macroscopic beings, so a math based on our macroscopic experience of discrete objects is what seems "natural" to us. I also agree with DaveS. Rovelli doesn't "stop short of saying that 2+2=5": what he has to say has nothing to do with the silly 2 + 2 = 5 meme, or whatever "war on math" might be being waged (which makes no sense to me). I thought the article by Falk was a pretty good description of the age-old controversy about the nature of math, and I'm glad this site pointed it out to me.Viola Lee_{September 26, 2020
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Rovelli is correct. No need to imagine Jovian aliens. We wouldn't treat objects as discrete and countable if our perception was somewhat different. If we sensed electrostatic fields or acoustic signatures instead of visible light, the world would be far more continuous and less digital. To a mud-dwelling fish or a blind person, the electrostatic and acoustic auras of objects are gradual and often merged, not precise and separable.polistra_{September 25, 2020
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Moreover, as was alluded to in the preceding articles, the ‘plantonic perfection’ of a flat universe just so happens to be necessary for us to even be able to practice math and science, (and apply technology in our world), in the first place: i.e. it is necessary for the universe to 'make sense'. In fact, all of the constants also play into the universe 'making sense'
Scientists Question Nature’s Fundamental Laws – Michael Schirber – 2006 Excerpt: “There is absolutely no reason these constants should be constant,” says astronomer Michael Murphy of the University of Cambridge. “These are famous numbers in physics, but we have no real reason for why they are what they are.”,,, The observed differences are small-roughly a few parts in a million-but the implications are huge (if they hold up): The laws of physics would have to be rewritten, not to mention we might need to make room for six more spatial dimensions than the three that we are used to.”,,, The speed of light, for instance, might be measured one day with a ruler and a clock. If the next day the same measurement gave a different answer, no one could tell if the speed of light changed, the ruler length changed, or the clock ticking changed. http://www.space.com/2613-scientists-question-nature-fundamental-laws.html
Another interesting thing about the 'platonically perfect' flatness of the universe is that it allows us to see that the "tiny temperature variations (in the Cosmic Microwave Background Radiation(CMBR)) correspond to the largest scale structures of the observable universe."
How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017 Excerpt: With the most sensitive space-based telescopes they have available, astronomers are able to detect tiny variations in the temperature of this background radiation. And here’s the part that blows my mind every time I think about it. These tiny temperature variations correspond to the largest scale structures of the observable universe. A region that was a fraction of a degree warmer become a vast galaxy cluster, hundreds of millions of light-years across. The cosmic microwave background radiation just gives and gives, and when it comes to figuring out the topology of the universe, it has the answer we need. If the universe was curved in any way, these temperature variations would appear distorted compared to the actual size that we see these structures today. But they’re not. To best of its ability, ESA’s Planck space telescope, can’t detect any distortion at all. The universe is flat.,,, We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,, Since the universe is flat now, it must have been flat in the past, when the universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing. In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts. Which seems like an insane coincidence. https://phys.org/news/2017-06-universe-flat-topology.html
Moreover, in regards to the largest scale structures of the universe, Radio Astronomy now reveals a surprising rotational coincidence for Earth in relation to the quasar and radio galaxy distributions in the universe:
Is there a violation of the Copernican principle in radio sky? - Ashok K. Singal - May 17, 2013? Abstract: Cosmic Microwave Background Radiation (CMBR) observations from the WMAP satellite have shown some unexpected anisotropies (directionally dependent observations), which surprisingly seem to be aligned with the ecliptic\cite {20,16,15}. The latest data from the Planck satellite have confirmed the presence of these anisotropies\cite {17}. Here we report even larger anisotropies in the sky distributions of powerful extended quasars and some other sub-classes of radio galaxies in the 3CRR catalogue, one of the oldest and most intensively studies sample of strong radio sources\cite{21,22,3}. The anisotropies lie about a plane passing through the two equinoxes and the north celestial pole (NCP). We can rule out at a 99.995% confidence level the hypothesis that these asymmetries are merely due to statistical fluctuations. Further, even the distribution of observed radio sizes of quasars and radio galaxies show large systematic differences between these two sky regions. The redshift distribution appear to be very similar in both regions of sky for all sources, which rules out any local effects to be the cause of these anomalies. Two pertinent questions then arise. First, why should there be such large anisotropies present in the sky distribution of some of the most distant discrete sources implying inhomogeneities in the universe at very large scales (covering a fraction of the universe) What is intriguing even further is why such anisotropies should lie about a great circle decided purely by the orientation of earth's rotation axis and/or the axis of its revolution around the sun? It looks as if these axes have a preferential placement in the larger scheme of things, implying an apparent breakdown of the Copernican principle or its more generalization, cosmological principle, upon which all modern cosmological theories are based upon. ?http://arxiv.org/abs/1305.4134?
