Godel's Ontological Argument

[iplaw]

This is my first thread...my very own, how special.  This is an interesting argument that I discovered a couple of years ago.  This argument is a refined version of St. Anselm's ontological argument.  For those who don't know who Godel is, there is a brief bio of him on the first page.  

Godel's Ontological Argument

[Revenant]

Disclaimer: I have no background in philosophy, and my grasp of logic is merely that as required by someone with a couple of decades of computer programming experience. As such, modal logic of the sort employed here is new to me. I'm also new here so be nice!

I haven't got as far as Gödel's argument yet, but it was interesting looking at Hartshorne's ontological argument.

One of the things I noticed was in the modal axiom M1, which states that "If A is possible, then A is not necessarily false."

The immediate thought that struck me was that the converse is also true: If A is possible, then A is not necessarily true either. Or to put it another way, if A is possible, then not-A is also possible; therefore, not-A is not necessarily false.

However, this rather obvious corollary appears to have been excluded from the axiom set and the subsequent argument. It doesn't become clear why until you get to H9 and H10 of the formal argument itself, which state:

H1. God possibly exists.
H2. If god exists, then god exists necessarily.
..
..
..
H9. Either God necessarily exists, or God necessarily does not exist.
H10. (From M1 and H1: It is possible for God to exist.) It is not necessary for God not to exist. (Or,) The proposition that God necessarily does not exist, is false. (Thus negating the second part of H9.)
H11. Therefore, God necessarily exists. (From H9 and H10.)

However, this excludes the corollary "It is not necessary for God to exist", which is also valid. Indeed, if one were to (equally disingenuously, but just to illustrate a point) substitute this for the H10 supplied in Harsthorne's argument, H11 thereby becomes "Therefore, God necessarily does not exist" (from H9 and H10).

Given that either version of H10 is valid, one is left pretty much where one started: either the proposition that God doesn't exist necessarily is false, or the proposition that God exists necessarily is false; therefore, God either exists necessarily or does not exist necessarily. Impasse.

In short, it occurs to me that the problem here isn't with the argument; the problem lies with the very axioms of the modal logic upon which it is based. In short, the modal logic itself artificially elevates a possibility to a necessity by excluding the consideration that if A is possible, A is not necessarily true.

It would seem, therefore, that the old maxim - that you can prove anything you like with philosophy so long as you pick and choose the axioms that suit the case you're trying to prove - is quite clearly evident here.

Unless I've made a boo-boo and haven't spotted it. I thought I would raise this before I got any further as I do not have a background in philosophy; if I've made an error, it's safer to stop before I get any further. Apologies for not writing this out formally, but I don't know how to do squares and diamonds on this keyboard.

[Spoonboy]

I only got as far as page 10, which isn't the entire argument, but this is pretty heavy going. I don't know that much about modal logic as I only had 1 lecture on it. My response is: I think that axiom H2 "If God exists then it is necessary for God to exist" is nonsensical. In modal logic, we have possible worlds, which range over all logical possibilities. Whether or not g is true depends on which possible world we are in. The meaning of "it is necessary for God to exist" is basically, g is true in all possible worlds. Now why on earth would you say (as axiom H2 does) that if g is true in some world, then g is true in all worlds? This is daft! The idea behind it is that God is the greatest thing imaginable, and so if God did not exist in all possible worlds, then we could conceive of an even greater God that did. But these are possible worlds in our logic we're talking about. They have no dependency on each other. This is like saying God is so great that he trumps the logic we use to describe him. Just because g is true on some possible worlds doesn't mean that g is true in all possible worlds.

[Will]

Axioms work in the hypothetical. It's fun to play along for a time, but when rubber hits the road the stuff falls apart. It's the same as arguments by other meta-philosophers like Plantinga. For one, they all presuppose god's existence, whether they want to admit it or not. For two, there is a mighty assumption that god is by definition perfect. Let's say that I have P, a potato chip that has infinite surface, height, and perfect taste. This is the greatest potato chip ever, ever. P is the greatest potato chip that can exist - existing is greater than not existing, therefore P must have existed (before I ate it). See when the rubber hits the road, it falls apart, because the perfect potato chip never existed. In the name of the potato, the salt, and the holy vegetable oil. Amen.

