Michael Egnor: Mathematics can prove the existence of God

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July 31, 2022

Intelligent Design, Mathematics, Philosophy, Religion

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Darwinian evolutionary biologist Jerry Coyne finds that difficult to believe but neurosurgeon Michael Egnor says it’s really a matter of logic:

What’s remarkable about the reality of universals as proof for God’s existence is that it points in a simple and clear way to some of God’s attributes, such as infinity, eternity, and omnipotence. To see how, consider again the set of natural numbers, which is infinite. Therefore:
The Mind that contains them must itself be infinite.
Because the Mind in which natural numbers exists is infinite, it is also omnipotent. Limitations on power are finite and are inconsistent with an infinite Mind.
Because numbers exist independently of the material universe, they are eternal (e.g., the truth that 1+1=2 is independent of time) and thus the Mind that contains them is eternal.
I find the Augustinian Proof of God’s existence via the reality of universals in the Divine Mind a compelling proof. It is a highly satisfying and an even beautiful concept — our abstract thoughts have a real existence in the Mind of our Creator, and we, who are created in His image, participate in His thoughts.
Michael Egnor, “Mathematics can prove the existence of God” at Mind Matters News (July 31, 2022)

Takehome: Because mathematics can show infinity, eternity, and omnipotence, it can only have proceeded from a mind with those characteristics. That’s God.

You may also wish to read: The Divine Hiddenness argument against God’s existence = nonsense. God in Himself is immeasurably greater than we are, and He transcends all human knowledge. A God with whom we do not struggle — who is not in some substantial and painful way hidden to us — is not God but is a mere figment of our imagination. (Michael Egnor)

Comments

I disagree. We can construct a rational abstract framework such as the hyperreals, and they include now a tamed version of infinitesimals that are quite useful and reflect frequent use, thanks. KFkairosfocus_{August 10, 2022
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Infinite numbers are bunk. A trick. They don’t exist in any meaningful way. Although the symbols are sometimes used for convenience
I agree! Though I would say “useful for convenience.” Very definitely useful. We discussed this almost an infinite number of times. But like some other concepts that people cannot live without and that don’t really have any physical counterpart, it will always be with us ad infinitum.jerry_{August 10, 2022
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Paxx at 11, I'm absolutely sure... but maybe not. There should be an automatic search and delete function for posts like that.relatd_{August 10, 2022
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Paxx@11 To the contrary, in physics, and therefore reality, infinities exist, and are extremely useful if not absolutely essential in the mathematics. In quantum physics infinities really occur. An infinite number of real photons (the particles of light) are emitted and absorbed by any and every accelerated electric charge. A given detector will only ever detect a finite number of these photons because the rest (an infinite number) will have too low an energy to be detected. But they are still present. As you increase the detector's sensitivity the number of photons seen rises asymptotically to infinity. Ref: Kaku, Michio (1993). Quantum Field Theory: A Modern Introduction. New York: Oxford University Press. ISBN 0-19-507652-4., pages 177-184 and appendix A6 Other examples: One major use of infinity is in limits. Consider, for instance, a moving object. What is the maximum speed that it can attain? This can be determined by taking the limit as the particle's kinetic energy goes to infinity. According to special relativity, the limit of a particle's velocity as energy goes to infinity is the speed of light. Using an approximation such as this one not only makes the math easier, but is sometimes necessary to solve a problem without the use of a computer (i.e. to find an analytic solution). Knowledge of the theory will sometimes tell if the approximation is valid, otherwise it will have to be by experiment, which could be extremely difficult or impossible. And in the history of mathematics it was essential. In the invention of calculus, Newton and Leibniz both tried to deal with infinity, and specifically the “infinitesimal,” directly. To these inventors of calculus, the “infinitesimal” was treated as a real thing: and it was closely related to infinity. It was the opposite, or reciprocal, of infinity. More precisely, the “infinitesimal” is a quantity infinitely close to zero, but not actually equal to zero itself. This is how you cheat and divide by 0. It is still arguable that the "infinitesimal" is a real thing.doubter_{August 10, 2022
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Infinite numbers are bunk. A trick. They don't exist in any meaningful way. Although the symbols are sometimes used for convenience, they are not necessary for any physics. The Root Reality, whatever It is, is not "infinite". It's ontological "nature" is so different than our ontologiy and reasoning powers that it's useless to speculate about It, and infinite numbers don't help. But I could be wrong.Paxx_{August 4, 2022
