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pycyn@hidden.email scripsit:
> ???! 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.
Not at all; in this case I recognize only one universal: numbers. The
distinctions between different kinds of numbers are purely functional:
I no more think that integers are not reals than I think that primes are
not integers. It might be useful to *map* primes and composites differently,
say if I were representing primes Neumann-style but composites as sets of
primes. But then I wouldn't go around saying that "the prime number 2
is not the integer 2", because I mapped the former to {{}, {{}}, {{{}, {{}}}}
and the latter to the set thereof.
> That is the sort of thing that
> can happen only in the confused world of shadows, not in The Real World.
Au contraire. To identify numbers with sets may be useful, bu to say that
numbers *are* certain sets is rank {consequenti,operation}alism.
--
And through this revolting graveyard of the universe the muffled, maddening
beating of drums, and thin, monotonous whine of blasphemous flutes from
inconceivable, unlighted chambers beyond Time; the detestable pounding
and piping whereunto dance slowly, awkwardly, and absurdly the gigantic
tenebrous ultimate gods -- the blind, voiceless, mindless gargoyles whose soul
is Nyarlathotep. (Lovecraft) John Cowan|jcowan@hidden.email|ccil.org/~cowan