Re: What is "true" in mathematics

Aatu Koskensilta wrote:

On 2008-03-28, in sci.logic, Frederick Williams wrote:
What turns out to be true in mathematics depends on the choice of
logical constants, _that_ is a matter of convention.

What do you mean by "logical constants" here, and in what sense is the
choice of "logical constants" a matter of convention?

Consider this:

p v ~p

(if you have intuitionist sympathies you may wish to put ~~ in front of
it(*)). 'p' is a variable 'v' and '~' logical constants. When one
determines whether p v ~p is true or not one substitutes different
values 'true' and 'false' for p, but v and ~ are always interpreted as
'or' and 'not'. One can't interpret v as 'and' for example.

Now, is $\in$ a logical constant? I don't mind whether you say yes or
no, but your choice is purely a conventional one. Also: same point with
=, and with v and ~.

(* The fact that one might distinguish between classical and
intuitionist views (and others) is already a hint of the conventional
nature of truth.)

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