[FOM] Is mathematical realism compatible with classical reasoning?

tchow tchow at alum.mit.edu
Wed Jul 26 14:55:09 EDT 2017

Colin McLarty wrote:
> The idea that "we should reason entirely in terms of propositions that 
> can
> be verified in principle by" any specified set of procedures is usually
> considered a kind of verificationism and thus not realism.  It seems 
> that
> you are actually questioning whether mathematical verificationism 
> (using
> your specified means of verification) is compatible with classical 
> logic.

Yes.  In fact, even the desire for "is true" to be expressible as a 
mathematical predicate seems to be something that a mathematical realist 
would not necessarily have.  According to most forms of realism, reality 
exists independently of us, and if we find ourselves having trouble 
describing reality linguistically, then (so to speak) that's our 
problem, not reality's problem.  Language, even foundational language, 
is not seen as defining or creating reality; it's just putting into 
words (as best as we can) what we know and/or believe about reality.


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