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Kevin Moran, an optical engineer who studied the Shroud, describes the Shroud Image in this way, “The unique front-and-back only image can be best described as gravitationally collimated. The radiation that made the image acted perfectly parallel to gravity. There is no side image. The radiation is parallel to gravity,,,”
Optically Terminated Image Pixels Observed on Frei 1978 Samples – Kevin E. Moran – 1999 Discussion Pia’s negative photograph, from 1898, showed what looked to be a body that was glowing, but slightly submerged in a bath of cloudy water. This condition is more properly described as an image that is visible, at a distance, but by locally attenuated radiation. The unique front-and-back only image can be best described as gravitationally collimated. The radiation that made the image acted perfectly parallel to gravity. There is no side image. The radiation is parallel to gravity and, if moving at light speed, only lasted about 100 picoseconds. It is particulate in nature, colliding only with some of the fibers. It is not a continuum or spherical-front radiation that made the image, as visible or UV light. It is not the X-ray radiation that obeys the one over R squared law that we are so accustomed to in medicine. It is more unique,,, Theoretical model It is suggested that the image was formed when a high-energy particle struck the fiber and released radiation within the fiber at a speed greater that the local speed of light. Since the fiber acts as a light pipe, this energy moved out through the fiber until it encountered an optical discontinuity, then it slowed to the local speed of light and dispersed. Discussion The fact that the pixels don’t fluoresce suggests that the conversion to their now brittle dehydrated state occurred instantly and completely so no partial products remain to be activated by the ultraviolet light. This suggests a quantum event where a finite amount of energy transferred abruptly. The fact that there are images front and back suggests the radiating particles were released along the gravity vector. The radiation pressure may also help explain why the blood was “lifted cleanly” from the body as it transformed to a resurrected state.” https://www.shroud.com/pdfs/moran.pdf
Moreover, besides gravity being dealt with on the Shroud of Turin, the Shroud also gives us evidence that Quantum Mechanics itself was dealt with. In the following paper, it was found that it was not possible to describe the image formation on the Shroud in classical terms but they found it necessary to describe the formation of the image on the Shroud in discrete quantum terms.
The absorbed energy in the Shroud body image formation appears as contributed by discrete (quantum) values – Giovanni Fazio, Giuseppe Mandaglio – 2008 Excerpt: This result means that the optical density distribution,, can not be attributed at the absorbed energy described in the framework of the classical physics model. It is, in fact, necessary to hypothesize a absorption by discrete values of the energy where the ‘quantum’ is equal to the one necessary to yellow one fibril. http://cab.unime.it/mus/541/1/c1a0802004.pdf
Moreover, the following rather astonishing study on the Shroud, found that it would take 34 Trillion Watts of what is termed VUV (directional) radiation to form the image on the shroud.
Astonishing discovery at Christ’s tomb supports Turin Shroud – NOV 26TH 2016 Excerpt: The first attempts made to reproduce the face on the Shroud by radiation, used a CO2 laser which produced an image on a linen fabric that is similar at a macroscopic level. However, microscopic analysis showed a coloring that is too deep and many charred linen threads, features that are incompatible with the Shroud image. Instead, the results of ENEA “show that a short and intense burst of VUV directional radiation can color a linen cloth so as to reproduce many of the peculiar characteristics of the body image on the Shroud of Turin, including shades of color, the surface color of the fibrils of the outer linen fabric, and the absence of fluorescence”. ‘However, Enea scientists warn, “it should be noted that the total power of VUV radiations required to instantly color the surface of linen that corresponds to a human of average height, body surface area equal to = 2000 MW/cm2 17000 cm2 = 34 thousand billion watts makes it impractical today to reproduce the entire Shroud image using a single laser excimer, since this power cannot be produced by any VUV light source built to date (the most powerful available on the market come only to several billion watts)”. Comment The ENEA study of the Holy Shroud of Turin concluded that it would take 34 Thousand Billion (trillion) Watts of VUV radiation to make the image on the shroud. This output of electromagnetic energy remains beyond human technology. – per predator
So thus in conclusion, when we rightly allow the Agent Causality of God back into physics, as the Christian founders of modern science originally envisioned, then a very plausible solution to the number one unsolved mystery in science today, of finding a reconciliation between General Relativity and Quantum Mechanics, readily pops out for us in that, as the Shroud of Turin itself gives witness to, both Gravity and Quantum Mechanics were dealt with in Christ’s resurrection from the dead. Verses.
