John Page

I don't think your comment was stupid. While formal logic battles can be entertaining (you have to be there) and may prove there are no logical monotheists its a weak argument to a believer.

Like they used to tell us in church when a pithy question came up "God works in mysterious ways, his wonders to perform". What we need is a godless church so we can just commandeer the years of tradition, the wonderful songs, the social ceremonies and inspiring sermons. This will scientifically prove that the magic ingredient *god* makes no difference to Aunt Alice's arthritis. Think I'm joking... wasn't there a study that people who went to church lived longer? I also read about a clinical trial where placebos had a better success rate than the drug! Better marketing, that's what we need, not more logic.

Cheers, John

AdamWho

John Page:
In several posts you seem to have confused logic and reason.
Logic is tautologies, there can be no new information gained; they are only useful when ALL the information is presented in the premises, which can’t happen in this discussion.
Reason is the integration of empirical data into a coherent body of knowledge using logic.
So if you are arguing against logic, you are probably really arguing about certain premises. However, if you are arguing against reason; then are you claiming that reason is not a valid way to gain knowledge about the world?

curbyIII

To TheJesusConspiracy:

You admitted that G is NOT a proposition. Since G is not a proposition the laws of logic do not apply to it. It cannot be either true or false. Reductio ad Absurdum can't be applied to it. Your entire argument falls apart.

I would like to point out that even if you are right (God can't prove G, but you can), this in no way implies that the concept of omnipotence is "meaningless." One can simply redefine it to mean that god can do anything that is logically possible for him to do. I'm sure that nearly all theists would be satisfied by such a definition.

Although this entire thread has been an interesting logical/mathematical discussion, it does not challenge theism in any way.

Automaton

This assumes it is logically possible for God to duplicate himself. I would doubt it, and would be similar to God willing himself out of existence.

Jobar

"This assumes it is logically possible for God to duplicate himself. I would doubt it, and would be similar to God willing himself out of existence. "

Automaton, haven't you read Hitchhikers Guide to the Galaxy, and the babelfish proof of God's nonexistence?

I admit we are moving farther away from our central subject here- EoG- but I want to ask a question of TJC while I am speaking to a formal logician. Consider these two sentences-

1. This sentence refers to itself.
2. This sentence does NOT refer to itself.

Now, which of these is the less truthful?

As I understand it, both are meaningless in that they are completely self-referential. They are as sealed off from the universe of normal discourse as a black hole is from the physical universe. But- can the second be considered less 'true' in that it is paradoxical as well as self-referential?

-Jobar, the intellectually curious.

Clutch

Jobar, maybe you know all this already. But it is not generally accepted that all self-referential statements are meaningless. As Susan Haack points out, there are lots of self-referential statements that seem not just meaningful, but clearly true. Eg, "This sentence is short."

The problem with "This sentence is false", according to the famous diagnosis proposed by Tarski, is not simply the self-reference, but rather the "semantic closure" -- Tarski's term for the inclusion of a truth-predicate *for* some language L *within* L itself. His solution was just this: when we formally regiment a fragment of natural language (ie, that sentence), we must regiment it in such a way that the semantic notions (incl. truth) in the fragment are formally represented as belonging to a different (formal) language than that in which the rest of the fragment is represented.

Hope some of that is useful.

RogerLeeCooke

Hello, all. I haven't visited for many many months, but I'm glad to see this site is just as active as ever.

It struck me as odd that variants of Gödel's incompleteness theorem would be invoked as disproofs of the existence of an omnipotent being. But after thinking it over, I think it's very natural. Most of modern set-based mathematics is speculation about total abstractions. A century ago, when presented with a proof of the Hilbert basis theorem couched in such language, Paul Gordan said, "That is not mathematics any more, it's theology."

And I think he is right. Mathematicians are always being plagued by eager amateurs who think they have succeeded in trisecting any angle with compass and straightedge. The amateurs have no concept of proof, of course, but they lack something else, from the mathematician's point of view: the concept of a real number. The only numbers they know are usually decimal fractions, and they don't understand that the construction has to be *infinitely precise*. Bertrand Russell once pointed out that we have no experience of infinite precision in ordinary life. It is a pure abstraction. I can argue for its usefulness, but one can certainly excuse laypeople for not grasping it.

To get back to the point, abstract mathematics is as content-free as theology. The difference is that mathematics and logic are useful. As for proofs of God, I agree with Dawkins that theology isn't even a subject.

Synaesthesia

Curby,
Defining a sentence by whether it is true or false within the system is a very natural response to Godel's theorem. (I understand Russel tried to smooth out problems in formal systems by a similar method.) However, unless we hamstring the system, it doesn't even solve the problem.

I don't know how useful it is to ban such statements. Many logicians deal with it by saying "yes the statement is true, but it's truth cannot be determined without going outside the system."

However, I think we all agree that omnipotence does not require God to assign a truth-value to a statement within a system that denies the truth-value of that statement. God would simply say "Oh that's an undecidable preposition. I should know, I invented them.", making the Godelization of God somewhat futile.

Mike Rosoft

But God can go the same way:

G: "I can't soundly prove G."

1. Assume not-G.
2. If not-G I can soundly prove G.
3. If I can soundly prove G, then G.
4. From 1-3, G and not-G.
5. Therefore, by indirect proof 1-4, my assumption is necessarily false, and it is the case that G.
6. But I have soundly proven G.

Can you see something wrong? Looks like either the system you are working in is inconsistent, or G is an invalid preposition like "This statement is false" which cannot be either true or false.


Mike Rosoft

Synaesthesia

I don't frankly see the need to eliminate undeciable prepositions from formal systems. The fact is that Godel demonstrated the impossibility of powerful but finite aximatic systems to exist without some unprovable but true statements.

Perhaps we should accept that as an addition to our understanding rather than reject it as a flaw. Seeing Godel's theorem as a flaw rather than an eludication of the nature of truth is TJC's essential mistake.