Synaesthesia

MuslimIdealist,
If God does prove G, he's simply proving that he cannot prove G.

Consideration's of God's ability to enumerate and infinite set aside(which certainly has implications for Godel's theorem) why would omnipotence require God to prove absolutely anything true? Wouldn't he simply say "Gee, that preposition is undecidable within the system defined."

My point is, that God does not require a bifurcated truth-value to be omnipotent. He can simply recognize every possible implication of the fact that within formal systems not every true preposition can be proven true or false within it's system.

[ June 10, 2002: Message edited by: Synaesthesia ]</p>

seebs

Good point.

echidna

TJC, forgive me if I usually don’t judge character quite so quickly as on Friday, but your opener left me a little doubting as to your credentials. What’s more, you seemed to be posing it as a new idea (which others have pointed out), it just seemed akin to posting a questionable Pythagorean proof (although in contrast Pythag is actually beyond debate) in S&S, and then sounding a triumphant fanfare. Call me slow (but not all at once), but somehow I don’t think 2000 years of modern philosophy and theology are quite so simple ? It’s just that most of the intellectual posts I’ve read would have prefaced themselves with something a little to this effect.

FWIW, you over-estimate my own character. As an engineer, sadly I don’t even count as a scientist. I’m good at lifting things.

seebs

I generally assume that, if someone has to *tell* you that he's an intellectual, he must not be very good at it. I also observe that being an intellectual correlates only loosely with being right, or even coherent, on most points; mostly, it's all about the joy of the game, and questions of whether or not a conclusion is "true" are left to the sorts of mundane people who care about such nonsense.

TheJesusConspiracy

Another member implied that I was not a true intellectual and I responded in turn. Yet the criticisms have come from my response, not the original attack. No matter. I shall remain more emotionally neutral from here on.

Regarding the possibility of G having a truth value, I'd like to posit the following addendum to my proof. As for my critics, I'd like you all to keep in mind I wasn't putting this out there to shatter heaven and sky. It's a fun little proof at best. I don't expect to break up the 700 Club.

....

Anyways, let's agree that G has no truth value because it is a self-referential pseudostatement. In that case, my original assumption supposedly falls apart, for it will be impossible to provide a proof of G (since G is not a sentence, it cannot be proven true); moreover, one cannot start by assuming not-G, as G is not a real sentence and cannot be false.

Thus, to say that God will never prove G is trivial, for G is not a sentence and cannot be proven or disproven by anything. I shall officially concede this point to the detractors. It's the equivalent of saying God will not prove "1+1". "1+1" is just an expression and there's nothing to prove. One might as well argue about whether chickens are odd or even.

So, given that G is not a sentence, God will never prove G. In order to prove G, G must be eligible as a provable object.

Of course, G claims that God won't prove G.

Thus, by reductio ad absurdum, if one concedes that G is not sentence, one shows that G is true.

......

I'd also like to talk about modality.
If the proof works, it shows that necessarily God will never prove G, i.e. it is logically impossible for God to prove G because this is a contradiction. In modal logic, if it is necessary that God does not prove G, then it is not possible that God proves G, which means that God cannot prove G.

If anyone objects to that, that's fine with me. The meaning of modal language is still a topic of fierce debate. To say, in S5 modal language, that God can prove G is to say that there is some logically possible world in which God does prove G. But the proof establishes that there is not possible world. I take this to be sufficient to show God cannot prove G. If the proof only showed that God doesn't prove G but could, it would have to show that G is a contigency, not a necessity. Another post-writer disagrees. I don't see much hope of overcoming this until the dilemma of modal language is solved.

echidna

Modal language will be solved about 2 weeks before Post Modernist language is solved.

Adrian Selby

Again interfering with a thread that I'm weak on, the following statement:

"So, given that G is not a sentence, God will never prove G. In order to prove G, G must be eligible as a provable object.

Of course, G claims that God won't prove G.

Thus, by reductio ad absurdum, if one concedes that G is not sentence, one shows that G is true.
"

Let me fumble around a bit.

What you're saying is that God can never prove that G, where G is a sentence stating that God can never prove that G.

There seems to be a meta-statement here implicit in what you're describing.

If the sentence is meaningless, because it refers to itself, then God cannot prove a meaningless sentence, of course. However, a sentence cannot be true and meaningless. At best you have a paradox. I wonder whether you can say the statement is true only because you are conflating

"God cannot prove G"
with
"God cannot prove that (God cannot prove G)"

The latter is a statement about the sentence.

Again, as I walk on thin soil here, if someone does see a legitimate point here, perhaps they'd do me the honour of illustrating it better.

Clutch

TJC, you were doing fine until you said this: No. The question is not whether G is a sentence -- syntactically, for example -- but whether G is meaningful. (Cf, "Colourless green ideas..." is syntactically sentential, but meaningless). You are supposing here that G is *not* meaningful. And this being the case, G does not claim that God will not prove G, nor does it claim anything else. The reductio fails.

Adrian, I don't know whether that adds anything or not; your point was very well expressed.

[ June 11, 2002: Message edited by: Clutch ]</p>

bd-from-kg

TheJesusConspiracy:

As Clutch pointed out, the question is not whether G is a sentence, but whether it expresses a proposition. Many perfectly good sentences do not express propositions – for example, “Is Mary your mother?”, “Close the door”, “`Twas brillig, and the slithy toves did gyre and gimble in the wabe”, and “This sentence is false”.

Any expression that does not express a proposition cannot be said to be true or false, for the simple reason that to say that an expression is true or false is to say that the proposition it expresses is true or false.

Saying that God will never prove G is exactly as meaningful as saying that God will never incubate a square circle. If you wish, you can say that it is a contradiction to say that God will incubate a square circle; I’d prefer to say that it is meaningless.

In any case, you seem to have lost sight of the original objective, which was to show that God cannot do something that can be done. As you put it in the OP:

By the way, I do not believe that all proofs that “omni” properties are self-contradictory are invalid. See my <a href="http://iidb.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=50&t=000101&p=" target="_blank">Incoherence of Omniscience</a> thread (which is still open if you want to add a comment, by the way).

luvluv

Um, I'm kinda stoopid and don't generally follow when you folks start resorting to letters and squigly symbols, but why couldn't God just incarnate himself in another rational form that was god, but not ALL of God and then disprove the thingy-ma whatchamacallit. I mean many Christians believe that Jesus was God in the flesh, so if He were to disprove such a statement wouldn't that be God disproving it? I mean, it would be him, but it wouldn't be Him.

If this is really stupid please skip over it.