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Topic: Mathematics as a language
Replies: 35   Last Post: Nov 8, 2010 1:53 AM

 Messages: [ Previous | Next ]
 Daryl McCullough Posts: 2,871 Registered: 1/29/05
Re: Mathematics as a language
Posted: Nov 6, 2010 8:33 AM

herbzet says...

>I guess the problem people are having with my thesis is that they
>are willing to accept (a) the mathematical existence of S, similar
>to that of the object 6, and they are willing to accept (b) the
>mathematical existence of a bijection f from w_1 to P(N), similar
>to that of the object 6, but they are not willing to accept both
>(a) and (b), because the object 6 is special -- it really and truly
>exists in some sense, and that property of really existing cannot be
>shared by contradictory objects like S and f.

I don't think that's right at all. It doesn't have anything
to do with 6 being special.

there is a strong man, Hercules, who can lift any rock,
no matter how heavy. Let's also say that there is a rock, the
Heavystone, that is so heavy that no man can lift it.

It's conceivable that there could be a Hercules. It
is conceivable that there could be a Heavystone. But
certainly it is impossible for *both* to exist. If
Heavystone exists, then there is no man who can lift
any rock. If Hercules exists, then there is no rock
that is too heavy to lift.

Some pairs of defined objects are mutually inconsistent:
they can't both exist.

Now, there might be a way to weasel out of it by talking
about "possible universes": Hercules exists in one possible
universe, and Heavystone exists in a different possible
universe. But then you're waffling about the meaning of
the word "exists". Do you mean exists within *one* universe,
or exists within *any* universe?

--
Daryl McCullough
Ithaca, NY

Date Subject Author
11/2/10 Aatu Koskensilta
11/3/10 herb z
11/3/10 Herman Jurjus
11/3/10 Marshall
11/3/10 Herman Jurjus
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11/6/10 Brian Chandler
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11/7/10 Daryl McCullough
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11/3/10 Daryl McCullough
11/4/10 Bill Taylor
11/4/10 Daryl McCullough
11/5/10 herb z
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11/4/10 Daryl McCullough
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