An interview on God and mathematics

_{Denyse O'Leary

January 17, 2021

Intelligent Design, Mathematics, theism}

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Some of us think mathematics is the best argument for God available. Anyway, here’s Jerry Bowyer’s interview with philosopher Vern Poythress:

The standard modern culture-war revolves around God vs. the mathematical sciences. Take your choice: Faith or physics. Then there are the voices of mutual toleration, which attempt to leave room for science among the faithful and for faith among the scientific. Poythress, though, taps into a different tradition entirely, one which is seldom heard in modern debate: That God and science are neither enemies, nor partners, but rather that God is the necessary foundation for mathematics and therefore of every science which uses it.
The argument is that mathematical laws, in order to be properly relied upon, must have attributes which indicate an origin in God. They are true everywhere (omnipresent), true always (eternal), cannot be defied or defeated (omnipotent), and are rational and have language characteristics (which makes them personal). Omnipresent, omnipotent, eternal, personal… Sounds like God. Math is an expression of the mind of God. Sound strange? It isn’t. Modern natural science was created by people who said that they were trying to “think God’s thoughts after Him.”
Jerry Bowyer, “God In Mathematics” at Forbes

See also: Things exist that are unknowable: A tutorial on Chaitin’s number

Hat tip: Philip Cunningham

Comments

Thanks! Yeah though I walk through the valley of innumeracy, I shall fear no fallacies. My theorems and axioms comfort me.
I shall tighten my Gödel and... Oh ****Bob O'H_{January 18, 2021
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Viola Lee: Good luck, JVL. Thanks! Yeah though I walk through the valley of innumeracy, I shall fear no fallacies. My theorems and axioms comfort me.JVL_{January 18, 2021
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ET: In a mechanistic scenario “who knows?” is death. No, it just means we haven't figure it out yet. Question begging. It's not question begging unless you have predetermined assumptions. I'm asking: could intelligent agents have existed before mathematics? AND, are they subject to the laws of mathematics? Who knows? What do you think? Cause only pertains to things that had a beginning Does math have a beginning? If you think that math was created by some designer then your answer would be yes. The ultimate designer 'caused' math. Is that ultimate designer constrained by the laws of mathematics? If no then the laws of mathematics are not universal and invariant. If yes, the designer is constrained by the laws of mathematics, then wouldn't it have had to come into existence AFTER the laws of mathematics were already in existence?JVL_{January 18, 2021
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Viola Lee/20
As a math teacher, I’m sorry to hear that! ? I think I’ve made it fun, interesting, and/or satisfying for a lot of students. Sorry you had such bad experiences.
I don't blame you or other math teachers. I know I was just unlucky. I'm sure you work very hard to make your lessons fun and interesting. My mother was a teacher of 5-7 year-olds and I know she also worked very hard to make the lessons fun and interesting for her students. She told me that one of her most satisfying experiences as a teacher was to suddenly see the light of understanding dawn in the eyes of a child who had struggled to grasp something for so longSeversky_{January 18, 2021
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Head, meet brick wall. Good luck, JVL.Viola Lee_{January 18, 2021
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Bornagain77: JVL gets his questioned answered and refuses to acknowledge it. You didn't answer my question actually. You repeated and misinterpreted a lot of statements about Godel's incompleteness theorem but you didn't actually say whether or not mathematics could have existed before intelligent agents. Perhaps you think you answered the question because you think Godel's theorems imply some God-like being. But they don't. They are merely a statement about what is logically possible given a set of axioms. There's no God there. Argue with someone else JVL, I have better things to do. Like arguing with a brick wall. At least a brick wall won't disagree with you eh? You seem to get very annoyed when anyone disagrees with you. Godel, with his incompleteness theorem(s) dropped a bomb on the foundation of mathematics and proved that mathematics could not provide a foundation for its own existence. i.e. Godel’s incompleteness proves that mathematics is contingent in its existence, not necessary! That is not correct. From Wikipedia:
Gödel published his incompleteness theorems in Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme (called in English "On Formally Undecidable Propositions of Principia Mathematica and Related Systems"). In that article, he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g., the Peano axioms or Zermelo–Fraenkel set theory with the axiom of choice), that: If a (logical or axiomatic formal) system is consistent, it cannot be complete. The consistency of axioms cannot be proved within their own system.