Moreover, there are also anomalies in the CMBR itself that 'strangely' line up with the earth, Here is an excellent clip from the documentary "The Principle" that explains, in an easy to understand manner, how these ‘anomalies’ that line up with the earth and solar system were found, via 'averaging out', in the tiny temperature variations in the CMBR data.
Cosmic Microwave Background Proves Intelligent Design (disproves Copernican principle) (clip of “The Principle”) - video https://www.youtube.com/watch?v=htV8WTyo4rw
In other words, the "tiny temperature variations" in the CMBR, and the large scale structures in the universe, both reveal teleology, (i.e. a goal directed purpose, a plan, a reason), that specifically included the earth and solar system from the start. ,,, The earth, from what our best science can now tell us, is not some random cosmic fluke as atheists had presupposed.
Job 38:4-5 “Where were you when I laid the earth’s foundation? Tell me, if you understand. Who marked off its dimensions? Surely you know! Who stretched a measuring line across it? Genesis 1:1 In the beginning God created the heaven and the earth.
Of supplemental note: To give us a glimpse at just how delicately balanced this solar system actually is, (so as to allow the earth to host life over long periods of time), the following article states that “As an example, shifting your pencil from one side of your desk to the other today could change the gravitational forces on Jupiter enough to shift its position from one side of the Sun to the other a billion years from now.”,,,
Is the Solar System Stable? By Scott Tremaine – 2011 Excerpt: So what are the results? Most of the calculations agree that eight billion years from now, just before the Sun swallows the inner planets and incinerates the outer ones, all of the planets will still be in orbits very similar to their present ones. In this limited sense, the solar system is stable. However, a closer look at the orbit histories reveals that the story is more nuanced. After a few tens of millions of years, calculations using slightly different parameters (e.g., different planetary masses or initial positions within the small ranges allowed by current observations) or different numerical algorithms begin to diverge at an alarming rate. More precisely, the growth of small differences changes from linear to exponential:,,, As an example, shifting your pencil from one side of your desk to the other today could change the gravitational forces on Jupiter enough to shift its position from one side of the Sun to the other a billion years from now. The unpredictability of the solar system over very long times is of course ironic since this was the prototypical system that inspired Laplacian determinism. Fortunately, most of this unpredictability is in the orbital phases of the planets, not the shapes and sizes of their orbits, so the chaotic nature of the solar system does not normally lead to collisions between planets. However, the presence of chaos implies that we can only study the long-term fate of the solar system in a statistical sense, by launching in our computers an armada of solar systems with slightly different parameters at the present time—typically, each planet is shifted by a random amount of about a millimeter—and following their evolution. When this is done, it turns out that in about 1 percent of these systems, Mercury’s orbit becomes sufficiently eccentric so that it collides with Venus before the death of the Sun. Thus, the answer to the question of the stability of the solar system—more precisely, will all the planets survive until the death of the Sun—is neither “yes” nor “no” but “yes, with 99 percent probability.” https://www.ias.edu/about/publications/ias-letter/articles/2011-summer/solar-system-tremaine
Might I be so bold as to suggest that Liebniz, Newton, and even LaPlace would all be very impressed by the 'wisdom and power of God' that has been revealed by modern cosmology?
