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Date Posted: 11:20:53 05/24/02 Fri
Author: No name
Subject: Re: Limits on Godel's Theorem
In reply to: The Cosmic Muffet 's message, "Re: To be extremely technical..." on 02:45:55 05/24/02 Fri

What Godel's theorem *actually* says is that, in any mathematical system, there will be things that you can *tell* are true, can *logically* PROVE are true, but can never *mathematically* prove... and Godel's theorem itself will always be one of them. The proof of Godel's theorem in any mathematical system requires momentarily stepping *out* of the system and looking at things from a philosophical/logical standpoint. In other words, Godel's theorem can be proved in words, but NOT numbers.
The same is true of *false* theorems -- every system will have things you can logically tell are false, but never rigorously prove.
As for conceptual difference between 1.1 and 1... 1 is not an arbitrary quantity. Certain numbers are built into the fabric of the universe in which we live... 0, 1, infinity, pi, e... any sentient being would encounter these numbers and find the same properties for them. 0, 1, and infinity actually are even less arbitrary, because they are EXACTLY THE SAME in any base. Each *must* have a unique symbol in any system of showing numbers... which, now that I think about it, is a Godelian statement.

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