Can God be proved mathematically?

[C C]

https://www.scientificamerican.com/artic...matically/

EXCERPTS: Who would have thought about God as an apt topic for an essay about mathematics? Don’t worry, the following discussion is still solidly grounded within an intelligible scientific framework. But the question of whether God can be proved mathematically is intriguing.

In fact, over the centuries, several mathematicians have repeatedly tried to prove the existence of a divine being. They range from Blaise Pascal and René Descartes (in the 17th century) to Gottfried Wilhelm Leibniz (in the 18th century) to Kurt Gödel (in the 20th century), whose writings on the subject were published as recently as 1987. And probably the most amazing thing: in a preprint study first posted in 2013 an algorithmic proof wizard checked Gödel’s logical chain of reasoning—and found it to be undoubtedly correct. Has mathematics now finally disproved the claims of all atheists?

As you probably already suspect, it has not. Gödel was indeed able to prove that the existence of something, which he defined as divine, necessarily follows from certain assumptions. But whether these assumptions are justified can be called into doubt. For example, if I assume that all cats are tricolored and know that tricolored cats are almost always female, then I can conclude: almost all cats are female. Even if the logical reasoning is correct, this of course does not hold. For the very assumption that all cats are tricolored is false. If one makes statements about observable things in our environment, such as cats, one can verify them by scientific investigations. But if it is about the proof of a divine existence, the matter becomes a little more complicated.

While Leibniz, Descartes and Gödel relied on an ontological proof of God in which they deduced the existence of a divine being from the mere possibility of it by logical inference, Pascal (1623–1662) chose a slightly different approach: he analyzed the problem from the point of view of what might be considered today as game theory and developed the so-called Pascal’s wager...

[...] Ontological approaches dealing with the nature of being are more convincing, even if they will most likely not change the minds of atheists. Theologian and philosopher Anselm of Canterbury (1033–1109) put forward his ideas at the beginning of the last millennium...

[...] It took a few centuries for this idea to be revisited—by none other than Descartes (1596–1650). Supposedly unaware of Anselm’s writings, he provided an almost identical argument for the divine existence of a perfect being. Leibniz (1646–1716) took up the work a few decades later and found fault with it...

[...] From a mathematical point of view, however, these thought experiments became really serious only through Gödel’s efforts...

[...] This does not settle the final question of the existence of one (or more) divine beings. Whether mathematics is really the right way to answer this question is itself questionable—even if thinking about it is quite exciting... (MORE - missing details)

[Yazata]

It seems to be a trivial task to concoct a valid logical proof of the existence of God.

1. For all x, if x exists, then a sufficient reason for x's existence exists (The Principle of Sufficient Reason)

2. Physical reality exists (seemingly self-evident)

3. God is the sufficient reason why physical reality exists (Traditional in natural theology)

4. Physical reality has a sufficient reason why it exists (from 1 and 2)

5. God exists (from 3 and 4)

Of course as CC notes above, the conclusion of a valid argument is only as strong as the assumptions that went into it.

We can question the Principle of Sufficient Reason (and some have). But tossing it might have some unwanted implications for science. Science seems to expect (for some reason that's rarely if ever stated) that everything has an explanation. If we are talking about bird flight, science wants to know how they do it, and isn't satisfied with 'It's just the nature of birds to fly'. One of the biggest differences between me and my dog is that I don't just accept everything around me as 'the way it is'. I want to know why. The principle of sufficient reason is built into human cognition I think, a distinguishing mark of how humans think. (I'm inclined to accept the Principle of Sufficient Reason intuitively for that reason, as a heuristic if nothing else.)

We can question the equation of God with the sufficient reason for physical reality. It's a traditional usage of the word 'God' from natural theology sure enough. But one could argue on theological grounds that it isn't right. And just philosophically, all that equating God with the sufficient reason for physical reality gives us is whatever unknown something that fullfills a metaphysical function, not a religious deity what's a suitable object of human worship. It doesn't produce anything remotely like the deities of the Bible, Quran or Gita. (This is the objection that I find most persuasive and it's part of what lies behind my agnosticism.)

We could even question whether physical reality exists. Certainly individual things in physical reality exist. But can we leap from acknowledging that to treating physical reality as a whole as if it was a particular thing, part of the contents of physical reality? (I'm willing to accept that physical reality in its entirety exists, but one could certainly question it.)

There's also the theologically problematic implication that

6. A sufficient reason for God's existence exists (from 1 and 5)

which would seemingly trap us in an infinite regress since every sufficient reason would require its own sufficient reason

[Magical Realist]

I take issue with premise #1. Do we really know if everything has a sufficient reason for existing? What's the sufficient reason for a rock existing, or a tree, or a star for that matter? It seems to me it is rather anthropocentric to assume everything comes to be due to some prexisting reason, as if it were manufactured by a purposive agent. Thus a chair has a reason for existing because the chairmaker created it for that purpose. But natural objects seem to me to be gloriously purposeless in their state of existing. The whole universe in fact seems to be wildly superfluous--a serendipitous result of what seems to be nothing but blind and haphazard creative energy. Sartre was right: "Existence precedes essence."