Tuesday, December 04, 2007

Are Numbers Numerals?

Issue 8 of The Reasoner is out; and with it Hartley Slater’s suggestion that numbers be taken to be such things as that ‘8’ (where, since that numeral is not to be regarded as a name for something else, I’m not sure that I need the quotes around it); to be precise, he ‘solves’ Frege’s Caesar Problem via the following definitions (where ‘n’ is a schematic variable):
......The number of the F’s = 0 iff there are no F’s,
......The number of the F’s = n iff the F’s are equinumerous (can be put into one-to-one correspondence) with the successive nonzero numerals up to ‘n’. There are probably lots of problems with that suggestion; e.g. I wonder what we would then say of mathematics on a distant planet?

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