CardinalMan

Just to set the record straight (since it seems that you may be referring to me), I am not a Christian, I am a logician, and I do think that my objections are extremely relevant. Once again, I have no qualms with your proof (it is not circular, and I have never claimed that it was), but your statement is self-referential. I do not see how you can consistently say that "This sentence is false" is technically meaningless while maintaining that your form of self-reference is not. Once again, please explain to me the distinction, and carefully distinguish when forms of self-reference are allowed and when they are not.

By the way, I have never in my life seen the First Fundamental Theorem of Calculus proved using contradiction (of course, you can artificially change it into one, but that seems kind of ridiculous). You simply form the difference quotient and directly bound it using the assumed continuity of the function. Not that this is relevant to the situation at hand, but please get your facts straight before making such statements.

CardinalMan

[ June 08, 2002: Message edited by: CardinalMan ]</p>

bd-from-kg

TheJesusConspiracy:

I’m afraid that you are underestimating my refutation of your argument.

Wrong. Stating that God will never create a planet larger than Jupiter in an orbi intermediate between the orbits of Mercury and Venus is not the same as saying that God cannot do so.

I did not point out the distinction between “will not” and “can not” just to raise a pointless quibble. It wasn’t possible to show that the assumption that G expresses a proposition leads to a contradiction because it doesn’t lead to a contradiction. The reason is that “God will not do X” is logically consistent with God’s omnipotence for almost any X. (If “do” is interpreted broadly enough there are exceptions, but that need not concern us here.) So I replaced G with G' because it was necessary to construct a more logically rigorous version of the argument in order to show what’s wrong with it.

If you mean that “X has soundly proven G” is equivalent to “X is capable of providing a sound proof of G”, obviously you’re wrong: “is capable of” does not entail “has”, nor does “has” entail “is capable of”. If you mean only that “has” entails “was capable of”, of course you’re right. I mention this only because in arguments of this type it is essential to be absolutely precise, and you’re being sloppy.

Quite right. But if you were to agree that Euclid was able to refer unambiguously to a sound proof that there are infinitely many primes, but still ask whether he was able to soundly prove that there are infinitely many primes, I would have no idea what you meant.

Again you’re being sloppy: P represents an unspecified proposition, not a proof of a proposition. To clarify your statement, let’s say that K is a sound proof whose conclusion is P and which uses only P1,P2,P3 as premises. Then to say that that K is a sound proof is equivalent to saying that K proves P, which in turn entails that P1,P2,P3 entail P. Certainly, to say that X proves P (where X is a being) is not logically equivalent to saying that K proves P; rather, it is to say that X refers unambiguously to K (or some other sound proof of P).

My point is that it is absurd to claim that this argument shows that, although there is a K such that K is a sound proof of G', it is impossible in principle that God might produce K.

The absurdity can be demonstrated more clearly by looking at the statement:

S: Smith cannot soundly prove S.

Assuming that S expresses a proposition, I can prove that S is true as follows:

1. Assume not-S.
2. If not-S, then Smith can soundly prove S.
3. If Smith can soundly prove S, then S.
4. From 1-3, S and not-S.
5. Therefore S.

Now if S expresses a proposition, this is clearly a sound proof of S. But suppose that this proof is written out on a piece of paper which is placed in front of Smith, who reads it and understands that it is a sound proof of S. Surely you agree that (if this really is a sound proof of S) Smith’s copying of this proof onto another piece of paper would constitute his soundly proving S? And surely you agree that it is not logically impossible that this might happen? But in that case it is not logically impossible that Smith might soundly prove S. Which is to say that S is false. But if S is false, there is no sound proof of S.

Therefore S does not express a proposition.

But if S doesn't express a proposition, neither does G'.

TollHouse

But how long is your schlong?

It's funny how such a super genius brags about himself in a manner commonly found on a school playground.

Conspiracy, it really doesn't matter what you think your I.Q. or doctorate says about you, it doesn't make you any less of a smug [insult deleted].


Edited to remove a gratuitous insult. -PB

[ June 09, 2002: Message edited by: Pompous Bastard ]</p>

CardinalMan

Are you implying that humans can solve the halting problem? In other words, humans can devise one universal procedure that, when employed on any one fixed input of a computer program, will determine whether or not the given program halts on its own description?

CardinalMan

Adrian Selby

I'm thinking aloud here, and am glad to be corrected as I'm not completely clear on issues of formal logic.

JesusConspiracy claims to have shown that God cannot do something that he can, which is prove the proposition G 'God cannot prove proposition G'.

Is this true? I wonder because if we had a proposition H 'JesusConspiracy cannot prove that God cannot prove proposition G' then he cannot prove that he proved it if we set up the proof again. (Perhaps that should be proposition G 'JesusConspiracy cannot prove that God cannot prove proposition G')

If someone knows where I'm going with this who's tighter on formal logic, please either correct me sharply or expand, I'm keen to be illuminated either way. I think I'm trying to create a proposition that tries to include JesusConspiracy's proof of G that asserts that he cannot prove it.

Adrian

[ June 09, 2002: Message edited by: Adrian Selby ]</p>

seebs

No, but rather, that I've met people who claim that, since they can describe things computers can't do, that computers are inherently "incapable of intelligence".

seebs

Actually, this shows nothing.

Let's expand the variables.

Can God create an object that cannot be moved by an omnipotent being?

The phrase "an object that cannot be moved by an omnipotent being" is obviously semantically busted.

All you've done is show that you can create a verb phrase in English that does not denote any meaningful action.

AdamWho

Seebs:
Sure my argument was like a child’s (as noted), but that hardly matters, since any argument claiming to refute or prove the existence or qualities of an unknowable being is doomed.
As you said:
Invalid arguments are all equally invalid; I just skipped all the intellectual huffing-puffing.

[ June 09, 2002: Message edited by: AdamWho ]</p>

MuslimIdealist

If God isn't self-contradictory, then He cannot make Himself powerless.

MuslimIdealist

Why would God never soundly prove something to us, and if He were to not prove something to us that we didn't know, then how would we know?

I question your assumption that God will never soundly prove G. What sense would it make for God to never soundly prove anything, let alone G?

[ June 09, 2002: Message edited by: MuslimIdealist ]</p>