Nam Nguyen wrote: > On 26/05/2013 7:54 AM, Peter Percival wrote: >> Nam Nguyen wrote: >> >>> Such application isn't purely logical. Finiteness might be a purely >>> logical concept but recursion isn't: it requires a _non-logical_ >>> concept (that of the natural numbers). >> >> What do you mean when you write "Finiteness might be a purely logical >> concept"? > > FOL requires the concept of finite strings of symbols, the concept of > there being only finitely many steps in making logically inferences; > and as such the word "finite" is a priori we have to accept we > understand its meaning and usage: we can't define that "finite" priori > further.
That makes it seem as if a notion of finiteness is needed before ever one does logic.
-- I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne