# Can you mathematically prove the existence of God?

So I came across this video (https://www.youtube.com/watch?v=z0hxb5UVaNE), which claims to prove the existence of God using math.

I then searched and found stuff like this: mathematician Kurt Gödel's work on proving that God exists with math.

Can math actually prove the existence of God 100% or it is all just abstract? Can it prove the existence of something divine?

• No, it cannot. But mathematics, or rather formal logic, can verify whether God's existence follows from the premises you adopt, which is what Gödel did with his argument. Oct 8, 2023 at 19:54
• Depends on what you mean by prove, but most say no.
– J D
Oct 8, 2023 at 23:34
• Your proof would have this form: `Exists(god)=True`. But, considering that math and logic are just abstractions of reality, what would be the reality that corresponds to such abstraction? Oct 9, 2023 at 7:29
• I dunno. Define "God". Oct 10, 2023 at 3:42
• Kurt Gödel was, first and foremost, a logician. His version of Anselm's ontological proof is, well, numberless. Nov 14, 2023 at 15:47

You can't mathematically prove any fact of reality "100%".

You need to start from some axioms about what's in reality or how reality behaves to start applying maths to it, and those axioms would come with at least some uncertainty (if they aren't just altogether unjustified). Note that one can't even be completely sure that anything beyond one's own mind exists.

If you start with some axioms, then you could arguably prove that something "100%" follows from that (although there is still the possibility of there being some flaw in your proof).

On the topic of God, in the absence of a concrete proof (maybe I'll watch the video at some point), all I can really say is that there are plenty of atheists who'll disagree that the existence of God can or has be proven. Many theists would even disagree with this, as they say belief should be a matter of faith (my objection to this aside). Although some theists do consider some arguments to prove God's existence.

* The issue with Gödel's ontological proof, based on my limited recollection, is that he's mostly just defining God into existence, rather than actually proving much. This might come in the form of suggesting that the existence of God in one possible world implies the existence of God in all possible worlds, and then saying that God exists in one possible world. I went through that in detail at some point, although that was a long time ago. The complexity of the proof makes it harder to notice the flaws.

• Lots of facts can get you killed though, which is pretty conclusive. Non-repeatable, anyway. Oct 9, 2023 at 21:56
• As I recall, the problem with Gödel's proof is precisely the fact that he takes God's possible existence (under S5, with the specific definition that Gödel introduces) as a premise. Conventionally, we allow the introduction of more or less arbitrary premises under the diamond operator, because we assume that "most" premises are at least conceivable. The problem with Gödel's "God predicate" is that it escapes from the modal operator, and so this convention is called into question. I do not believe Gödel provides a serious argument for ◇∃x G(x) other than that convention. Mar 5 at 0:10

Formal logic is a domain of mathematics. Like all logic, the point of maximal vulnerability is in the premises, which in mathematical logic is the definition of terms and their relationships. The ontological argument doesn't have formal fallacies, it just doesn't prove anything - either its premises return absurdity, and/or its premises are identical to the conclusion. For example, if you start with:

1. existence is a characteristic, not a prerequisite for characteristics (that is: there's a substantive difference between a nonexistent cat and a nonexistent carrot)

2. existence is a perfection (a serial killer that exists is more perfect than a serial killer that doesn't)

3. there exists exactly one entity which is most perfect

Then it follows that a maximally perfect entity exists, but that's one of the premises, so it already doesn't prove anything, and that's not counting the very dodgy claims in 1 and 2.

When mathematics is applied in a way so as to corroborate, or at least anticipate, the existence of something, we take something previously accepted (by whichever occurrent audience) as existent and intricate, with some sort of mathematical gap that the new postulate fills in. For example, black holes appeared as solutions in the theory of relativity/gravity, and so were anticipated for being these solutions.

So there are those, such as Pierre Teilhard de Chardin (among others), who asserted a temporal system bracketed in the forward direction by a singularity of ultimate convergence— something with an importance, in terms of final causality (cosmological teleology)—that they adjudged as meriting the name of God. This is akin to an applied-mathematics proof of God, then, but only on the assumption of the relevant background system (the unification postulate of the "omega point" in time).

