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| In a message dated 10/30/2002 3:27:08 PM Central Standard Time, cowan@hidden.email writes: << Umm, rather specious. Saying that the integers are reals does not mean that >> Actually, the speciousness lies -- if I remember correctly -- in the fact that "is an integer" cannot even be defined in analysis, which seems an even stronger reason to doubt that integers are reals. And, if that is the case, integer operations ae not even subsets of real operations -- at least not specificable subsets. << Well, if you take the view that a natural number n *is* the set of sets of cardinality n (Frege) or that it *is* a Zermelo set, or whatever, then you may have trouble identifying the rest of the numeric tower with these particular sets. But I don't take that viewpoint: I'm an unabashed Platonist. >> ???! More a Platonist than Frege or Zermelo! Or Platon, for that matter, who clearly distinguishes between arithmetic numbers (natural) and geometric (real). It is an odd Platonist who thinks that two things that lie under different universals are nontheless the same. That is the sort of thing that can happen only in the confused world of shadows, not in The Real World. |