Luke 22:42 saying, “Father, if Thou be willing, remove this cup from Me; nevertheless not My will, but Thine be done.” Matthew 28:18 Then Jesus came to them and said, “All authority in heaven and on earth has been given to me,” Colossians 1:15-20 The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.
Of supplemental note:
,,, the Copernican Principle and/or the Principle of Mediocrity has now been overturned by both General Relativity and Quantum Mechanics, our two most powerful theories in science, as well as by several other lines of scientific evidence (i.e. we are NOT ‘chemical scum’ as Stephen Hawking once infamously claimed.) March 2022 https://uncommondescent.com/evolution/neil-thomas-on-evolutionary-theory-as-magical-thinking/#comment-748883
Verse:
Matthew 10:30-32 …And even the very hairs of your head are all numbered. So do not be afraid; you are worth more than many sparrows. Therefore everyone who confesses Me before men, I will also confess him before My Father in heaven.…
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As Dr. Meyer further explains, "it is an order that is contingent upon the will of the Creator. It could have been otherwise."
“That was a huge concept (that was important for the founding of modern science). The historians of science call that ‘contingency’. The idea that nature has an order that is built into it. But it is an order that is contingent upon the will of the Creator. It could have been otherwise. Just as there are many ways to make a timepiece, or a clock,,, there are many different ways God could have ordered the universe. And it is up to us not to deduce that order from first principles, or from some intuitions that we have about how nature ought to be, but rather it is important to go out and see how nature actually is.” – Stephen Meyer – 5:00 minute mark – Andrew Klavan and Stephen Meyer Talk God and Science https://idthefuture.com/1530/
And indeed, the belief in contingency, and/or ‘divine will’, played an integral role in Sir Isaac Newton’s founding of modern physics.
Newton — Rationalizing Christianity, or Not? – Rosalind W. Picard – 1998 Excerpt: The belief that it was by divine will and not by some shadow of necessity that matter existed and possessed its properties, had a direct impact on Newton’s science. It was necessary to discover laws and properties by experimental means, and not by rational deduction. As Newton wrote in another unpublished manuscript, “The world might have been otherwise,,” (see Davis, 1991) https://web.media.mit.edu/~picard/personal/Newton.php “Newton’s Rejection of the “Newtonian World View”: The Role of Divine Will in Newton’s Natural Philosophy – (Davis, 1991) Abstract: The significance of Isaac Newton for the history of Christianity and science is undeniable: his professional work culminated the Scientific Revolution that saw the birth of modern science,,, Newton’s voluntarist conception of God had three major consequences for his natural philosophy. First, it led him to reject Descartes’ version of the mechanical philosophy, in which matter was logically equated with extension, in favor of the belief that the properties of matter were freely determined by an omnipresent God, who remained free to move the particles of matter according to God’s will. Second, Newton’s voluntarism moved him to affirm an intimate relationship between the creator and the creation; his God was acted on the world at all times and in ways that Leibniz and other mechanical philosophers could not conceive of, such as causing parts of matter to attract one another at a distance. Finally, Newton held that, since the world is a product of divine freedom rather than necessity, the laws of nature must be inferred from the phenomena of nature, not deduced from metaphysical axioms — as both Descartes and Leibniz were wont to do. http://home.messiah.edu/~tdavis/newton.htm
Moreover, that the infinite Mind of God must be behind any mathematics that describe this universe is not just some archaic Christian belief that is left over from the ‘dark ages’ of Medieval Christian Europe, but the belief that the infinite Mind of God must be behind any mathematics that describe this universe is also testified to in modern physics. Specifically, both Eugene Wigner and Albert Einstein called the applicability of mathematics to the universe a quote-unquote ‘miracle’. In fact, Eugene Wigner, (who’s insights into the foundations of quantum mechanics earned him a Nobel prize and have fostered a ‘second quantum revolution’; per A. Zeilinger), went so far as question Darwinism’s ability to produce our ‘reasoning power’, when he called the applicability of mathematics to the universe a ‘miracle’,
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. https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf
and Albert Einstein, who needs no introduction, even went so far as to chastise ‘professional atheists’ in the process of calling the applicability of mathematics to the universe a ‘miracle’
On the Rational Order of the World: a Letter to Maurice Solovine – Albert Einstein – March 30, 1952 Excerpt: “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 weakness 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 http://inters.org/Einstein-Letter-Solovine
Last time I checked, miracles are considered to be the sole province of God,
mir·a·cle noun: miracle; plural noun: miracles a surprising and welcome event that is not explicable by natural or scientific laws and is therefore considered to be the work of a divine agency.