“Leibniz, in his controversy with Newton on the discovery of infinitesimal calculus, sharply criticized the theory of Divine intervention as a corrective of the disturbances of the solar system. “To suppose anything of the kind”, he said, “is to exhibit very narrow ideas of the wisdom and power of God’.” – Pierre-Simon Laplace
bornagain77_{September 24, 2020
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Ever since modern science was born in medieval Christian Europe, science has had a history of looking for ‘platonic perfection’, and assuming the Mind of God to be behind that ‘platonic perfection’. That is to say, that science has a history of reaching for perfect agreement between the immaterial mathematics that might describe a certain facet of this universe and the experimental results that measure those mathematical predictions of that facet, and assuming the Mind of God to be behind any perfect mathematical description of the universe that might be found. Copernicus, (who was heavily influenced by Platonic thinking), imagined (incorrectly) that the planets move in perfect circles (rather than ellipses). Later, Newton, for allowing God could adjust the orbits of the planets, was chastised by Leibniz, (and even Laplace) for having a “very narrow ideas about the wisdom and the power of God.”.. i.e. For having a narrow view of the perfection of God.
“Leibniz, in his controversy with Newton on the discovery of infinitesimal calculus, sharply criticized the theory of Divine intervention as a corrective of the disturbances of the solar system. “To suppose anything of the kind”, he said, “is to exhibit very narrow ideas of the wisdom and power of God’.” – Pierre-Simon Laplace
And indeed for most of the history of modern science in the Christian west, finding ‘platonic perfection’ for the mathematical descriptions of the universe has been a very elusive goal. For instance Newton's mathematical description of gravity could not take into account the precession of Mercury's orbit. That is to say that Newton's theory of Gravity was not a perfect mathematical description of the universe. This all changed with the discoveries of Special Relativity, General Relativity and Quantum Mechanics. That is to say, as far as experimental testing will allow, there is no discrepancy to be found between what the mathematical descriptions of Relativity and Quantum Mechanics predict for the universe and what our most advanced scientific testing of those predictions are able to measure.
“Recent experiments have confirmed, to within one part in one hundred million billion (10^17), that the speed of light does not change when an observer is in motion.” Douglas Ell – “Counting To God” – pg. 41 – 2014 “When this paper was published (referring to the circa 1970 Hawking, Penrose paper) we could only prove General Relativity’s reliability to 1% precision, today we can prove it to 15 places of decimal.” Hugh Ross PhD. Astrophysics – quote taken from 8:40 mark of the following video debate Hugh Ross vs Lewis Wolpert – Is there evidence for a Cosmic Creator https://www.youtube.com/watch?v=VLMrDO0_WvQ Introduction to The Strange World of Quantum Mechanics Excerpt: quantum mechanics is the most successful theory that humanity has ever developed; the brightest jewel in our intellectual crown. Quantum mechanics underlies our understanding of atoms, molecules, solids, and nuclei. It is vital for explaining aspects of stellar evolution, chemical reactions, and the interaction of light with matter. It underlies the operation of lasers, transistors, magnets, and superconductors. I could cite reams of evidence backing up these assertions, but I will content myself by describing a single measurement. One electron will be stripped away from a helium atom that is exposed to ultraviolet light below a certain wavelength. This threshold wavelength can be determined experimentally to very high accuracy: it is 50.425 929 9 ± 0.000 000 4 nanometers. The threshold wavelength can also be calculated from quantum mechanics: this prediction is 50.425 931 0 ± 0.000 002 0 nanometers. The agreement between observation and quantum mechanics is extraordinary. If you were to predict the distance from New York to Los Angeles with this accuracy, your prediction would be correct to within the width of your hand. In contrast, classical mechanics predicts that any wavelength of light will strip away an electron, that is, that there will be no threshold at all. - per oberlin edu Experimental non-classicality of an indivisible quantum system – Zeilinger 2011 Excerpt: Page 491: “This represents a violation of (Leggett’s) inequality (3) by more than 120 standard deviations, demonstrating that no joint probability distribution is capable of describing our results.” The violation also excludes any non-contextual hidden-variable model. The result does, however, agree well with quantum mechanical predictions, as we will show now.,,, https://vcq.quantum.at/fileadmin/Publications/Experimental%20non-classicality%20of%20an%20indivisible.pdf
