15 Mar
1996
15 Mar
'96
1:53 p.m.
There's certainly a clear distinction between "definition" and "semantics". They are -- to echo PeterJ -- in different categories. But Vaughan's point about the calculus is well taken. I must back down a bit. Yes, a semantics for the real numbers and for limits and for continuity and -- hardest these days to believe -- for the very notion of function were indeed needed by 19th C mathematicians. So let me try again. Core mathematics in the 20th C did not provide a problem for semantics and for that reason the inadequacy of formal set theory was not noticed. Inadequate for what? Well, let's start with the Church polymorphic notion of number.