[FOM] Platonism and Formalism

Sandy Hodges SandyHodges at alamedanet.net
Tue Sep 9 14:15:50 EDT 2003

Arnon Avron writes:
I became a "Platonist"
with repect to the natural numbers when I realized two things: that
even a formalist should accept some mathematical statements as true or
false in an absolute sense, namely: statement of the form that a
certain formal sentence is provable in a certain formal system (and so
sentences stating that a given formal system is consistent or not).
Otherwise formalism makes no sense.

S.H. If I confine myself to asserting:
S |- F
when I know that F is provable in system S, and to asserting:
~ ( S |- F )
when I know that F is not so provable, and if I demur when some
Platonist proposes
( \/ S, F ) ( ( S |- F ) V ~ ( S |- F ) )
as a metamathematical axiom, then I fail to see that I have done
anything that makes no sense.   Have I?

It is less clear, but I think I could even describe myself as behaving
in this way, were I indeed a formalist, without saying anything that
makes no sense.

If I could behave as a formalist, and describe what it means to behave
as a formalist, without making any utterances that make no sense, then
in what sense does formalism make no sense?

------- -- ---- - --- -- --------- -----
Sandy Hodges / Alameda,  California,   USA
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