[FOM] Is mathematical realism compatible with classical reasoning?
tchow
tchow at alum.mit.edu
Fri Jul 28 22:28:52 EDT 2017
Andre writes:
> The crux of the argument in my FOM posting is that if
> classical reasoning is valid for this truth predicate also, then it
> appears to have all the features of a mathematical predicate.
Appearances can be deceiving. In this case, we have a mathematical
proof that the truth predicate is not a mathematical predicate. What
stronger reason could we have for rejecting the hypothesis that this
truth predicate---"appearances" notwithstanding---than a mathematical
proof?
> I agree that mathematical realism does not require that there be a
> uniform sense in which a sentence may be true or false. Truth may be
> treated as a trivial operator, so that the truth of each sentence is
> taken to be equivalent to that sentence. In this variant of
> mathematical realism, the validity of classical reasoning for the
> mathematical universe cannot be expressed as a general principle,
> mathematically or otherwise.
Why can it not be expressed as a non-mathematical general principle?
Tim
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