Dear Jon, lists - I think I can understand how Peirce would need to emphasize realism in certain arguments or for certain audiences, imaginary or otherwise.
To Peirce, realism does not seem restricted to certain arguments or audiences - cf. classic expositions like Boler's 1963 book on P and scholastic realism or Max Fisch's paper on P's development from nominalism to realism. By that standard, though, all mathematicians would be extreme realists, as opposed to the garden variety Platonists they really are in practice. In all but the most paradoxical or pathological circumstances, it makes sense to say that a set is something other than its elements, and the rest of the claim you cite would depend on the definitions of choice for terms like "comprise", "more than", "possible number", and "instantiations". These are just my shorthand expressions. The argument refers to the connection between P's realism and his continuity metaphysics - I dealt with this in more detail in ch. 2 of Diagrammatology (2007) Still, I have a long history of using a principle like that to argue for a measure of rationalism to leaven any mix of naive empiricism, so I guess that makes me an extremist, too. Certainly … Best F
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