As well, quantum electrodynamics (QED), which is a combination of special relativity and quantum mechanics, also now joins the list of perfect mathematical descriptions of the universe in which we can find no deviation from what the mathematics predict and what our best experimental testing can discern. In other words, as far as we can tell, ‘platonic perfection’ is reached for QED:
The Most Precisely Tested Theory in the History of Science – May 5, 2011 Excerpt: So, which of the two (general relativity or QED) is The Most Precisely Tested Theory in the History of Science? It’s a little tough to quantify a title like that, but I think relativity can claim to have tested the smallest effects. Things like the aluminum ion clock experiments showing shifts in the rate of a clock set moving at a few m/s, or raised by a foot, measure relativistic shifts of a few parts in 10^16. That is, if one clock ticks 10,000,000,000,000,000 times, the other ticks 9,999,999,999,999,999 times. That’s an impressively tiny effect, but the measured value is in good agreement with the predictions of relativity. In the end, though, I have to give the nod to QED, because while the absolute effects in relativity may be smaller, the precision of the measurements in QED is more impressive. Experimental tests of relativity measure tiny shifts, but to only a few decimal places. Experimental tests of QED measure small shifts, but to an absurd number of decimal places. The most impressive of these is the “anomalous magnetic moment of the electron,” expressed is terms of a number g whose best measured value is: g/2 = 1.001 159 652 180 73 (28) Depending on how you want to count it, that’s either 11 or 14 digits of precision (the value you would expect without QED is exactly 1, so in some sense, the shift really starts with the first non-zero decimal place), which is just incredible. And QED correctly predicts all those decimal places (at least to within the measurement uncertainty, given by the two digits in parentheses at the end of that). http://scienceblogs.com/principles/2011/05/05/the-most-precisely-tested-theo/ Bohemian Gravity – Rob Sheldon – September 19, 2013 Excerpt: Quanta magazine carried an article about a hypergeometric object that is as much better than Feynman diagrams as Feynman was better than Heisenberg’s S-matrices. But the discoverers are candid about it, “The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity. “Both are hard-wired in the usual way we think about things,” said Nima Arkani-Hamed, a professor of physics at the Institute for Advanced Study in Princeton, N.J., and the lead author of the new work, which he is presenting in talks and in a forthcoming paper. “Both are suspect.”” What are these suspect principles? None other than two of the founding principles of materialism–that there do not exist “spooky-action-at-a-distance” forces, and that material causes are the only ones in the universe.,,, http://rbsp.info/PROCRUSTES/bohemian-gravity/
As Nima Arkani-Hamed, the discoverer of the amplituhedron, stated “It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation.”,,,
Physicist: It’s Not The Answers We Lack, It’s The Question – February 24, 2019 Excerpt: “It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation. But what might such an explanation look like?” Nima Arkani-Hamed https://uncommondescent.com/intelligent-design/physicist-its-not-the-answers-we-lack-its-the-question/
Another very important place where ‘platonic perfection’ has now been found in the universe, (as far as our most precise testing will allow), is for the ‘flatness’ of the universe.
How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017 Excerpt: We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,, https://phys.org/news/2017-06-universe-flat-topology.html Why We Need Cosmic Inflation By Paul Sutter, Astrophysicist | October 22, 2018 Excerpt: As best as we can measure, the geometry of our universe appears to be perfectly, totally, ever-so-boringly flat. On large, cosmic scales, parallel lines stay parallel forever, interior angles of triangles add up to 180 degrees, and so on. All the rules of Euclidean geometry that you learned in high school apply. But there’s no reason for our universe to be flat. At large scales it could’ve had any old curvature it wanted. Our cosmos could’ve been shaped like a giant, multidimensional beach ball, or a horse-riding saddle. But, no, it picked flat. https://www.space.com/42202-why-we-need-cosmic-inflation.html “When a geometry is described by a set of axioms, the notion of a line is usually left undefined (a so-called primitive object).” per wikipedia
bornagain77_{September 24, 2020
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Carlo Rovelli stops short of saying that 2+2=5 but the article gives every sense that many would love to go there if only they could get some kind of a nudge.
