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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