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

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herb z

Posts: 1,187
Registered: 8/26/06
Re: Mathematics as a language
Posted: Nov 8, 2010 12:56 AM
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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 self-contradictory -- 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 co-exist 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


Date Subject Author
11/2/10
Read Re: Mathematics as a language
Aatu Koskensilta
11/3/10
Read Re: Mathematics as a language
herb z
11/3/10
Read Re: Mathematics as a language
Herman Jurjus
11/3/10
Read Re: Mathematics as a language
Marshall
11/3/10
Read Re: Mathematics as a language
Herman Jurjus
11/4/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
Marshall
11/5/10
Read Re: Mathematics as a language
herb z
11/5/10
Read Re: Mathematics as a language
Herman Jurjus
11/6/10
Read Re: Mathematics as a language
herb z
11/6/10
Read Re: Mathematics as a language
James Dolan
11/6/10
Read Re: Mathematics as a language
Tim Little
11/6/10
Read Re: Mathematics as a language
Daryl McCullough
11/6/10
Read Re: Mathematics as a language
Marshall
11/6/10
Read Re: Mathematics as a language
Brian Chandler
11/6/10
Read Re: Mathematics as a language
Tim Little
11/7/10
Read Re: Mathematics as a language
lwalke3@lausd.net
11/8/10
Read Re: Mathematics as a language
Brian Chandler
11/7/10
Read Re: Mathematics as a language
herb z
11/7/10
Read Re: Mathematics as a language
Daryl McCullough
11/8/10
Read Re: Mathematics as a language
herb z
11/3/10
Read Re: Mathematics as a language
lwalke3@lausd.net
11/3/10
Read Re: Mathematics as a language
Marshall
11/4/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
herb z
11/3/10
Read Re: Mathematics as a language
Daryl McCullough
11/4/10
Read Re: Mathematics as a language
Bill Taylor
11/4/10
Read Re: Mathematics as a language
Daryl McCullough
11/5/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
herb z
11/4/10
Read Re: Mathematics as a language
Daryl McCullough
11/5/10
Read Re: Mathematics as a language
herb z
11/5/10
Read Re: Mathematics as a language
Daryl McCullough
11/4/10
Read Re: Mathematics as a language
VK

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