On 29 Jan 2012, at 23:42, meekerdb wrote:

On 1/29/2012 7:47 AM, Bruno Marchal wrote:

Math, even just arithmetic is already outside logic

Why exactly is that? Is it just because arithmetic has "..." in it, i.e. it posits a potential infinity of operations?

Russell and Whitehead thought, like most of their contemporaries, that elementary arithmetic can be deduced from logic. Today we know that it is not the case, and we separate clearly the logical axioms (the deduction means that we allow), and the non logical axioms, which defines and assumes the non logical object we want to talk about (numbers, strings, programs, sets, functions, etc.).



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