[FOM] Falsify Platonism?

[rgheck]

On 04/25/2010 10:14 PM, Timothy Y. Chow wrote:
>
> This is precisely the kind of proposal that philosophers might find
> satisfying but that is not likely to satisfy the typical mathematician.
> If everything hinges on drawing a sharp distinction between the natural
> numbers and our concept of the natural numbers, then the mathematician is
> going to be perplexed, since this is not the kind of sharp distinction
> that is customarily demanded in mathematical discourse.
>
>    
I was not trying to draw any complicated distinction that should be 
controversial. Surely we can all agree that there is a rather large 
difference between stars and our concept of stars. Surely it is patently 
obvious that the stars themselves could not care less about what we 
think of them. If this is not obvious, then one need only reflect upon 
the fact that our present concept of a star is a fairly recent creation, 
whereas the starts themselves are (one would have thought) rather older. 
Moreover, if our theory of what stars are proves to be false, then we 
will not declare the stars at fault but revise our theory.

Mutatis mutandis then for numbers and our concept of them.

What I am about to say may not be (and probably isn't) quite right, but 
it will serve to fix ideas: Concepts are *psychological* in nature. 
Stars and numbers are not remotely psychological in nature.

> After all, which mathematical properties are satisfied by the natural numbers but
> not by our concept of the natural numbers, or vice versa? After all, which
> mathematical properties are satisfied by the natural numbers but not by
> our concept of the natural numbers, or vice versa?  Are they isomorphic or
> not?  If they're isomorphic, or if asking that question is a category
> error, then why should the mathematician care about the distinction?
>
>    
Not being a mathematical object, our concept of the natural numbers does 
not have mathematical properties; so yes, it is a "category error" to 
ask these questions. I suppose that the mathematician should care about 
the distinction because he or she wants to think clearly and not confuse 
facts about us with facts about numbers. E.g., not confuse questions 
about numbers with question about what we think about numbers.

Richard