That is not saying a system is contingent at all. You and others always misinterpret the theorems. Axioms are what you ASSUME to be true. They are not contingent on anything. AND, not being able to 'prove' a foundation does not give you a God-like being. It just doesn't. That's your interpretation. As Ron Tagliapietra succinctly put it, “Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous.” No one says math is playing the role of God. Honestly, theologians should not talk about mathematics unless they are trained in it. You don't hear . . . famous apologist, English, trained mathematician . . . can't remember his name! Anyway, you don't hear him make arguments like that. All I asked was: could it have been around before any intelligent beings? If it's invariant then it's true always and forever . . . Just how ‘shocking’, and humbling, Godel’s incompleteness theorem actually was, and is, to atheistic mathematicians is nicely summarized in the following video and article: Nothing about God in there because it has nothing to do with theology! Second problem for JVL, the ‘necessitarian’ view of mathematics that he champions actually prevented the rise of modern science. It was only by overcoming the necessitarian view of mathematics of the Ancient Greek philosophers, and viewing mathematics, especially any mathematics that might describe this universe, as being the product of the Mind of God, that modern science was finally able to sprout, take root, and eventually blossom in medieval Christian Europe: Sigh. During the Dark Ages some people were still producing new mathematics. It has NOTHING to do with a view on God. It's not based on any kind of theology whatsoever. It just takes some curiosity, good pattern recognition and the ability to think a bit abstractly. What did happen was that, for a long time, being educated was not valued or even practical. For a vast majority of Europeans it was not an option. THAT'S why science and math faltered in Europe. Not so in Baghdad or Beijing, non-Christian cultures. Remember too that Greek and Egyptians helped get the ball rolling in the first place. Every proven mathematical theorem from 2000 years ago is still true. Math does not retreat or back away. You don't need to start over as you do with physics and chemistry. It doesn't work that way. As Edward Fesser notes in the following article, for Christian scholastic philosophers of the medieval period “Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts,” whereas for ancient Greek philosophers, “mathematical objects such as numbers and geometrical figures exist not only independently of the material world, but also independently of any mind,” The Christian scholars put that spin on it because they were fascinated by questions like: how many angels can dance on the head of a pin. C'mon! The Greeks discovered irrational numbers! They may have even been edging towards Calculus. The notion that math stopped because of the Greek view is just rubbish. The math stopped because the culture of learning stopped and there were no more classes and lectures on mathematics. In the minds of the Christian founders of modern science, mathematics, especially any mathematics that might describe the universe, were certainly not held to be necessary, but were instead held to be contingent upon God’s thoughts. A theological veneer of rationalisation doesn't make it so. Almost all people with a philosophical bent during the medieval period thought they saw God in everything. Again, just because some people thought math represented God's thoughts doesn't make it so. AND, for centuries, the only people who could read or write or had the time to do anything other than survive and fight wars were monks and nuns. And you think their religious bias means it was only by viewing God in every equation and leaf and creature that science progressed? Really? I guess you haven't ever even considered or looked up what other cultures have contributed to science and mathematics. Perhaps the best example that I can give for the fact that the Christian founders of modern science held mathematics, especially any mathematics that might describe the universe, to be God’s thoughts is the following quote by Kepler, (which he made shortly after discovering the laws of planetary motion),, Again, that doesn't make it so. Nor does it say that Kepler WOULDN'T have done what he did if he thought he wasn't chasing God. He was trying to solve a problem, an empirical, famous problems. AND, guess what, he came to a conclusion different from what most theologians thought at the time. So, you're saying Christian thought created modern science even though science contradicted a lot of Christian philosophy. Really? Thus for modern day theoretical physicists. i.e. string theorists and the like, to take a necessatarian view of mathematics, instead of taking a contingent view of mathematics, in which mathematics is dependent upon the Mind of God for its existence, is for them to take a gigantic step backwards into ancient Greek philosophy. Uh huh. What about Quantum Mechanics? What about Relativity? What about Cantor's work? And Euler? And Gauss? And Newton himself who figured out that orbits are ellipses. Where in theology does that come from? It doesn't. I guess regressing back into the stagnation that the necessitarian view of mathematics, that the ancient Greeks held, is far better for him than for him to ever honestly admit that God exists. It's not holding back math and science at all. Because most mathematicians and scientists don't even think about such things. They just do the work and find stuff. You think because almost everyone who was alive in Europe during the Middle Ages (especially all those who could read or write) were Christians and claimed to be trying to find God's thoughts in the world that that made a difference in what they chose to work on or what they found? I don't think it made a blind bit of difference except that the Church had the money and the time to teach at least some of its followers to read and write. They gave them access to Greek and Roman texts so those scholars started out with the Greek and Roman mind-sets. Which they then laid a God-interpretation onto. But that didn't make any difference to the work. The Fibonacci numbers were not 'discovered' because someone was trying to find the hand of God.JVL_{January 18, 2021
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JVL:
Who knows?