Moreover, Seeing that the 'divine will' of God, (sustaining the universe in its continual existence), played such an integral part in Newton’s ‘science’, (and although modern science has certainly come a long way since Newton first started the Scientific Revolution), let’s just simply say that Newton would be very pleased to see the recent closing of the “freedom of choice” loophole within quantum mechanics,
Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars – Anton Zeilinger – 14 June 2018 Abstract: This experiment pushes back to at least approx. 7.8 Gyr ago the most recent time by which any local-realist influences could have exploited the “freedom-of-choice” loophole to engineer the observed Bell violation, excluding any such mechanism from 96% of the space-time volume of the past light cone of our experiment, extending from the big bang to today. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.080403
Moroever, when we rightly allow the Agent causality of God ‘back’ into physics, (as the Christian founders of modern science originally envisioned, Johann Kepler, Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders), and as quantum mechanics itself now empirically demands with the closing of the “freedom-of-choice” loophole by Anton Zeilinger and company), then rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead bridges the infinite, 'non-renormalizable', mathematical divide that exists between General Relativity and Quantum Mechanics and provides us with an empirically backed reconciliation, via the Shroud of Turin, between Quantum Mechanics and General Relativity into the much sought after ‘Theory of Everything” In regards to gravity being dealt with on the Shroud of Turin, the following article states that ‘The bottom part of the cloth (containing the dorsal image) would have born all the weight of the man’s supine body, yet the dorsal image is not encoded with a greater amount of intensity than the frontal image.’
Particle Radiation from the Body – July 2012 – M. Antonacci, A. C. Lind Excerpt: The Shroud’s frontal and dorsal body images are encoded with the same amount of intensity, independent of any pressure or weight from the body. The bottom part of the cloth (containing the dorsal image) would have born all the weight of the man’s supine body, yet the dorsal image is not encoded with a greater amount of intensity than the frontal image. Radiation coming from the body would not only explain this feature, but also the left/right and light/dark reversals found on the cloth’s frontal and dorsal body images. https://academicjournals.org/journal/SRE/article-full-text-pdf/CC774D029455
And in the following video, Isabel Piczek states,,, ‘The muscles of the body are absolutely not crushed against the stone of the tomb. They are perfect. It means the body is hovering between the two sides of the shroud. What does that mean? It means there is absolutely no gravity.’
“When you look at the image of the shroud, the two bodies next to each other, you feel that it is a flat image. But if you create, for instance, a three dimensional object, as I did, the real body, then you realize that there is a strange dividing element. An interface from which the image is projected up and the image is projected down. The muscles of the body are absolutely not crushed against the stone of the tomb. They are perfect. It means the body is hovering between the two sides of the shroud. What does that mean? It means there is absolutely no gravity. Other strange you discover is that the image is absolutely undistorted. Now if you imagine the clothe was wrinkled, tied, wrapped around the body, and all of the sudden you see a perfect image, which is impossible unless the shroud was made absolutely taut, rigidly taut.” Isabel Piczek – Turin shroud – (Particle Physicist explains the ‘event horizon’ on the Shroud of Turin) – video https://www.youtube.com/watch?v=27Ru3_TWuiY
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Yet, as was touched upon in the preceding citation, Godel proved that mathematics does not have a necessary existence, as Hilbert had presupposed, but that it has a contingent existence. As the late Stephen Hawking himself honestly admitted when commenting on the 'contingent' implications of Godel's incomplete theorems for mathematics, "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”."
“Gödel’s incompleteness theorem (1931), proves that there are limits to what can be ascertained by mathematics. 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”. – Stephen Hawking & Leonard Miodinow, The Grand Design (2010)
And as the following article states, "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."
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/
And as Ron Tagliapietra succinctly stated, "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."
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
Thus, St. Augustine's claim that mathematics has a contingent existence that is dependent upon the Mind of God is born out rather dramatically via Godel's incompleteness theorems. In short, the Augustinian Proof of God’s existence, despite what anyone's personal opinion may be, is now to be considered, by all rights, mathematically, and logically, 'compelling'. In fact to make the problem that much worse for secularists, Chaitin has now shown that the 'incompleteness' problem in mathematics is much worse for secularists than Godel had originally shown. Specifically, "what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms."
