Why omnipotent is a paradox.

TechnoCore writes:

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Since Gdel proved that to be able to prove every conceivable statement within a logical system, you must go outside that system.

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No, he didn't.Instead, he showed that certain systems are incomplete. Not all systems fall within that category.Pressburger arithmetic, for example, is complete and consistent.The Incompleteness Theorems only apply to axiomatic systems of number theory.I am not sure the universe can be considered such a thing.------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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Instead, he showed that certain systems are incomplete. Not all systems fall within that category.

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I'm by no means the expert here, but if I recall what I've read, the systems that this does apply to are the ones that are able to self-reference. ("Model number theory" was another/the same requirement, I believe.)

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Incorrect.The statement is that all axiomatic systems of number theory sophisticated enough to model arithmetic.Do you have evidence that the universe is an axiomatic system of number theory?

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Clearly the universe is able to model number theory.

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So you're saying that numbers do exist as part of existence, then?Over on the other thread, you seem to be saying that they don't.

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Ergo, Godels proof might apply to it.

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It might...if you can show that the universe is an axiomatic system of number theory.Remember, not everything in math is such a thing.------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to John:

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I think he resists because Godel's proof drops a big hole right in the middle of his perfect mathematics, I suspect.

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Or, perhaps, you don't have a clue as to what I'm talking about.Where did I say mathematics was perfect?Quote, please. I want to see where I said that mathematics was perfect or even hinted at such.Seeing as how I've been the one who has been getting the most technical about the mathematics, including what Godel's proofs actually say, I'm having a hard time figuring out how you came to the conclusion that I think math is perfect.

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That may be why he continually downplays the significance of the proof.

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Or, perhaps, it may be that he is more concerned with people being accurate and not over-stating themselves.Do you think the Heisenberg Uncertainty Principle applies to interpersonal relations?So what makes you think the Incompleteness Theorems apply to things that aren't axiomatic number systems?I didn't ask it directly, so I'll ask it here:Could you show how the universe is an axiomatic number system?That means you'll need to provide us with a way to actually calculate what the axioms of the universe are. I don't know about you, but I haven't heard of any yet.------------------
Rrhain
WWJD? JWRTFM!

John responds to me:

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Where did I say mathematics was perfect?

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The tone of your posts across several threads strongly imply such a conclusion.

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I wouldn't say that at all.To paraphrase the remake of D.O.A.:What I mean? That's "imply." The way you take it? That's "infer."

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I imagine that if you were to take a poll of those here, you'd find that this is the impression you leave-- to a greater or lesser extent, depending on the reader. If this is not your intent, you might consider the effectiveness of your communication.

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Or perhaps you might consider being more careful. It wouldn't be the first time that many people are simply wrong.

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Do you think the Heisenberg Uncertainty Principle applies to interpersonal relations?

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Oh, yes. Most certainly-- kindof a hyper-uncertainty principle really.

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Oh really? And how does one determine Planck's constant in the example of a child by the cookie jar when he knows his mother is watching and when he doesn't? After all, that would be one way of calculating the constant: Determining the change in position and velocity...but that leads to the question of what it is that is changing position and velocity.And then there is the problem of how the child behaves when he only thinks his mother is around when she really isn't.

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Could you show how the universe is an axiomatic number system?

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The universe itself? Who knows?

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Then what makes you think the Incompleteness Theorems apply?------------------
Rrhain
WWJD? JWRTFM!