
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 >know how to answer it.
Well, it's about your contention that if something is logically 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