The Limits Of Reason – Gregory Chaitin – 2006 Excerpt: Unlike Gödel’s approach, mine is based on measuring information and showing that some mathematical facts cannot be compressed into a theory because they are too complicated. This new approach suggests that what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms. https://www.cs.virginia.edu/~robins/The_Limits_of_Reason_Chaitin_2006.pdf
This leaves the atheist in quite the conundrum. As the late Steven Weinberg himself, an atheist, put it, "I don't think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don't describe the world as we know it. And we will always be left with a question 'why are the laws nature what they are rather than some other laws?'. And I don't see any way out of that."
"I don't think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don't describe the world as we know it. And we will always be left with a question 'why are the laws nature what they are rather than some other laws?'. And I don't see any way out of that. The fact that the constants of nature are suitable for life, which is clearly true, we observe,,," (Weinberg then comments on the multiverse conjecture of atheists) "No one has constructed a theory in which that is true. I mean,, the (multiverse) theory would be speculative, but we don't even have a theory in which that speculation is mathematically realized. But it is a possibility." Steven Weinberg – as stated to Richard Dawkins at the 8:15 minute mark of the following video Leonard Susskind – Richard Dawkins and Steven Weinberg – 1 in 10^120 Cosmological Constant points to intelligent design – video https://youtu.be/z4E_bT4ecgk?t=495
And while "an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms" faces the atheist with an irresolvable dilemma, the Christian Theist has a ready answer for the dilemma. As Dr. Bruce Gordon explains, "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.”
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.,,, Universes do not “spontaneously create” on the basis of abstract mathematical descriptions, nor does the fantasy of a limitless multiverse trump the explanatory power of transcendent intelligent design. What Mr. Hawking’s contrary assertions show is that mathematical savants can sometimes be metaphysical simpletons. Caveat emptor. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/
Dr. Gordon's claim that "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" is born out in conservation of information theorems. Specifically, and as Douglas S. Robertson states, "Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information."
Algorithmic Information Theory, Free Will and the Turing Test - Douglas S. Robertson Excerpt: Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information. http://cires.colorado.edu/~doug/philosophy/info8.pdf
Moreover, the free will of God also just so happened to be an essential Judeo-Christian presupposition that lay behind the founding of modern science. This essential presupposition of the free will of God that lay behind the founding of modern science is referred to as "The contingency of nature",,
“Science in its modern form arose in the Western civilization alone, among all the cultures of the world”, because only the Christian West possessed the necessary “intellectual presuppositions”. – Ian Barbour Presupposition 1: The contingency of nature “In 1277, the Etienne Tempier, the bishop of Paris, writing with support of Pope John XXI, condemned “necessarian theology” and 219 separate theses influenced by Greek philosophy about what God could and couldn’t do.”,, “The order in nature could have been otherwise (therefore) the job of the natural philosopher, (i.e. scientist), was not to ask what God must have done but (to ask) what God actually did.” Presupposition 2: The intelligibility of nature “Modern science was inspired by the conviction that the universe is the product of a rational mind who designed it to be understood and who (also) designed the human mind to understand it.” (i.e. human exceptionalism), “God created us in his own image so that we could share in his own thoughts” – Johannes Kepler Presupposition 3: Human Fallibility “Humans are vulnerable to self-deception, flights of fancy, and jumping to conclusions.”, (i.e. original sin), Scientists must therefore employ “systematic experimental methods.” (Francis Bacon’s championing of inductive reasoning over and above the deductive reasoning of the ancient Greeks) – Stephen Meyer on Intelligent Design and The Return of the God Hypothesis – Hoover Institution https://www.youtube.com/watch?v=z_8PPO-cAlA
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As to:
