[FOM] Logic/Syntax versus Arithmetic
Timothy Y. Chow
tchow at math.princeton.edu
Mon Mar 2 20:42:15 EST 2020
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
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