I don't think many are eager to go there, actually. Certainly not Rovelli. But the question of whether the natural numbers exist independently of our minds is very interesting. Perhaps they are simply an artifact of the way our minds function? I can barely conceive of that, tbh. However, there are challenges to Platonism which I don't have a good response to as well.daveS_{September 24, 2020
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I'm wondering about the motivation behind this kind of chatter. Is someone just enjoying a flight of fancy? Is someone banking on "discovering" a new field of mathematics and being famous for it? Is someone trying to soothe the hurt feelings of innumerates? Is someone laying the groundwork for dismissing sound arguments when there's math involved? I think the last of these is the most dangerous. When disputes cannot be settled by reason, they will be settled by force.EvilSnack_{September 24, 2020
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As to establishing the objective existence of math,,, George Ellis takes the 'pragmatic view' of causation and existence, in which "If Y is a physical entity made up of ordinary matter, and X is some kind of entity that has a demonstrable causal effect on Y as per Definition 1, then we must acknowledge that X also exists (even if it is not made up of such matter)."
Recognising Top-Down Causation - George Ellis Excerpt: Causation: The nature of causation is highly contested territory, and I will take a pragmatic view: Definition 1: Causal Effect If making a change in a quantity X results in a reliable demonstrable change in a quantity Y in a given context, then X has a causal effect on Y.?Example: I press the key labelled “A” on my computer keyboard; the letter “A” appears on my computer screen.,,,? Definition 2: Existence If Y is a physical entity made up of ordinary matter, and X is some kind of entity that has a demonstrable causal effect on Y as per Definition 1, then we must acknowledge that X also exists (even if it is not made up of such matter).? This is clearly a sensible and testable criterion; in the example above, it leads to the conclusion that both the data and the relevant software exist. If we do not adopt this definition, we will have instances of uncaused changes in the world; I presume we wish to avoid that situation.,,, Causal Efficacy of Non Physical entities: Both the program and the data are non-physical entities, indeed so is all software. A program is not a physical thing you can point to, but by Definition 2 it certainly exists. You can point to a CD or flashdrive where it is stored, but that is not the thing in itself: it is a medium in which it is stored. The program itself is an abstract entity, shaped by abstract logic. Is the software “nothing but” its realisation through a specific set of stored electronic states in the computer memory banks? No it is not because it is the precise pattern in those states that matters: a higher level relation that is not apparent at the scale of the electrons themselves. It’s a relational thing (and if you get the relations between the symbols wrong, so you have a syntax error, it will all come to a grinding halt). This abstract nature of software is realised in the concept of virtual machines, which occur at every level in the computer hierarchy except the bottom one [17]. But this tower of virtual machines causes physical effects in the real world, for example when a computer controls a robot in an assembly line to create physical artefacts.,,, The mind is not a physical entity, but it certainly is causally effective: proof is the existence of the computer on which you are reading this text. It could not exist if it had not been designed and manufactured according to someone’s plans, thereby proving the causal efficacy of thoughts, which like computer programs and data are not physical entities. http://fqxi.org/data/essay-contest-files/Ellis_FQXI_Essay_Ellis_2012.pdf ?
And if we adopt Ellis's more than reasonable criteria for assessing whether a immaterial entity, such as logic and/or mathematics, exists, then we are forced to conclude that mathematics certainly exists. We are forced to this conclusion that mathematics must certainly exist simply by the 'real' causal effects that mathematics brings about in the world. As Peter Tyson pointed out, "Mathematics underlies virtually all of our technology today."
Describing Nature With Math By Peter Tyson – Nov. 2011 Excerpt: Mathematics underlies virtually all of our technology today. James Maxwell’s four equations summarizing electromagnetism led directly to radio and all other forms of telecommunication. E = mc2 led directly to nuclear power and nuclear weapons. The equations of quantum mechanics made possible everything from transistors and semiconductors to electron microscopy and magnetic resonance imaging. Indeed, many of the technologies you and I enjoy every day simply would not work without mathematics. When you do a Google search, you’re relying on 19th-century algebra, on which the search engine’s algorithms are based. When you watch a movie, you may well be seeing mountains and other natural features that, while appearing as real as rock, arise entirely from mathematical models. When you play your iPod, you’re hearing a mathematical recreation of music that is stored digitally; your cell phone does the same in real time. “When you listen to a mobile phone, you’re not actually hearing the voice of the person speaking,” Devlin told me. “You’re hearing a mathematical recreation of that voice. That voice is reduced to mathematics.” http://www.pbs.org/wgbh/nova/physics/describing-nature-math.html
Such technology simply would not be possible if mathematics were merely a 'invention' of man. Moreover, given that Godel's incompleteness theorem proves that mathematics cannot be a cause unto itself, then we are further forced to conclude that the Mind of God must be behind the causal efficacy that we witness in immaterial mathematics.