In a mechanistic scenario "who knows?" is death.
How could intelligent agents arise before mathematics?
Question begging.
How could intelligent agents just be around without coming from somewhere?
Who knows?
Or does cause and effect end some time going backwards?
Cause only pertains to things that had a beginningET_{January 18, 2021
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Sev writes, "I recognize the power and value of mathematics but, after my traumatic experiences of being taught it in school, I came to loathe the subject. If God is anything like the math teachers I encountered it would explain a lot about the world. ?" As a math teacher, I'm sorry to hear that! :-( I think I've made it fun, interesting, and/or satisfying for a lot of students. Sorry you had such bad experiences.Viola Lee_{January 18, 2021
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JVL gets his questioned answered and refuses to acknowledge it. Argue with someone else JVL, I have better things to do. Like arguing with a brick wall.bornagain77_{January 18, 2021
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Bornagain77: So I guess JVL’s argument, (in so far as you can even call it an argument), boils down to, “Never mind that I have absolutely no clue how the materialistic processes of Darwinian evolution can possibly create intelligent creatures with a unique capacity to understand and use this immaterial ‘platonic’ realm of mathematics, I still hold that mathematics itself has a necessary existence and that mathematics itself is not contingent upon anything else, especially the Mind of God, for it’s existence. First of all, I am not making an argument, just asking a question. That question is: if mathematics is universal and invariant then why should it not have existed before any intelligent agents? AND: are all intelligent agents subject to the laws of mathematics? Why or why not? There are many other points in your reply I'd like to address but you'll have to wait as it's make-dinner-time in my household. But I shall return to answer more points.JVL_{January 18, 2021
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JVL asks "Why couldn’t it (mathematics) exist before there were intelligent agents?" So I guess JVL's argument, (in so far as you can even call it an argument), boils down to, "Never mind that I have absolutely no clue how the materialistic processes of Darwinian evolution can possibly create intelligent creatures with a unique capacity to understand and use this immaterial 'platonic' realm of mathematics, I still hold that mathematics itself has a necessary existence and that mathematics itself is not contingent upon anything else, especially the Mind of God, for it's existence. There are a couple of problems with JVL's desperate attempt to exclude God as the necessary Being upon which all contingent reality, including mathematics, exists. First problem, Godel's incompleteness theorem(s)
THE GOD OF THE MATHEMATICIANS - DAVID P. GOLDMAN - August 2010 Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel's critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes. http://www.firstthings.com/article/2010/08/the-god-of-the-mathematicians
Godel, with his incompleteness theorem(s) dropped a bomb on the foundation of mathematics and proved that mathematics could not provide a foundation for its own existence. i.e. Godel's incompleteness proves that mathematics is contingent in its existence, not necessary! As Ron Tagliapietra succinctly put it, "Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous."
