Comments on “Predicativity as a philosophical position” by G. Hellman
| Abstract | In his provocative article for this issue, Geoffrey Hellman has astutely attacked the philosophical grounds for predicativity from several angles. Though I am not now nor never have been a predicativist, I have to admit to being a sympathizer since I am an avowed anti-platonist, at least insofar as set theory is concerned, and I grant the natural numbers a position of primacy in our mathematical thought. Philosophically, the predicative position may be characterized as the restriction to that which is implicit in accepting the natural number structure. The subject has thus been of great interest to me and has periodically commanded much of my attention research-wise over the last forty years, especially as concerns its logical and mathematical potentialities. A caveat: a confirmed predicativist--if there be any such--would perhaps have stronger reasons than those marshalled here to defend the position on philosophical grounds. | |||||||||
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