Taking God Out of the Equation - Biblical Worldview - by Ron Tagliapietra - January 1, 2012 Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties. 1. Validity ... all conclusions are reached by valid reasoning. 2. Consistency ... no conclusions contradict any other conclusions. 3. Completeness ... all statements made in the system are either true or false. The details filled a book, but the basic concept was simple and elegant. He (Godel) summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem. Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation. Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3). http://www.answersingenesis.org/articles/am/v7/n1/equation
Supplemental notes:
An Interview with David Berlinski - Jonathan Witt? Berlinski: There is no argument against religion that is not also an argument against mathematics. Mathematicians are capable of grasping a world of objects that lies beyond space and time…. Interviewer:… Come again(?) … Berlinski: No need to come again: I got to where I was going the first time. The number four, after all, did not come into existence at a particular time, and it is not going to go out of existence at another time. It is neither here nor there. Nonetheless we are in some sense able to grasp the number by a faculty of our minds. Mathematical intuition is utterly mysterious. So for that matter is the fact that mathematical objects such as a Lie Group or a differentiable manifold have the power to interact with elementary particles or accelerating forces. But these are precisely the claims that theologians have always made as well – that human beings are capable by an exercise of their devotional abilities to come to some understanding of the deity; and the deity, although beyond space and time, is capable of interacting with material objects. http://tofspot.blogspot.com/2013/10/found-upon-web-and-reprinted-here.html KEEP IT SIMPLE - Edward Feser - April 2020 Excerpt: Mathematics appears to describe a realm of entities with quasi-divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our experience lack. Mathematical objects seem immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order. How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect.,,, https://www.firstthings.com/article/2020/04/keep-it-simple July 2020 This view the mathematics exists “because they are God’s thoughts” and the Christian view that God created the universe and that the universe has not always existed, (as Aristotle had held), were necessary presuppositions for modern science to take root in Medieval Christian culture. https://uncommondescent.com/neuroscience/michael-egnor-talks-with-podcaster-lucas-skrobot-about-how-we-can-know-we-are-not-zombies/#comment-706254 BRUCE GORDON: Hawking’s irrational arguments – October 2010 Excerpt: ,,,The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,, Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.” Anything else invokes random miracles as an explanatory principle and spells the end of scientific rationality. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/ "You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way.. the kind of order created by Newton's theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the 'miracle' which is constantly reinforced as our knowledge expands. There lies the weaknesss of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but "bared the miracles." - Albert Einstein - Goldman - Letters to Solovine p 131. The Unreasonable Effectiveness of Mathematics in the Natural Sciences - Eugene Wigner - 1960 Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.,,, It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind's capacity to divine them.,,, The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. - per Dartmouth edu
Verse and quote:
John 1:1 “In the beginning was the Word, and the Word was with God, and the Word was God” What is the Logos? Logos is a Greek word literally translated as “word, speech, or utterance.” However, in Greek philosophy, Logos refers to divine reason or the power that puts sense into the world making order instead of chaos.,,, In the Gospel of John, John writes “In the beginning was the Word (Logos), and the Word was with God, and the Word was God” (John 1:1). John appealed to his readers by saying in essence, “You’ve been thinking, talking, and writing about the Word (divine reason) for centuries and now I will tell you who He is.” https://www.compellingtruth.org/what-is-the-Logos.html
bornagain77_{September 24, 2020
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It is the same old question of whether we "develop" or "discover" math. I am firmly in the camp that we discover it (as the Designer was kind enough to give us the ability. He did not give the same ability to animals). This then allows us to start understanding the grand design of our world, as it is all based on math. Obviously the Designer knows math. The aliens from Jupiter would know the exact same math. The statements like "Rovelli believes that math “works” because we crafted it for its usefulness." are from the people in that other camp, who believe that we "develop" math, and it just so happens to also describe everything in our world. What a convenient coincidence!Eugene_{September 23, 2020
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