> On Feb 6, 2017, at 11:36 AM, Jeffrey Brian Downard <[email protected]> > wrote: > > As an example, why don't we compare historical examples of nominalist and > realist positions in logic, such as what we find in Mill's System of Logic > and Peirce's logical theory. When we do, we find very different philosophical > accounts of the principles that govern valid reasoning.
Do you think these end up being tied to nominalism? I’d be extremely interested if you can give some examples of that. I confess I’m skeptical since to my eyes from a logical perspective there’s not a lot of difference between a real general and a term indexing to a bunch of real particulars. Now the logical properties of various notions of infinity do of course matter a great deal. There you find say an Aristotilean potential infinity playing a very different role. But I think many nominalists are perfectly content to allow terms to refer to an infinite number of entities even if some are more like mathematical constructivists requiring a bit more care. As I think I said a week or two ago when we get to set theory things may get a bit trickier since of course famously allowing loose set membership leads to paradoxes. Perhaps one can make a stronger argument in set theory and set construction that realism vs. nominalism matters far more.
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