TheJesusConspiracy

I certainly didn't claim that Godel pointed out a flaw in truth systems. Be careful what you attribute to me. I'm with Nagel in my pro-Godel stance.

As for people who don't quite get the point of my that the proposition (I'm sorry I used 'sentence' before...I'd had a long day), let's be real clear again.

1. If G is not a meaningful proposition, then G cannot be proven by anything.
2. If G is not a meaningful proposition, God will never and can never prove G, for proving G is a logical absurdity.
3. The proposition claiming that God will never prove G is thus true per 2.
4. G claims that that God will never prove G. G is true.

I wouldn't argue at this point that G is not a meaningful proposition. G quite clearly states that it is an object that God will not prove. Assuming G is not a proposition leads to the conclusion that G is a true proposition. So G is a meaningful proposition.

And G is necessarily true. Regardless of whether we start by assuming G is false or that G is meaningless, we cannot remain consistent and must come to the conclusion that G is true and meaningful.

Quod erat demonstratum

TheJesusConspiracy

Not a challenge to theism whatsoever? I venture to say nothing challenges an astute theist. Using reason to come to the aid of a devote theist is to offer rescue to a suicidal man.

Anyways, I've already pointed out how useless this definition of omnipotence is.

We can't say that God can literally do anything, for if he could, then he would be able to make a rock so heavy that he could not life it (if you add in a qualifier like God would unmake himself blah blah blah, then the algorithm for this is that God couldn't lift it without doing your qualifier...)

We can't say that God can do anything logically possible, for there are things it is logically possible for me to do that God cannot. For example, it is logically possible for me to be an entity that is not God.

If we simply say that God can do anything which it is logically possible for him to do, we've said nothing. It doesn't tell us what God can do. It merely asserts that if God is capable of doing x without contradiction, God can do x. Similarly, if I am capable of doing x without contradiction, I can do x. If we want to make a distinction between logical and material possibility, then perhaps this is useful. Maybe God can do anything logically possible whereas I can only do what is materially (and thus also logically) possible.

But what can God do? Any answer will have to show itself to be non-arbitrary. I could posit the existence of Unies that are capable of doing whatever Unies do. What do they do? They kill Gods for a living. Want me to prove it? I have as much justification as any theist out there.

TheJesusConspiracy

Since no explicit claim was made that I am an amateur, if that was not intended, the following does not matter.

If however, this is meant to be a sweeping attack on my arguments, I beg to differ.
I may not be a professor of philosophy yet, but I am not adequately characterized as a layman or amateur either. I am a doctoral student studying philosophy. I've done extensive work in logic and foundational mathematics.

If you think there's an error made, please point it out. Otherwise I would take this argument to be little more than an ad hominem at best and an argument from intimidation at worst.

I agree with Dawkins as well, though.
Additionally, I think we're both aware of the crisis that mathematics has been having with just what the true nature of numbers is. It's not as though this a closed subject.

Mike Rosoft

Let's try the same argument with proposition H:
"This statement (H) is not true."

1. If H is not a meaningful proposition, then H is neither true nor false.
2. Therefore, H is not true.
3. The proposition claiming that H is not true is thus true per 2.
4. H is therefore true.

Assuming that H is not a meaningful proposition leads to a conclusion that H is a true proposition. Therefore, H is a meaningful proposition - or is it not?


Mike Rosoft

curbyIII

To TheJesusConspiracy:
Bollocks!

I can't do anything that's logically possible for me to do. For example: it is logically coherent for me to suddenly change into a purple dinosaur. But I can't do it. There is an infinite amount of such things that I can't do but which are LOGICALLY possible (involve no contradiction).

If you enjoy being hyper-pedantic I will give you another definition of God's omnipotence: God can do anything which is not logically impossible for him to do.

I am not going to give any proof that God is actually omnipotent as this is beyond the scope of this argument. You have tried to say that the concept of omnipotence is meaningless. This is obviously not true.

Adrian Selby

"1. If G is not a meaningful proposition, then G cannot be proven by anything.
2. If G is not a meaningful proposition, God will never and can never prove G, for proving G is a logical absurdity.
3. The proposition claiming that God will never prove G is thus true per 2.
4. G claims that that God will never prove G. G is true."

