From: Samantha Atkins (samantha@objectent.com)
Date: Sun May 26 2002 - 01:04:28 MDT
Lee Corbin wrote:
> Giu1i0 Prisc0 writes
>
>
>>Or perhaps a overestimation of the power of logic. I recall that the
>>discussion started when the Principles were used in support of statements
>>that just did not feel right to others. I think we have to live with this:
>>perhaps no thinking system can be so watertight to imply all statements that
>>one "likes" and exclude all statements that one does not like (there are
>>analogies in mathematical logic e.g. the Godel proof).
>>
>
> Yes, I agree with every phrase of your paragraph. But what do we mean by
> logic, exactly? I think that you're right because I believe that what we
> should mean by "logic" plays---and should play---almost no role in our
> discussions. I know that that sounds funny, but read on.
>
>
>>I am convinced of the importance of rational and analytic system
>>thinking
>>
>
> Yes indeed!
>
>
>>but believe that, at times, basic gut feelings on what is right
>>or wrong may be a better guide.
>>
>
> Quite right. One has to be very careful with logic. Consider
> the following theorem:
>
> Theorem: God Exists.
>
> Proof: If this sentence is true, then God exists. Therefore,
> God exists because that sentence is indeed true. How do we
> know that it's true? Simple. A sentence is true when the claim
> that it makes is correct (or true). Well, what claim does that
> sentence make? It claims that if it itself were true, then God
> would exist. But that's so! If indeed the sentence were true,
> then God would exist. Since what the sentence claims is so, then
> the sentence is true, and so God exists. Q.E.D.
>
> There is *no* logical flaw in the above proof, despite the
> frenzied attempts it will provoke to find a flaw. The flaw
> in the proof is semantical, not logical. It turns out that
> words cannot always be thrown around with impunity---careful
> thought and good judgment are always necessary.
>
There is an obvious flaw. Point 1 merely restates the theorem
supposedly but in fact says something different. It says "if it
is true then it is true" effectively. This is worthless. Point
2 assumes what is to be proved is already known to be true by a
more convoluted reiteration of the totally empty Point 1. It
ends up saying the theorem says what it does not. It says "God
exists". It does not say, "If this theorem is true then God
exists." The latter, if it did say that is perfectly valid when
F -> F just as well as when T -> T. And no, the flaw is not a
matter of semantics.
- samantha
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