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#
Just how 'shocking', and humbling, Godel's incompleteness theorem actually was, and is, to atheistic mathematicians is nicely summarized in the following video and article:
Cantor, Gödel, & Turing: Incompleteness of Mathematics - video (excerpted from BBC's 'Dangerous Knowledge' documentary) https://www.facebook.com/philip.cunningham.73/videos/vb.100000088262100/1119397401406525/?type=2&theater Mathematicians Bridge Finite-Infinite Divide - May 24, 2016 A surprising new proof is helping to connect the mathematics of infinity to the physical world. Excerpt: Hilbert tasked mathematicians with proving that set theory and all of infinitistic mathematics is finitistically reducible, and therefore trustworthy. “We must know; we will know!” he said in a 1930 address in Königsberg — words later etched on his tomb. However, the Austrian-American mathematician Kurt Gödel showed in 1931 that, in fact, we won’t. In a shocking result, Gödel proved that no system of logical axioms (or starting assumptions) can ever prove its own consistency; to prove that a system of logic is consistent, you always need another axiom outside of the system. This means there is no ultimate set of axioms — no theory of everything — in mathematics. When looking for a set of axioms that yield all true mathematical statements and never contradict themselves, you always need another axiom. Gödel’s theorem meant that Hilbert’s program was doomed: The axioms of finitistic mathematics cannot even prove their own consistency, let alone the consistency of set theory and the mathematics of the infinite. https://www.quantamagazine.org/20160524-mathematicians-bridge-finite-infinite-divide/
Second problem for JVL, the 'necessitarian' view of mathematics that he champions actually prevented the rise of modern science. It was only by overcoming the necessitarian view of mathematics of the Ancient Greek philosophers, and viewing mathematics, especially any mathematics that might describe this universe, as being the product of the Mind of God, that modern science was finally able to sprout, take root, and eventually blossom in medieval Christian Europe:
The War against the War Between Science and Faith Revisited - July 2010 Excerpt: If science suffered only stillbirths in ancient cultures, how did it come to its unique viable birth? The beginning of science as a fully fledged enterprise took place in relation to two important definitions of the Magisterium of the Church. The first was the definition at the Fourth Lateran Council in the year 1215, that the universe was created out of nothing at the beginning of time. The second magisterial statement was at the local level, enunciated by Bishop Stephen Tempier of Paris who, on March 7, 1277, condemned 219 Aristotelian propositions, so outlawing the deterministic and necessitarian views of creation. These statements of the teaching authority of the Church expressed an atmosphere in which faith in God had penetrated the medieval culture and given rise to philosophical consequences. The cosmos was seen as contingent in its existence and thus dependent on a divine choice which called it into being; the universe is also contingent in its nature and so God was free to create this particular form of world among an infinity of other possibilities. Thus the cosmos cannot be a necessary form of existence; and so it has to be approached by a posteriori investigation. The universe is also rational and so a coherent discourse can be made about it. Indeed the contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos. http://www.scifiwright.com/2010/08/the-war-against-the-war-between-science-and-faith-revisited/
As Edward Fesser notes in the following article, for Christian scholastic philosophers of the medieval period “Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts,” whereas for ancient Greek philosophers, “mathematical objects such as numbers and geometrical figures exist not only independently of the material world, but also independently of any mind,”
KEEP IT SIMPLE – by 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. There is also a very different answer, in which the mathematical realm is a rival to God rather than a path to him. According to this view, mathematical objects such as numbers and geometrical figures exist not only independently of the material world, but also independently of any mind, including the divine mind. They occupy a “third realm” of their own, the realm famously described in Plato’s Theory of Forms. God used this third realm as a blueprint when creating the physical world, but he did not create the realm itself and it exists outside of him. This position is usually called Platonism since it is commonly thought to have been Plato’s own view, as distinct from that of his Neoplatonic followers who relocated mathematical objects and other Forms into the divine mind. (I put to one side for present purposes the question of how historically accurate this standard narrative is.) https://www.firstthings.com/article/2020/04/keep-it-simple
In the minds of the Christian founders of modern science, mathematics, especially any mathematics that might describe the universe, were certainly not held to be necessary, but were instead held to be contingent upon God’s thoughts. As Ian H. Hutchinson notes in the following article on Faraday and Maxwell, “Lawfulness was not, in their thinking, inert, abstract, logical necessity, or complete reducibility to Cartesian mechanism; rather, it was an expectation they attributed to the existence of a divine lawgiver.”
The Genius and Faith of Faraday and Maxwell – Ian H. Hutchinson – 2014 Conclusion: Lawfulness was not, in their thinking, inert, abstract, logical necessity, or complete reducibility to Cartesian mechanism; rather, it was an expectation they attributed to the existence of a divine lawgiver. These men’s insights into physics were made possible by their religious commitments. For them, the coherence of nature resulted from its origin in the mind of its Creator. http://www.thenewatlantis.com/publications/the-genius-and-faith-of-faraday-and-maxwell
Perhaps the best example that I can give for the fact that the Christian founders of modern science held mathematics, especially any mathematics that might describe the universe, to be God’s thoughts is the following quote by Kepler, (which he made shortly after discovering the laws of planetary motion),,
“O, Almighty God, I am thinking Thy thoughts after Thee!” – Johannes Kepler, 1619, The Harmonies of the World.
