FOM: Hersh's fingers

[wtait@ix.netcom.com]

No doubt there are propositions which are mixed mathematical and 
empirical (e.g. if I have five fingers, then I have an odd number of 
fingers.) But these are easily decomposed into a mathematical component 
and an empirical one. (Interestingly, Plato discussed this matter in the 
_Phaedo_.) There may, as Charles P. suggests, an empirical meaning of 
`five' involved in the statement that I have five fingers. Charle's 
argument for this can also be regarded as an explication of what he 
means: Children can learn to count the number of fingures on someone's 
hand without having, in any reasonable sense, a grasp of the number 
concept (every number has a successor, math induction, etc.)

But mathematics is not about what children do and FOM is about 
foundations of _mathematics_. For Charles' or Hersh's remarks to be 
relevant to this, one would have to argue that our empirical 
understanding of numbers or whatever is relevant to the truth of 
_mathematical_ propositions---not in the causal sense of explaining why 
we come to have such and such mathematical concepts, but in the logical 
sense of being the grounds for the truth of mathematical propositions. I 
doubt that Charles would want to argue for this.

Bill Tait