Speaking to idea that what we can conceive of in our minds is possible in reality: let me put this as simple as possible, because set theory is a bitch. That which we conceive in our minds is not necessarily possible. With the knowledge of the rules, one can imagine outside of the rules. An example would be I can picture hot snow falling up in my mind right now. Divine simplicity is a joke as the concept of god is the most complex idea in history. Can you imagine how many laws of physics he'd have to break?

[SteveS]

Revenant, I'm not philosophically educated either, and like you my logic development was enforced through computer coding!

I'll try to read through this whole thing, but ultimately I suspect Spoonboy hit the nail on the head.  If A exists in one "scenario" why does A necessarily exist in all "scenarios"?  I'm not buying this either.

Willravel - I agree.  I'm highly suspicious of theological arguments that start from some new and fabulous axiom - axioms really have to be axioms.  If they are not self-evident, then they are not axioms.  So many god arguments seem to want to start from some "axiom" that is anything but axiomatic!  And most of theirs encapsulate assumptions that really should not necessarily be made.  I figure it's just a game to try to hide the fact that they're really presupposing god's existence.  And then hope nobody is smart enough to realize they've just been bambuzzled.

[Will]

Precisely. We atheists should never feel intellectually outgunned, especially by a theist. If you get bested, go home, sharpen the old mind, and come back with the factual ammunition. At the end of the day, reason is always on our side. If all else fails post it here. One of the smart people around here is bound to be able to help, even against well established philosophers.

[SteveS]

reason is always on our side.

When I realized that I no longer felt afraid to jump in and argue - I figure if I get turned around I've probably just messed something up, and another atheist will be quick to point out my error.

[SteveS]

Okay, I've struggled my way through about half of this paper.  Thanks, iplaw, for posting this --- its making me think, which is always a good thing!

As the author seems to predict, my objections are fundamentally axiomatic.  In particular, I'm having a hard time buying H1 and H2.  The modal logic is really interesting to me, and I don't really have a problem with the inference the argument makes - I can't find a hole in the deduction (but that's expected, since the guy who wrote this was apparently a master logician - and I most clearly am not :wink: ).  But, like all arguments, they only function if we accept the premise - if we can question the premise, we can question the conclusion.

H1 seems like a sleeper attack: to say an atheist will admit its possible that god exists, I'm not sure that the same atheist will concede that god must necessarily be perfect in all aspects - I do not find it "self-evident" that anything can exist "perfectly in all regards".  And if not, then H2 is a sure bust.  In particular, I think the idea of a totally unlimited god is self contradictory (omniscient and omnipotent combined, for example, seems impossible to me - so while I will concede something god-like may exist because I can't prove it cannot exist, I do not have to accept any particular definition of god, namely omni-everything, as being possible - but the argument seems to require this definition of god - its screwing around with the ambiguous nature of the word "god").

Also, some of the great philosophers have pointed out that it is possibly incorrect to argue that something that exists is necessarily more perfect than something that does not exist - which would also undermine H2.

Which leads me to my problem, in general, with the ontological arguments: I get a queezy feeling that we haven't really proven god exists, but instead have proven that "perfection" exists?  Which is also troublesome.  Why can't I use this argument to prove a perfect tree must exist?  Or, in the same vein, have we really just proven that a perfect "idea" exists?

Anyway - just my thoughts so far - its 1:20 AM here in Lemont and I've had several beers, so maybe I'm full of it.  The mental ramblings of an alcohol sodden atheistic mind!

P.S. to Revenant, since you mentioned a software background, I once heard a humorous argument that every computer program contains at least one bug, and every computer program could be reduced by at least one instruction through optimization - so every computer program can theoretically be reduced to one instruction that doesn't work!  

P.P.S. I think I'm still arguing against Anselm and Hartshorne - it seems I have to read further to get to Godel.  Oh well :?

[Will]

You're absolutely right about the assumption that the god character is perfect. If you believe what the Torah and Bible teach, then god committed mass murder and even genocide. That would be the opposite of perfect. I'd go as far as to call it pure evil, and if goodness = perfection, than the evil label would automatically disqualify god from perfection. I'm sure someone could argue with that, but because 'perfection' is objective we can both be right. So if god isn't perfect in just one opinion, the whole thing falls apart.

God isn't perfect. Neither is the flying spaghetti monster, but his glorious delicious makes up for it by inspiring my culinary soul.