Mathematics Can Prove the Existence of God - Michael Egnor - July 2022 Excerpt: The solution proposed by Augustine (and many other philosophers and theologians, most notably Gottfried Wilhelm Leibniz) is called scholastic realism. Scholastic realism posits that God’s Mind is the Platonic realm of Forms. Augustine proposed that universals such as numbers, mathematics in general, propositions, logic, necessities and possibilities exist in the Divine Intellect, which is infinite and eternal. What’s remarkable about the reality of universals as proof for God’s existence is that it points in a simple and clear way to some of God’s attributes, such as infinity, eternity, and omnipotence. To see how, consider again the set of natural numbers, which is infinite. Therefore: – The Mind that contains them must itself be infinite. – Because the Mind in which natural numbers exists is infinite, it is also omnipotent. Limitations on power are finite and are inconsistent with an infinite Mind. — Because numbers exist independently of the material universe, they are eternal (e.g., the truth that 1+1=2 is independent of time) and thus the Mind that contains them is eternal. I find the Augustinian Proof of God’s existence via the reality of universals in the Divine Mind a compelling proof. It is a highly satisfying and an even beautiful concept — our abstract thoughts have a real existence in the Mind of our Creator, and we, who are created in His image, participate in His thoughts. https://mindmatters.ai/2022/07/mathematics-can-prove-the-existence-of-god/
And as Edward Feser puts it,
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. https://www.firstthings.com/article/2020/04/keep-it-simple
Vern Poythress taps into the same line of reasoning here
God In Mathematics – 2016 Jerry Bowyer – Interview with Vern Poythress Excerpt: 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.” https://www.forbes.com/sites/jerrybowyer/2016/04/19/where-does-math-come-from-a-mathematiciantheologian-talks-about-the-limits-of-numbers/
For me personally, the Augustinian proof, as far as it goes, is compelling. But some commenters here have said that they don't find the "Augustinian Proof" particularly compelling, So to add some fairly recent modern findings to it, particularly to add Godel's incompleteness to it, in order to make the proof more compelling for those who now find it less than compelling. In contemporary theoretical physics today it is, consciously or not, held that mathematics does not need God in order to explain its existence. Which is, in technical terms, (in the vast majority of instances today), to say that it is held that mathematics has a necessary existence, not a contingent existence. The late David Hilbert was, and still is, a shining example of this current belief that mathematics has a necessary existence that is independent of God, not a contingent existence that is dependent upon the Mind of God. David Hilbert, who gave Einstein a run for his money in being the first to formulate General Relativity,,,
David Hilbert Excerpt: By 1907, Einstein had framed the fundamentals of the theory of gravity, but then struggled for nearly 8 years to put the theory into its final form.[40] By early summer 1915, Hilbert's interest in physics had focused on general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject.[41] Einstein received an enthusiastic reception at Göttingen.[42] Over the summer, Einstein learned that Hilbert was also working on the field equations and redoubled his own efforts. During November 1915, Einstein published several papers culminating in The Field Equations of Gravitation (see Einstein field equations).[h] Nearly simultaneously, Hilbert published "The Foundations of Physics", an axiomatic derivation of the field equations (see Einstein–Hilbert action). Hilbert fully credited Einstein as the originator of the theory and no public priority dispute concerning the field equations ever arose between the two men during their lives.[i] See more at priority. https://en.wikipedia.org/wiki/David_Hilbert#Physics
David Hilbert, who gave Einstein a run for his money, "argued that mathematical truth was independent of the existence of God or other a priori assumptions."
David Hilbert Excerpt: Hilbert was baptized and raised a Calvinist in the Prussian Evangelical Church.[a] He later left the Church and became an agnostic.[b] He also argued that mathematical truth was independent of the existence of God or other a priori assumptions.[c][d],,, https://en.wikipedia.org/wiki/David_Hilbert#Personal_life
In fact, Hilbert, in putting forth his mathematical research program, specifically stated that "it (mathematics) is a conceptual system possessing internal necessity that can only be so and by no means otherwise."
David Hilbert Excerpt: In 1920, Hilbert proposed a research project in metamathematics that became known as Hilbert's program. He wanted mathematics to be formulated on a solid and complete logical foundation. He believed that in principle this could be done by showing that: all of mathematics follows from a correctly chosen finite system of axioms; and that some such axiom system is provably consistent through some means such as the epsilon calculus.,,, Hilbert wrote in 1919: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise."[38] https://en.wikipedia.org/wiki/David_Hilbert#Hilbert's_program
In fact, Hilbert's vision for finding the 'internal necessity' of mathematics is summed up by his rather dramatic statement', “We must know. We shall know.”, in fact that statement in engraved on Hilbert's tombstone.