Thus for modern day theoretical physicists. i.e. string theorists and the like, to take a necessatarian view of mathematics, instead of taking a contingent view of mathematics, in which mathematics is dependent upon the Mind of God for its existence, is for them to take a gigantic step backwards into ancient Greek philosophy. A philosophy that impeded modern science from having a viable birth in the first place. As I stated previously, the birth of modern science was only possible with the ‘outlawing’ of that ‘necessatarian’ view of mathematics that the ancient Greeks had championed. But alas for JVL, being the dogmatic anti-Theist that he is, I guess regressing back into the stagnation that the necessitarian view of mathematics, that the ancient Greeks held, is far better for him than for him to ever honestly admit that God exists. It is a crying shame! Of supplemental note, the rejection of the Greeks necessitarian view of mathematics, (and the universe), besides giving birth to modern science, represented nothing less than a brand new form of 'inductive' reasoning over and above the deductive reasoning of the ancient Greeks
June 2020 - This new form of inductive reasoning, which led to the birth of the scientific method itself, apparently took a while to take hold in Medieval Christian Europe but this new form of reasoning was eventually, and famously, elucidated and championed by Francis Bacon in 1620 in his book that was entitled Novum Organum. Which is translated as ‘New Method’. In the title of that book, Bacon is specifically referencing Aristotle’s work Organon, which was Aristotle’s treatise on logic and syllogism. In other words, Organum was basically Aristotle’s treatise on deductive reasoning. https://uncommondescent.com/philosophy/asked-at-areo-magazine-did-the-catholic-church-give-birth-to-science/#comment-703354
bornagain77_{January 18, 2021
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JVL/1
Maybe there is no God, only mathematics? We know mathematics exists, do we know God exists?
That may explain why I have become agnostic/atheist. I recognize the power and value of mathematics but, after my traumatic experiences of being taught it in school, I came to loathe the subject. If God is anything like the math teachers I encountered it would explain a lot about the world. :-)Seversky_{January 18, 2021
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ET: How? Who knows? How could intelligent agents arise before mathematics? You don't know. You don’t know that. How could intelligent agents just be around without coming from somewhere? Or does cause and effect end some time going backwards?JVL_{January 18, 2021
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JVL:
Why couldn’t it exist before there were intelligent agents?
How?
After all, the intelligent agents had to come from somewhere too . . . didn’t they?
You don't know that.ET_{January 18, 2021
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ET: Mathematics came from somewhere. An we only know of one source- intelligent agencies. Why couldn't it exist before there were intelligent agents? After all, the intelligent agents had to come from somewhere too . . . didn't they?JVL_{January 18, 2021
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Mathematics came from somewhere. An we only know of one source- intelligent agencies.ET_{January 18, 2021
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Kairosfocus: The notion that one needs particular reference to some authority or other on such commonplace facts of the case, speaks. It could be I was just making a joke . . . or, it could be I was making a point. Or both.JVL_{January 18, 2021
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:-)Viola Lee_{January 18, 2021
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JVL, it is well known that it is part of the inherent nature of God that he is source and creator of everything that has been made. The issue would be whether God is, and as God is a necessary being at least as a serious candidate, to argue that he is not, is tantamount to arguing that God is impossible of being. The notion that one needs particular reference to some authority or other on such commonplace facts of the case, speaks. KFkairosfocus_{January 18, 2021
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Polistra: God MADE everything. References?JVL_{January 18, 2021
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Viola Lee: BA’s reply doesn’t follow. Not believing in God does not necessarily mean that one believes in a materialistic explanation for math: those are not the only two possibilities. Maybe he's just following one of mathematics' basic techniques: when you come across a problem you don't know how to solve see if you can transform it into one you do know how to solve. A kind of substitution technique. But then you have to do the reverse substitution afterwards.JVL_{January 18, 2021
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Bornagain77: But alas for JVL’s atheistic druthers, the existence of Mathematics itself is simply devastating to any materialistic and/or naturalistic explanation of Darwinian evolution since mathematics itself exists in a immaterial, beyond space and time, realm. A eternal “Platonic Realm” that simply is not reducible to any possible materialistic explanation. Well, where is it then? If you can't see it or point to it or visit it how do you know it exists? The fact that there is a structure to the universe which can be fairly well described by mathematics may just be due to the very basic building blocks of the universe. No undetectable Platonic realm, just a bunch of marginally intelligent creatures noticing and remembering patterns, learning to write them down, come up with generalised versions of them and extrapolating. You don’t have to have a PhD to understand why the materialistic explanations of Darwinian evolution cannot ever possibly explain man’s unique ability to ‘do mathematics’. Mathematics itself simply does not need the physical world in order for it to exist. No, but I proposed that man's journey of mathematical discovery first came from observing physical phenomena. Oh, by the way, some animals seem to be able to do some basic, crude mathematics. And I expect if there are intelligent aliens they will be able to 'do' mathematics as well. So maybe we're not so unique in that sense.JVL_{January 18, 2021
