[FOM] formalism

[Rupert McCallum]

I'm interested in understanding the formalist position better. One
version of it is that mathematics is "the science of formal systems",
but then the question arises in what metatheory do we study these
formal systems. 

Edward Nelson says he is a formalist and that he thinks the consistency
of Robinson Arithmetic is an open problem. This makes me wonder what
metatheory he accepts. (I have sent him an email asking him about
this). Is it just the set of true Sigma-1 sentences, for example? Or
the set of Sigma-1 sentences which we can feasibly prove?

Have any formalists expressed a position on this issue?


 
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