[ExI] logic

Dan TheBookMan danust2012 at gmail.com
Wed Apr 22 22:20:15 UTC 2020

> On Apr 21, 2020, at 8:42 AM, William Flynn Wallace via extropy-chat <extropy-chat at lists.extropy.org> wrote:
> If you can prove that God could exist by symbolic logic, higher math, or whatever you are using, then could you say the same thing for the Devil. empathy, witchcraft, a wife's love - just about anything?
> bill w

A problem here would be what is meant by 'god' above. I think you're positing something like the god of Christianity, in which case the problem is if you can prove it exists, then would this prove the whole package of Christian beliefs? (Or which flavor given that Christianity is a fairly diverse religion -- even more diverse in its early years if scholars like Bart Ehrman (see his _Lost Christianities: The Battles for Scripture and the Faiths We Never Knew_)?)

Many existence [of god] proofs involve simply proving there is a god -- often by only loosely defining what's meant by 'god' -- and not that there's a god of, say, Judaism or Christianity. For instance, many of the classic proofs (all of which seem to have been refuted or, if not, require accepting questionable premises) merely conclude there is something like a perfect being (ontological argument) or a creator (cosmological argument) or a guiding intelligence (design argument). These don't conclude -- at least not in their usual form -- in stating something like modern Christian theology is true. (This is ignoring that even modern Christian views are fairly diverse.)

You can use symbolic logic to examine the syntax of a given proof, given that you can treat elements of your proof as terms in first order or higher order logics. But the problem then is does this mean anything if the terms themselves are questionable? Therein lies the rub. Merely putting stuff into symbolic logic might help to spot problems with the overall structure of a given argument, but it won't necessarily help one to accept the terms or premises of the argument. For instance, imagine I put forth the argument that:

1. P -> Q (P implies Q)
2. P (positing P)
3. Q (therefore Q) [conclusion]

This is pretty solid (for classical propositional logic, but note not for relevance logic), but for any given argument, you'd have to know that 1 and 2 are true. If not, syntactically, the proof is valid, but it might not be true.

By the way, some here mentioned one can't prove there is no god. Well, this seems like a bit of nerd lore. Looking at actual non-existence proofs, it looks as if some people working in the field believe you can prove there is no god. See, for example, _The Impossibility of God_, edited by Michael Martin and Ricki Monnier. Whether you accept any of these proofs is another matter. (The same duo also edited another volume of improbability (of god) arguments, titled, not surprisingly, _The Improbability of God_. Haven't read that one yet.)

Of course, if you meant jumping from say pure logic or pure math (say, set theory or category theory) to god, I've seen attempts made, but none seems to pass muster as anything more then sneaking in what is to be proved. There is a famous story, which seems to be false, that Euler presented Denis Diderot with a mathematical proof of god's existence. (See http://www.fen.bilkent.edu.tr/~franz/M300/bell2.pdf ) 


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