herb z
Posts:
1,187
Registered:
8/26/06


Re: Mathematics as a language
Posted:
Nov 8, 2010 12:56 AM


Daryl McCullough wrote: > 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.
I didn't say that. I said that what logically could exist  that is, what is not inherently selfcontradictory  has mathematical existence.
I am distinguishing between "mathematical existence" and the default meaning we attach to the term "exists"  probably physical existence.
It would be uncontroversial to assert that the number 6 has mathematical existence, but I doubt that many would aver that it has a physical existence.
> Exists *where*? It doesn't necessarily > exist in our universe.
Right.
> >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
Lol  you crazy, man.
Ok, then I say back, this must be a logically necessary Heavystone, for which it would be inconsistent that it be liftable in any universe.
> and the definition of Hercules is: some person such that > there does not exist a [rock], in any possible universe, that he > cannot lift.
Ok, so Hercules must also be a logically necessary person  we might as well call him god. Or at least *a* god. There's no stone, actual or possible, that he couldn't lift.
But of course the definition of this Hercules contradicts the definition of the Heavystone, so it appears that we must understand the phrase "any possible universe" to be a relative term  there is no rock that Hercules can't lift in any universe /that is accessible to Hercules/  if we want him to coexist with the Heavystone, which of course must exist in a universe that is not accessible to Hercules (nor could Hercules' universe be accessible to the Heavystone).
Ok, I confess, I'm just fooling around now. > >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.
Well, that would seem to be sufficient as a cordon sanitaire.
But inevitably we're going to get some character who wants to consider the whole structure of possible universes as part of a unified whole, the real universe. Someone who is going to want to define things across different possible universes in order to cruelly make my head spin around.
> 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.
Well alright then  but I know that as the model existence theorem.
 hz