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VL, as I stated, my argument follows only "if a Darwinist were to try to be consistent in his arguments, (which would be a miracle in its own right), " :) As I've learned over the years, logical consistency is certainly not a top priority for Darwinists in their arguments. For instance, there is this self-refuting beauty from Coyne
THE ILLUSION OF FREE WILL - Sam Harris - 2012 Excerpt: "Free will is an illusion so convincing that people simply refuse to believe that we don’t have it." - Jerry Coyne https://samharris.org/the-illusion-of-free-will/
bornagain77_{January 18, 2021
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These parallel attributes are interesting but they miss the ONLY important and scientifically verifiable attribute of God. God MADE everything. Math doesn't make things. Math only describes things, in a way that can sometimes inspire people to make more things. (Useful formulas = useful parables). If you're going to 'personalize' math, it would be more like a prophet than a god, more like Moses or Jesus or Mohammed.polistra_{January 18, 2021
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At 1, JVL said: "Maybe there is no God, only mathematics? We know mathematics exists, do we know God exists?" BA replied,
But alas for JVL’s atheistic druthers, the existence of Mathematics itself is simply devastating to any materialistic and/or naturalistic explanation of Darwinian evolution since mathematics itself exists in a immaterial, beyond space and time, realm. A eternal “Platonic Realm” that simply is not reducible to any possible materialistic explanation.
BA's reply doesn't follow. Not believing in God does not necessarily mean that one believes in a materialistic explanation for math: those are not the only two possibilities. For instance, there are Platonists who nevertheless do not believe in a personal God. They do believe a world of Platonic mathematical forms imprints themselves on the physical world without a personal divine diety being involved. I know BA has many thousands of words prepared to support his belief in God, which I am not interested in. I just think he should be aware of, and acknowledge, that his theism/materialism dichotomy doesn't cover all the ground.Viola Lee_{January 18, 2021
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JVL states that,
Maybe there is no God, only mathematics? We know mathematics exists, do we know God exists?
So it appears that JVL is willing to believe in the "Platonic realm' of mathematics just so long as he does not have to believe in God??? But alas for JVL's atheistic druthers, the existence of Mathematics itself is simply devastating to any materialistic and/or naturalistic explanation of Darwinian evolution since mathematics itself exists in a immaterial, beyond space and time, realm. A eternal “Platonic Realm” that simply is not reducible to any possible materialistic explanation.
Platonic mathematical world – image http://abyss.uoregon.edu/~js/images/platonic_physical.gif
Hey, you don't have to take my word for it. In 2014, a group of Darwinists, who are leading experts in this area of research, authored a paper in which they honestly admitted that they have, "essentially no explanation of how and why our linguistic computations and representations evolved."
Leading Evolutionary Scientists Admit We Have No Evolutionary Explanation of Human Language - December 19, 2014 Excerpt: Understanding the evolution of language requires evidence regarding origins and processes that led to change. In the last 40 years, there has been an explosion of research on this problem as well as a sense that considerable progress has been made. We argue instead that the richness of ideas is accompanied by a poverty of evidence, with essentially no explanation of how and why our linguistic computations and representations evolved.,,, (Marc Hauser, Charles Yang, Robert Berwick, Ian Tattersall, Michael J. Ryan, Jeffrey Watumull, Noam Chomsky and Richard C. Lewontin, "The mystery of language evolution," Frontiers in Psychology, Vol 5:401 (May 7, 2014).) Casey Luskin added: “It's difficult to imagine much stronger words from a more prestigious collection of experts.” http://www.evolutionnews.org/2014/12/leading_evoluti092141.html
You don't have to have a PhD to understand why the materialistic explanations of Darwinian evolution cannot ever possibly explain man's unique ability to 'do mathematics'. Mathematics itself simply does not need the physical world in order for it to exist. As Dr. Michael Egnor put it, “Mathematics is entirely about concepts, which have no precise instantiation in nature,,,”
Naturalism and Self-Refutation – Michael Egnor – January 31, 2018 Excerpt: Mathematics is certainly something we do. Is mathematics “included in the space-time continuum [with] basic elements … described by physics”?,,, What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? Mathematics is entirely about concepts, which have no precise instantiation in nature,,, Furthermore, the very framework of Clark’s argument — logic — is neither material nor natural. Logic, after all, doesn’t exist “in the space-time continuum” and isn’t described by physics. What is the location of modus ponens? How much does Gödel’s incompleteness theorem weigh? What is the physics of non-contradiction? How many millimeters long is Clark’s argument for naturalism? Ironically the very logic that Clark employs to argue for naturalism is outside of any naturalistic frame. The strength of Clark’s defense of naturalism is that it is an attempt to present naturalism’s tenets clearly and logically. That is its weakness as well, because it exposes naturalism to scrutiny, and naturalism cannot withstand even minimal scrutiny. Even to define naturalism is to refute it. https://evolutionnews.org/2018/01/naturalism-and-self-refutation/
That is to say that mathematics, in its foundational nature, is immaterial, i.e. transcendent of space, time, matter and energy. This creates an insurmountable difficultly for Darwinian materialists who, via their theory, try to reduce everything to purely materialistic explanations. As M. Anthony Mills explains, “And yet — here’s the rub — these “abstract (mathematical) objects” are not material. Thus, one cannot take science as the only sure guide to reality and at the same time discount disbelief in all immaterial realities.”
