[FOM] Numbers vs writhmetic. was: n-th order ZFC

[W.Taylor at math.canterbury.ac.nz]

Quoting Roger Bishop Jones <rbj at rbjones.com>:

> ... one can believe in the objective truth of arithmetic
> without also believing in the existence of numbers.

I would like to hear more about this, if possible, as it touches on
a dichotomy that I have been hearing a lot about in the last few years.

If one (a) DOES accept the objective truth of arithmetic,
but    (b) does NOT accept the existence of numbers,
then wherein resides the objectivity of the arithmetic?

If one has no semantics for arithmetic (which seems to be what (b) says),
then on what grounds is truth to be defined for arithmetic?

(I do not intend to be combatively rhetorical, I would just like
  to understand this combination position better.)

-- Wondering William
fom at cs.nyu.edu


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