[SteveS]

Neither is the flying spaghetti monster, but his glorious delicious makes up for it by inspiring my culinary soul.

Amen - Blessed be his pastaness!

Yeah, you're right, perfection does seem subjective.

This is another example of how the idea of god seems hopelessly muddled and confused to me.  In an argument on a different thread, a poster asserted that "god is unable to lie".  But people also say god is omnipotent;  and is this not placing a clear limitation on god?  Saying god is all-powerful but chooses not to lie is one thing, but saying he is unable to lie seems to be placing a very non-omnipotent restriction upon god.  So which is it?  Omnipotent, or unable to lie?  He can't be both, right?

Before anyone proves that god exists, aren't they going to at least have an internally consistent definition of what god is?  Its ambiguity like this that makes it unclear to me what the ontological argument has actually said.  What about Thomas Aquinas's "first cause" argument, where he makes an equation?  Specifically, he says (approximately) whatever is first cause we call god.  But equations should be commutative, right, so if we flip this around is first cause god?  What if there is a first cause and its all natural, good old fashion physics.  Would it still be god?  This is what I'm getting at - if nobody narrows down what the heck god is supposed to be, then its very hard to even understand what assertion is being made by these funky theists  :wink:

[donkeyhoty]

here's a related question:  How do you guys/gals pronounce "Plantinga"?

I go with "Plan - ting - uh".  

Anyone think "Plant - in - guh"?

[SteveS]

 !!! I guess I go with your first one, "Plan - ting - uh"!

[Revenant]

P.S. to Revenant, since you mentioned a software background, I once heard a humorous argument that every computer program contains at least one bug, and every computer program could be reduced by at least one instruction through optimization - so every computer program can theoretically be reduced to one instruction that doesn't work!  

I like that. That goes back with me to work on Monday.

[Promethium147]

OH, what a HOOT!

To attempt to hang it all on the poor rotting corpse of Kurt Godel is inexcusable! How has this amazing, irrefutable conjecture of his only now suddenly come to light? This man so extensively lauded and studied in every detail proved the necessary existence of God so long ago - and no one noticed?

I studied Logic extensively, Classical, Predicate, and yes, some Modal.

In summary, Modal logic is an extension, not a replacement, for classical logic. If Modal logic defies Aristotelian logic - it loses. But - it doesn't.

To think for a moment that the possibility of God necessitates His (its) existence can be attributed to a Kurt Godel strains credulity, and breaks it immediately. What nonsense!

Here's MY basic argument.

First Cause - the only possible "necessity" of God is as Creator of Complex Things. Any objections? Didn't think so...

If we assume a Complex Thing requires a (more complex) Creator, then we simultaneously assume a More Complex Creator requires a Yet More Complex Creator, and so on - ad infinitum.

Thus the premise is not merely implausible, it is resoundingly False, reductio ad absurdum.

Crack it modally, if possible. If there is a hole, I sincerely want to know - shouldn't take long, it's awful small.

It is, however, one of the more extreme cases of PseudoSophistry I have seen - quite the presentation, Bud. If you believe it, you are Idiot; if you don't, you are Charlatan. I tend to think you are the latter.

Symbology is used here like so many pretty Tarot cards - another diversionary tactic. You may find it incomprehensible - that's the whole idea, I think.

Gotta watch for those "sophisticated" land mines, they're big time wasters - if you can consider a rousing Guffaw a waste of time.

[tomday]

First Cause - the only possible "necessity" of God is as Creator of Complex Things. Any objections? Didn't think so...

If we assume a Complex Thing requires a (more complex) Creator, then we simultaneously assume a More Complex Creator requires a Yet More Complex Creator, and so on - ad infinitum.

Thus the premise is not merely implausible, it is resoundingly False, reductio ad absurdum.

Promethium my friend: you know it, I know it, BUT, they, the deluded theists, have been indoctrinated with the notion that 'god has always existed' and no matter how stupid that is, it is part of their faith and you will NEVER get them to accept that they are wrong and you are right!

I would suggest that you are a hiding to nothing if you attempt to argue with these deluded theists in verbose manner - the majority of them are incapable of thinking for themselves and have never exercised their analytical skills sufficiently to be able to understand what you are trying to tell them (given that they even wanted to understand you in the first place).