[FOM] The Natural Language Thesis and Formalization

[hendrik@topoi.pooq.com]

On Sat, Jan 26, 2008 at 12:32:52PM -0500, Timothy Y. Chow wrote:
> Steven Gubkin <steven.gubkin at case.edu> wrote:
> > Is it 
> > reasonable to conclude that there are natural numbers which are also 
> > functions? Clearly this "result" is an artifact of the way we 
> > translate concepts into (and out of) ZFC.
> 
> This is a nice observation.  I don't find it particularly perplexing 
> though.  For starters, it's not so clear to me that the statement is 
> false.  It's a little odd, to be sure, but is it false?  If you're 
> convinced that it's false, can you prove that it's false?  I'm not sure 
> how I would go about proving that no natural number is a function.

If, for example, you use the Church numerals, all natural numbers are 
functions.

-- hendrik