David Hilbert Excerpt: The epitaph on his tombstone in Göttingen consists of the famous lines he spoke at the conclusion of his retirement address to the Society of German Scientists and Physicians on 8 September 1930. The words were given in response to the Latin maxim: “Ignoramus et ignorabimus” or “We do not know, we shall not know”:[25] Wir müssen wissen. Wir werden wissen. In English: We must know. We shall know. The day before Hilbert pronounced these phrases at the 1930 annual meeting of the Society of German Scientists and Physicians, Kurt Gödel—in a round table discussion during the Conference on Epistemology held jointly with the Society meetings—tentatively announced the first expression of his incompleteness theorem.[f] Gödel’s incompleteness theorems show that even elementary axiomatic systems such as Peano arithmetic are either self-contradicting or contain logical propositions that are impossible to prove or disprove. https://en.wikipedia.org/wiki/David_Hilbert#Death
bornagain77_{August 1, 2022
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Math, much like the laws of physics, could not have come about randomly. Math is universal, just like the laws. If the laws and math were random, there would be no universe.BobRyan_{August 1, 2022
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The proposition that God exists seems to be similarly irrational to the proposition that God doesn't exist. But the tie is greatly broken in God's favor by the obvious extreme, intricate perfection of the design of our Reality, starting with the immaterial existence of mathematics, which is obviously the essence of Mind. This is of course closely followed by the existence of natural law, which not only exists but is also finely tuned to allow life as we know it. And this is just the tip of an iceberg. There is still the intricate design of life itself. The atheist materialist argument that all this intricate design and order could be a random fluctuation of an uncreated Reality founders on these observations - why should an uncreated meaningless Reality just happen to exhibit such exquisite order and intelligence in its innermost nature, rather than chaos? There must be very very many more ways a random Reality would be chaotic and unintelligently (dis)organized in its innermost nature, and that would be very very much more likely.doubter_{July 31, 2022
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Even as a Christian, I don't find the Augustinian mathematics proof compelling. However, a mind that comprehends mathematics in ways that exceeds those of other primates by orders of magnitude defies any evolutionary expectation (which, with boring frequency, is usually the case anyway). The astonishing design complexity of life within the web of balanced ecosystems embarrasses and humbles all the creative genius of humanity. Physics and life sciences have never been shown to have a natural complexity ratchet at work, but rather it's simply presumed to exist in ultra-slow motion under the magical cloak of millions of years, random chance, and natural selection. This complexity includes molecular machinery operating on coded information within, around, and external to large and fragile DNA molecules. Can someone familiar with C++ or any other high-level computer language explain how a computer language itself might randomly evolve within a computer? Is there a digital ratchet? In addition, the Szilard engine points to information itself as an important factor in entropy. https://ebrary.net/190193/mathematics/szilard_engine But, in spite of the work done with Shannon Information theory (which I believe has more to do with data compression), we don't know how to measure information, which seems to be fundamental to reality and existence. Thus, I have no trouble in trusting the following:
In the beginning was the Logos*, and the Logos was with God, and the Logos was God. He was in the beginning with God. All things came into being through Him, and apart from Him nothing came into being that has come into being. In Him was life, and the life was the Light of men. The Light shines in the darkness, and the darkness did not comprehend it. - John 1:1-5 NASB 1995
* The Greek word, Logos is translated as "Word," although it can mean a word, discourse, communication, or reason. Logos encapsulates information and is also related to the word, logic. In the quoted passage, Logos is is personified, and Christians believe that Y'shua (aka Jesus) is the personified Word of God. -QQuerius_{July 31, 2022
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The OP seems to be a silly argument. Minds much more limited than God's seem to be able to understand the concept of infinity. I thought mine did after I learned it before high school. One doesn't have to hold a real infinity to understand and use the concept. While I believe in God, this argument isn't going to sway anyone who does not. Indeed, they may say, "is that all you've got?" and walk away convinced you are as stupid as they thought you were.Fasteddious_{July 31, 2022
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What would happen if God’s existence was obvious? People fail to take this into account when discussing proofs of God.
the set of natural numbers, which is infinite
Not in our universe.jerry_{July 31, 2022
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Not that I want to argue against the existence of a Creator, but the Augustinian proof given here seems to contain an unjustified assumption, that there necessarily must be a Mind that contains the mathematical universals like infinity. It seems to me that the atheist could simply say that that premise is no more irrational than the premise that an uncreated Reality of some kind has always existed. Of course saying that that Reality was always the physical Universe would have the objection of the strong evidence for a beginning, in the Big Bang.doubter_{July 31, 2022
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