Aren't you merely creating a paradox, rather than asserting G is true. If it is allowed that G is meaningless, and this entails G is meaningful, then we have not concluded that G is meaningful because that would contradict a premise on which the status of G is built. If a premise is allowed as true, you are saying it is true both that G is meaningless and its meaningful (and true).

How can something be meaningless and meaningful?

If you force the conclusion, saying, 'this shows G was meaningful all along' then you have a premise that is not true purporting to support a true conclusion.

I don't see how you can escape the paradox and assert that G must be meaningful, without also asserting it is wrong to assert that G is meaningless.

Adrian (out of his depth a touch)

Synaesthesia

The Jesus Conspiracy wrote,
Of course we agree that it's not a flaw in logical systems. I was pointing out that it does not need to be a flaw in God either. Even assuming that God is aminable to such Godelization (Which is contradictory by some definitions of God), that doesn't show he's not omnipotent. It shows merely a facet of what omnipotence is.

This aside from a God of arbitrary power, one who's nature cannot be plumbed with logic at all. In either case, you have failed to refute the notion of omnipotence.

(By the way, what is Nagel’s stance that you refer to?)

You're most certainly correct, Omnipotence is another way of saying arbitrarily powerful - it doesn't tell us a helluva lot. As such, your argument cannot prove it's incoherence because it is not necessarily true that God is able to prove formally unprovable prepositions.

One point that I don't think has been emphasized sufficiently is God is not a formal system. His 'reasoning' can be added to, meta-systems in his mind can be used to the point of infinite regress. Godel's theorem was developed to characterize formal system, not transcendence.

Regards,
Synaesthesia

TheJesusConspiracy

Nope, it's not. And that's not the same argument. H says that H is not true. G says that G will never prove G. It makes a world of difference.

As for the poster who asked isn't this a paradox because I start by assuming that G is not a meaningful proposition and show that this leads to the affirmation of G, that's just a reductio ad absurdam argument. It's not a paradox; rather it proves that the assumption of not the conclusion entails the conclusion, which means the conclusion is true and the assumption of not the conclusion false.

Finally, people need to settle down with God's omnipotence meaning he can do anything logically possible. I already mentioned that if you want to a make a distinction between material and logical possibility, you at least have a distinction between God and me. However, there are a fair # of philosophers (such as WVA Quine) who would argue that stating a man can turn into a chicken is as much a logical impossibility as a bachelor being married. I don't care to press the issue here, though, as that's a topic for another forum. Regardless, this proof allows us to limit the extension of the big anti-concept 'omnipotence'.

echidna

So from your opening post :

… it would appear very much from your opening post and then your subsequent replies to the numerous people who had problems with it, all the way through to your conclusion in hinduwoman’s thread :

… that you really hadn’t thought through your initial post very well. Had you worked this out in your opening post, many people probably could have saved themselves much time in trying to explain some of the basic problems. Can I also post a quick plug (that’s a positive advertisement in ‘Stralia) for the majority of the contributors & admin who provide such an educational site. TJC, you certainly seem to have gained a lot anyway.

So when you assert :

… I must ask at what institution do you study ? Your opening post really is a bit of an embarrassment isn’t it ? Seeing as you use the term, I expect you are familiar with the translation of “quod erat demonstrandum” ? Is this how you submit most of your theses ? Normally I might be able interpret the opener as a tongue-in-cheek jest, however your subsequent followup seems to indicate we were supposed to take it seriously.

To illustrate the meaning of the word “amateur”, it could be said that Einstein was an amateur in some ways, but an incredibly brilliant amateur, so amateur as such does not necessarily reflect on one’s abilities. But the adjective “amateur” is not the same as the adjective “amateurish” …

curbyIII

To TheJesusConspiracy:
I concur with echidna. Furthermore, if you still maintain that the concept of omnipotence is empty (and you obviously do) despite overwhelming proof that this is not so, then you are a fool. (I had the misfortune of having my last post be at the bottom of the previous page so you probably haven't read it. It gives a perfectly good description of God's omnipotence that completely avoids your questionable argument)

If you really are a doctoral student then God help us all.