What Does It Mean to Say That Science & Religion Conflict? – M. Anthony Mills – April 16, 2018 Excerpt: Barr rightly observes that scientific atheists often unwittingly assume not just metaphysical naturalism but an even more controversial philosophical position: reductive materialism, which says all that exists is or is reducible to the material constituents postulated by our most fundamental physical theories. As Barr points out, this implies not only that God does not exist — because God is not material — but that you do not exist. For you are not a material constituent postulated by any of our most fundamental physical theories; at best, you are an aggregate of those constituents, arranged in a particular way. Not just you, but tables, chairs, countries, countrymen, symphonies, jokes, legal contracts, moral judgments, and acts of courage or cowardice — all of these must be fully explicable in terms of those more fundamental, material constituents. In fact, more problematic for the materialist than the non-existence of persons is the existence of mathematics. Why? Although a committed materialist might be perfectly willing to accept that you do not really exist, he will have a harder time accepting that numbers do not exist. The trouble is that numbers — along with other mathematical entities such as classes, sets, and functions — are indispensable for modern science. And yet — here’s the rub — these “abstract objects” are not material. Thus, one cannot take science as the only sure guide to reality and at the same time discount disbelief in all immaterial realities. https://www.realclearreligion.org/articles/2018/04/16/what_does_it_mean_to_say_that_science_and_religion_conflict.html
Now if a Darwinist were to try to be consistent in his arguments, (which would be a miracle in its own right), then he could try to argue that mathematics is merely a abstract invention of man that does not really have an objective existence in the 'real' world of material and/or physical objects. Yet, as George Ellis pointed out, non-material entities are shown to be objectively real in that they bring about 'real' effects in the physical world. This simply would not be possible If mathematics, (and logic), were merely abstract inventions of man that had no 'real' and objective existence: As George Ellis himself states, "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.,,, 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."
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.,,, ,,,However there are many topics that one cannot understand by assuming this one-way flow of causation. The flourishing subject of social neuroscience makes clear how social influences act down on individual brain structure[2]; studies in physiology demonstrate that downward causation is necessary in understanding the heart, where this form of causation can be represented as the influences of initial and boundary conditions on the solutions of the differential equations used to represent the lower level processes[3]; epigenetic studies demonstrate that biological development is crucially shaped by the environment[4] What about physics? In this essay I will make the case that top-down causation is also prevalent in physics, even though this is not often recognised as such. This does not occur by violating physical laws; on the contrary, it occurs through the laws of physics, by setting constraints on lower level interactions. Excerpt: page 5: A: 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.,,,, Life and the brain: living systems are highly structured modular hierarchical systems, and there are many similarities to the digital computer case, even though they are not digital computers. The lower level interactions are constrained by network connections, thereby creating possibilities of truly complex behaviour. Top-down causation is prevalent at all levels in the brain: for example it is crucial to vision [24,25] as well as the relation of the individual brain to society [2]. The hardware (the brain) can do nothing without the excitations that animate it: indeed this is the difference between life and death. 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
Indeed, our most stunning, almost 'miraculous', modern technological innovations would not even be possible were it not for the ability of 'immaterial' mathematics to objectively bring about 'real' effects in the material/physical world.