If there would have been a mathematical axiom that might have been able to undergird Kurt Gödel's proof of God, though, it would have been the naive comprehension axiom: but as this principle led so readily to horrible paradox, it was much effaced from set theory down to this very day. Why would it have "proved" the existence of God? Because we could have taken something like positive set theory and combined it with Gödelian/Kantian talk of an ens realissimum, a maximum of positive concepts, and delivered "the set of all (other) positive sets," and transmuted this icon into a picture of a perfect nature, "and we would have been done."V

Incidentally, axiomatizing a mathematical deity instead of theoremizing It via naive comprehension results in the highly unusual set-theoretic situation where there are no nontrivial elementary embeddings of proper classes or universes into themselves or each other,U at least if we follow Cantor in replacing proper classes/universal sets with the holy and living Actus Purissimus et Ens Simplicissimum, which is not a set and does not contain Itself in a set-like manner. For such a being would not have anything like parts or substructures worthy of being embedded into themselves, each other, or anything else (save it were for the sake of some weird notion of a Trinity or an Incarnation, perhaps). But since much of higher set theory turns on imagining such embeddings and their many and varied ramifications, asserting that the equivalent of the universe of sets V = God (or more poetically ORD = God) threatens to take many of our toys away from us, banishing us perhaps at best to virtual or generic large infinite sets, which may or may not be appealing to everyone in this context/connection. Again, not really a proof per se so much, then, of atheism in this case, but at least a ground for looking for a different way than a clinically mathematical one, to ground (dis)belief in God besides.

VOr, with Alvin Plantinga later, we might've concocted a "victorious ontological argument" in the set-theoretic multiverse, i.e. we would at least have gotten that if there is an ante rem hyperrealm of Platonic/set-theoretic objects, then there is a deity-like presence there, a hypercreatrix of those objects.

UActually, the situation is rather more delicate and open than I have stated in the above. There are cataclysmically large embeddings of sets, above mere constructibility, such as of Vλ+2 into itself, so things don't look quite so bad for the Lord, then, if we look through the pertinent telescopes. (Or, that is, if I know what I'm talking about!)

Sometimes in mathematics we will talk about this thing we call "extrinsic justification." This is not the usual manner of deductive proof, since that is well-founded, whereas extrinsic justification is either:

1. Quasi-circular reasoning for axioms themselves, based on the "usefulness"/"fruitfulness" or even "elegance" of their consequences.
2. Erotetic reasoning: some overlap with (1), with an emphasis on the ability of some axioms to provide for nontrivial answers to otherwise given problems.

One could ask, then, about whether an axiom of deity would be mathematically useful. Again, the postulate seems to rule out an entire array of things mathematicians love to deal with (nontrivial elementary embeddings of universes into themselves or significant "parts" of themselves), which might testify against the postulate. But I'll leave it to the "audience" to think over other possible "fruitful" applications of such an axiom, and such as don't extrinsically testify against it.

I believe your question was posed incorrectly. The video does not say God (a Supreme Intelligence) can be proved mathematically, rather it says that the existence of MATH is a plausible proof of a Supreme Intelligence. Which is entirely different. This may not answer the question, but it removes some misunderstanding of the message in the video.

The term God is usually used as creator. If it creates all the things it must have permanent existence. If so, that means, God is the only existence. If you say others also have, they all have only temporary existence.

Even while we describe God as creator, in the video mentioned here, you can see room in Maths that the creator (God) has no place in the created (see @ 5:10 minutes). That means all parts of Maths is not created. This actually implies the name creator is not suitable to God.

IMHO, the term existence is not as simple as we believe. “I can prove your EXISTENCE”, means I am greater than or equal to you. And the implication of your question is, “I am greater than or equal to God”. This means that in the case of existence I can also decide who God is - God Himself or me. This is a folly when I am only a body.

Suppose God is the existence and you prove its existence but you cannot prove your own existence (even one of its creations) using Maths, it means, like the existence of numbers, your mathematical proof cannot prove existence of beingness/EXISTENCE because God must be existance itself.

Using logic you may be able to prove the uniqueness of God; but you cannot PROVE its EXISTENCE.

'Existence' and 'Uniqueness of existence' are two things. Nobody can find Maths in Existence unless it is connected to ideas like numbers. The former is something more than an IDEA. To exist what we call ideas, Existence MUST BE subtler/greater than ideas.

• Is there a reasonable, more-detailed way that this may be expanded upon? As it stands, it seems to be little more than a comment, but it points towards a response that I suspect could be well-backed up by at least some citations. Oct 9, 2023 at 1:37
• Why does “I can prove your EXISTENCE” mean I am greater than or equal to you? "I can also decide who God is" - how does that follow? Being able to prove something doesn't mean you can reach whatever conclusion you want. Oct 9, 2023 at 15:21
• It reminds me of Rumi saying, "There is no reality but God, there is only God." It feels right, but I can't apply it to anything, or convince anyone to agree. You see it, or not. Oct 9, 2023 at 21:54
• @NotThatGuy: Existence in its higher level is not like other ideas. Ideas emerges from the mind. We may say that they are in the mind. Oct 14, 2023 at 2:01

The closest to what you are looking for would probably be something along the lines of the Five Proofs of the Existence of God, by Edward Feser:

This book provides a detailed, updated exposition and defense of five of the historically most important (but in recent years largely neglected) philosophical proofs of God’s existence: the Aristotelian, the Neo-Platonic, the Augustinian, the Thomistic, and the Rationalist.

