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

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 Daryl McCullough Posts: 2,871 Registered: 1/29/05
Re: Mathematics as a language
Posted: Nov 7, 2010 8:34 AM

herbzet says...

>Daryl McCullough wrote:
>

>> Now, there might be a way to weasel out of it by talking
>> about "possible universes": Hercules exists in one [logically] possible
>> universe, and Heavystone exists in a different [logically] possible
>> universe. But then you're waffling about the meaning of the word "exists".

>
>The meaning of the term "mathematically exists" is indeed at issue here.
>

>> Do you mean exists within *one* universe, or exists within *any* universe?
>
>I really am having difficulty understand what is being asked, so I don't

possible, then it exists. Exists *where*? It doesn't necessarily
exist in our universe.

>Hercules exists in one logically possible universe, Heavystone exists in
>a different logically possible universe.

Suppose that the definition of Heavystone is: some rock such that
there does not exist a person, in any possible universe, that can
lift it, and the definition of Hercules is: some person such that
there does not exist a person, in any possible universe, that he
cannot lift.

>Both possible universes exist within the universe of logically
>possible universes -- I don't see the problem.

The only problem is that unless your careful, such a belief is
inconsistent. It's consistent if you insist that a proper definition
of an object cannot mention other universes.

What you're claiming can be made a theorem (Godel's completeness
theorem) if you say it this way: If you have any consistent first
order theory, then there is a model in which that theory is true.

--
Daryl McCullough
Ithaca, NY

Date Subject Author
11/2/10 Aatu Koskensilta
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11/3/10 Herman Jurjus
11/3/10 Marshall
11/3/10 Herman Jurjus
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11/7/10 lwalke3@lausd.net
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11/3/10 Daryl McCullough
11/4/10 Bill Taylor
11/4/10 Daryl McCullough
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11/4/10 Daryl McCullough
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