BLoggins02

Somebody's been smokin' some serious Hofstadter

Viti

Well Mr. Conspiracy, I don't have an intellectual-o-meter, but there is definite evidence that you are an arrogant boor.

[ June 07, 2002: Message edited by: LadyShea ]</p>

Jesus Tap-Dancin' Christ

The statement itself was circular. "X will never soundly prove this statement." The statement itself is contradictory, and impossible for X to prove--because by doing so, he disproves it. If he fails, then he proves it--simply by doing nothing.

I know damn well what logic is. And logically, there is no way that any person X can prove the statement "X will never soundly prove this statement."

Jesus Tap-Dancin' Christ

[QUOTE]Originally posted by TheJesusConspiracy:
<strong>By the way, watch the insults. There's about a 1 in 30000 chance that you qualify as more of an intellectual than I.</strong>[/QUOTE}
IQ is meaningless unnaplied. And you can be far more of an itnellectual with a lower IQ than yourself.

ShottleBop

Wouldn't a better approximation of the meaning of omnipotence be: "If it is logically possible to do X, then an omnipotent being is capable of doing X"?

HRG

True. X cannot do it.

But Y, who is different from X, can prove this statement. Thus Y can do something that X cannot do; that's the whole point.

HRG.

Jobar

This? Intellectual? Sorry TJC, but I heard this one on a George Carlin tape back in the 70s- "Toledo Window Box" maybe?

"Hey Fadda! Is God able to make a rock so big he himself cannot lift it?"

And I would guess that the originator of this conundrum might have lived in classical Greece, or even earlier.

You have expressed it in the language of formal logic very prettily- but our theist members will point out that *logical* impossibilities are not included in their definition of omnipotence.

I kind of hope you stick around, TJC- I want you to talk to a fellow named DaveJes. Ah, also, I would guess that your chances of finding someone with greater intelligence in this forum are quite good. We have PhD's in many sciences and even a few professors of philosophy, unless I am mistaken.

Automaton

Self-referential propositions such as this are meaningless and thus represent no challenge to omnipotence. Proposition G is that "God will never soundly prove G." Therefore, by substitution, it becomes G = "God will never soundly prove that God will never soundly prove G," and so forth ad infinitum. Why is this the case? Because nothing has been given to be soundly proven, it is the same as stating "God will never soundly prove [null]." Circular arguments, definitions, propositions and causal relationships all fail for much the same reason, instead of representing something that it is itself, it represents nothing at all.

CardinalMan

Although a proper formulation of your argument would not be circular, your statement G (as written) certainly is. The key technical point in the proof of Goedel's Theorem is how to simulate such a self-referential statement without being circular. This involves some coding of formal proofs and a clever fixed-point lemma alluded to by Clutch, and you haven't indicated how this is to be done. I think this is the core of Jesus Christ's objection, and I think that his argument stands until the details are clarified.

(Note: I'm not asking you to clarify the details. I've seen them plenty of times. I'm just saying that your argument, as written, is unconvincing and imprecise because it leaves out crucial details.)

CardinalMan

TheJesusConspiracy

Gosh, yawn, what the hell?

Anyways, the statement refers to itself, but the proof soundly proves the statement indirectly. It is possible to construct statements that refer to themselves that still have a truth value. For example, the statement P: Either P is false or if P, then P is self-referential but is necessarily true. It doesn't matter that figuring out what P says involves infinity...that's the beauty of it. But the statement P: either not-P or if P then P cannot be consistently denied.

The paradoxes that people referred to as having no truth value are those such as "This statement is false!". The preceding is technically meaningless. My statement, G, has a meaning. It's meaning is that God cannot soundly prove a statement G that claims that God cannot soundly prove it.

Let's get the definition of circular reasoning right so that we can stop throwing it around without justification. An argument is circular if and only if it assumes the conclusion somewhere in the premises. I NEVER assume my conclusion--rather I assume the opposite--so my argument isn't circular.

A statement is self-referential if it refers to itself. This is not a sufficient condition to tell us whether the statement has a truth value or not. A statement that is self-referential can be necessarily or contigently true or false, or have no truth value (and be a pseudostatement).

Religion is barren and sterile. Formal logic gives us hope of thinking through the idiocies of religion.