complexitystudies wrote:
>>I think it has been said several times :
>>The existence of a number/arithmetical proposition is the fact that its 
>>existence/truth does not depend on the fact that you exist/that it exists 
>>conscious beings capable of thinking of it.
>>So the truth value of a proposition is independant of me.
> Well, let's see: in Alice in Wonderland, Humpty Dumpty fell off a
> wall. This is true, isn't it? It is certainly true independent
> of our minds. Indeed, it is true in such a way that even when
> all humans have died, this universe will have a contained a life-form
> which produced an author who wrote a book in which Humpty Dumpty
> fell off a wall. But neither Humpty Dumpty nor the fact that he
> fell off a wall were ever true in this universe - only that this
> story was written, and that many people read about it and could
> converse about it.
> So if you believe that numbers have an independent existence, then you
> would definitely also have to believe that Humpty Dumpty exists.
> Both are products of the mind. Either both exist, or both don't
> (other than as brain patterns).
> As much as I would like Humpty Dumpty to exist, I'm afraid that
> it is not so.
> Regards,
> G√ľnther

I agree.  But truth need not imply existence.  That's the idea of "free logic" 
(i.e. free of existential suppositions).  So one can say "Shelock Holmes lived 
on Baker Street." is true and "Sherlock Holmes drove a car." is false.  But 
some statments, such as "Sherlock Holmes had a mole on his left side." are 
neither true nor false.

Brent Meeker

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