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
Moreover, the fact that man himself has access to, and can use, this transcendent, beyond space and time, immaterial world of mathematics, to bring about 'real' effects' in the material world, offers compelling evidence, in and of itself, that man in not a purely material being but that man must also possess a transcendent, beyond space and time, immaterial mind and/or soul. We simply could never discover, or use, these ‘eternal’ truths about mathematics unless we ourselves first possessed a transcendent, and 'eternal', component to our being,, i.e. a immaterial soul and/or mind that is not reducible to the material constituents of our material bodies, (as Darwinists presuppose). As Charles Darwin’s contemporary, Alfred Russel Wallace himself stated, “Nothing in evolution can account for the soul of man. The difference between man and the other animals is unbridgeable. Mathematics is alone sufficient to prove in man the possession of a faculty unexistent in other creatures. Then you have music and the artistic faculty. No, the soul was a separate creation.”
“Nothing in evolution can account for the soul of man. The difference between man and the other animals is unbridgeable. Mathematics is alone sufficient to prove in man the possession of a faculty unexistent in other creatures. Then you have music and the artistic faculty. No, the soul was a separate creation.” Alfred Russel Wallace – 1910
And again, Darwinists simply have no clue why we should have access to the immaterial realm of mathematics. As Dr. Michael Egnor pointed out, because of our unique ability to think abstractly among all creature on earth, "We are more different from apes than apes are from viruses. Our difference is a metaphysical chasm."
The Fundamental Difference Between Humans and Nonhuman Animals Michael Egnor - November 5, 2015 Excerpt: Human beings have mental powers that include the material mental powers of animals but in addition entail a profoundly different kind of thinking. Human beings think abstractly, and nonhuman animals do not. Human beings have the power to contemplate universals, which are concepts that have no material instantiation. Human beings think about mathematics, literature, art, language, justice, mercy, and an endless library of abstract concepts. Human beings are rational animals. Human rationality is not merely a highly evolved kind of animal perception. Human rationality is qualitatively different — ontologically different — from animal perception. Human rationality is different because it is immaterial. Contemplation of universals cannot have material instantiation, because universals themselves are not material and cannot be instantiated in matter.,,, We are more different from apes than apes are from viruses. Our difference is a metaphysical chasm. https://evolutionnews.org/2015/11/the_fundamental_2/
Moreover, since our own immaterial minds came into being and are therefore contingent, and are not eternally existent, and yet we can discover these eternal mathematical truths with our immaterial minds, then it necessarily follows that “there must exist an eternal mind in which these eternal (mathematical) truths reside.”
11. The Argument from Truth This argument is closely related to the argument from consciousness. It comes mainly from Augustine. 1. Our limited minds can discover eternal truths about being. 2. Truth properly resides in a mind. 3. But the human mind is not eternal. 4. Therefore there must exist an eternal mind in which these truths reside. https://www.peterkreeft.com/topics-more/20_arguments-gods-existence.htm#11
And please note that this argument for our immaterial minds, and for God, from the existence of mathematics is perfectly consistent with what we now know to be true about mathematics from Godel’s incompleteness theorem. Namely, that mathematics itself has a contingent existence and does not have a necessary existence,
Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything in his theorem that: “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”. Thus, based on the position that an equation cannot prove itself, the constructs are based on assumptions some of which will be unprovable.” - Stephen Hawking & Leonard Miodinow, The Grand Design (2010)
Thus, mathematics itself offers us compelling proof that we ourselves must possess immaterial minds and/or souls, and also offers us compelling proof that God must exist. And despite to how badly atheists may want God, (and our eternal souls), to not exist (for whatever severely misguided reason), the fact the matter is that, since we are all destined to die here on this earth, the undeniable fact that we must have eternal minds/souls in order to even 'do mathematics' in the first place, minds/souls that are not reducible to the material constituents of our temporal bodies, i.e. transcendent souls that can live beyond the death of our temporal bodies, is extremely good news for us the hear personally,,, I know that I myself am personally very happy to know it to be undeniably true, and that death does not have the final say in regards to my own life, and in regards to the lives of loved ones, and that I, and my loved ones, i.e. our eternal souls and minds, will continue to live, even though our material, temporal, bodies will perish,, Verses:
1 Corinthians 15:54-55 When the perishable has been clothed with the imperishable and the mortal with immortality, then the saying that is written will come to pass: “Death has been swallowed up in victory.” “Where, O Death, is your victory? Where, O Death, is your sting?” Mark 8:37 Is anything worth more than your soul? John 3:16 For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.
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Maybe there is no God, only mathematics? We know mathematics exists, do we know God exists?JVL_{January 18, 2021
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