[FOM] Logic/Syntax versus Arithmetic

[Timothy Y. Chow]

MK wrote:

> I have the impression again that you are talking about the metalanguage 
> three here.  Developing a formal object theory for "the" natural numbers 
> necessarily takes you beyond the metanaturals.

I don't disagree, but I feel that you and I may be talking about different 
things.  I'm just trying to argue for a parallelism between syntax and 
arithmetic.

So for example, if someone thinks that the word "string" makes enough 
sense that we can use that word meaningfully in a metalanguage, then I 
maintain that the word "number" makes enough sense that we can use that 
word meaningfully in a metalanguage.

Or if someone thinks that it makes sense to talk about infinitely many 
wffs, then I maintain that it makes sense to talk about infinitely many 
natural numbers.

Tim