It also offers a thorough treatment of each of the key divine attributes—unity, simplicity, eternity, omnipotence, omniscience, perfect goodness, and so forth—showing that they must be possessed by the God whose existence is demonstrated by the proofs. Finally, it answers at length all of the objections that have been leveled against these proofs.

This work provides as ambitious and complete a defense of traditional natural theology as is currently in print. Its aim is to vindicate the view of the greatest philosophers of the past— thinkers like Aristotle, Plotinus, Augustine, Aquinas, Leibniz, and many others— that the existence of God can be established with certainty by way of purely rational arguments. It thereby serves as a refutation both of atheism and of the fideism that gives aid and comfort to atheism.

For those interested, here are a few recorded debates between Edward Feser and Graham Oppy:

Regarding math specifically, William Lane Craig has in recent years been arguing for God's existence based on "the Unreasonable Effectiveness of Mathematics". He developed the following syllogism for God's existence:

1. If God does not exist, the applicability of mathematics to the physical world is just a happy coincidence.
2. The applicability of mathematics to the physical world is not just a happy coincidence.
3. Therefore, God exists.

Sources:

Of course, this view is debatable, and conveniently, there is another debate worth watching with the presence of Graham Oppy:

Hence, god exists. Reply! ~ Leonhard Euler (mathematician)

In one of the systems theories, cybernetics (or a more simplified version of the distributed network theory), we cannot say that micro system dynamics are absolutely self-governing. There is a incompleteness that there are one or more operating layers that are decentralized. From the point of view of materialism, this claim is unacceptable, since no concrete regularity has yet been proven in this. If the mathematical models show God, then there is not incompleteness. While God can be represented in the systems model, the absolute lack of the mathematical model shows that we cannot answer this question with existential clarity.

I think the YouTube video is a joke, even if the creator of the vid doesn't realize it yet.

I believe in the existence of God and I think this belief is reasonably well-justified epistemologically.

But nobody is "proving God". Nor is anyone disproving God, either. Proof is not exactly the same thing as evidence. I believe that there is evidence that is consistent with the existence of God.

I also like mathematics, am pretty good at applied mathematics, and I think that some mathematics can inform our epistemology regarding our beliefs. Specifically, for me, I believe that Bayesian inference or Bayesian epistemology can inform our reasoning regarding the evidence we observe, and that Bayesian reason might even have an equation or two. But these equations are no "proof" of God, but might help us or inform us about the relative likelihoods of different hypotheses that would explain the evidence we observe.

Only if there is interest, would I get into more detail, because it's a lotta work. If no one is interested, I won't put any more effort into this.

Video which you have posted proves that God is mind but it does not prove God has feelings. Math has no feelings except wonder and amazement which can be removed if we consider that Math is just a tool. Math doesn’t make you surrender before it with your life.

Consider a definition of God: God is someone (number of someone is 1) before whom we(not God but having numbers 1 or greater than 1) surrender with our life because God is omniscient,omnipotent,omnipresent.

Let us take a group called we (with number 1 million )which surrender to God then we are nothing but puppets in the hands of God. God commands and we follow. We are representatives of God and our acts is an act of God,( there is no free will )then we can say 1(someone) = 1 million and 1(we plus God)

Therefore if and when we find the equation 1>1 or 1= 1000001 or 1=1+ X where X is not zero or 1000000<1 or 1>X where X >1 ,then we say we have found God. Since such equations are outside or not yet discovered by traditional mathematics we say current Maths has not found God or has not proved God because God is all powerful and demands surrender and current maths fails to prove that). However I used mathematics to give idea of what is God therefore Maths has the capability to convey what is God.

• I know you are pitching "Hindu" ideas to an audience that probably doesn't have the background to recognize or at least appreciate them. Keep trying, but you might need smaller and more well-explained points. Oct 9, 2023 at 21:58

The fast answer is "No, using the normal definition of God, it is not possible to rigorously PROVE the existence of God by any means whatsoever, theoretical or practical." ("Theoretical" means by a logical process. "Practical" means by constructing a machine, a God-detector.)

The normal definition of "God" is an omniscient, omnipotent being---a being outside of space and time, not subject to any of the Universe's physical laws or limitations, knows absolutely everything, and able to change anything and everything in the Universe in whatever way He sees fit to do.

One being who controls everything.

And under that definition, it's not possible to rigorously prove the existence of God.

Because whatever method we choose to try to prove the existence of God, theoretical or practical, the method would have to be something the outcome of which God could not influence, a God-independent process. God would have to NOT be able to control the outcome.

And since the normal definition of God is "one who controls everything", such a process is not logically possible.

Since a God-independent process is not possible, it is therefore not possible to rigorously prove the existence of God.

Quod Erat Demostrandum