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” atMind 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)*

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.

What would happen if God’s existence was obvious?

People fail to take this into account when discussing proofs of God.

Not in our universe.

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.

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 existin 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

informationitself 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:

* The Greek word,

Logosis 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.-Q

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.

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.

As to:

And as Edward Feser puts it,

Vern Poythress taps into the same line of reasoning here

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, who gave Einstein a run for his money, “argued that mathematical truth was independent of the existence of God or other a priori assumptions.”

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.”

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.

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”.”

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.”

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.”

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.”

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.”

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.”

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.”

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”,,

As Dr. Meyer further explains, “it is an order that is contingent upon the will of the Creator. It could have been otherwise.”

And indeed, the belief in contingency, and/or ‘divine will’, played an integral role in Sir Isaac Newton’s founding of modern physics.

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’,

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’

Last time I checked, miracles are considered to be the sole province of God,

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,

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.’

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.’

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,,,”

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.

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.

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.

Of supplemental note:

Verse:

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@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.

Paxx at 11,

I’m absolutely sure… but maybe not. There should be an automatic search and delete function for posts like that.

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.

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. KF