On 2/27/2013 2:59 AM, Bruno Marchal wrote:

## Advertising

On 26 Feb 2013, at 21:40, meekerdb wrote:On 2/26/2013 1:24 AM, Bruno Marchal wrote:How did number arise? We don't know that, but we can show that if we don't assumethem, or equivalent (basically anything Turing Universal), then we cannot derive them.I'm not sure how you mean that?I meant that you cannot build a theory, simpler than arithmetic in appearance, fromwhich you can derive the existence of the numbers. All theories which want talk aboutthe numbers have to be turing universal.So I meant this in the concrete sense that if you write your axioms, and want talk aboutnumbers, you need to postulate them, or equivalent. You can derive the numbers from theequational theory:Kxy = x Sxyz = xz(yz) + few equality rules,But that theory is already Turing universal, and assume as much the number thanelementary arithmetic.We know that we experience individual objects and so we can count them by putting themin one-to-one relation with fingers or notches or marks. So what are you calling an"assumption" in this?A theory is supposed to abstract from the experiences. The experiences motivates thetheory, but does not justify it logically.

`But "justify logically" seems like a bizarre concept to me. We just make up rules of`

`logic so that inferences from some axioms, which we also make up, preserve 'true'. To say`

`that it is "justified logically" seems to mean no more than "we have avoided inconsistency`

`insofar as we know." Sure it's important that our model of the world not have`

`inconsistencies (at least if our rules of inference include ex contradictione sequitur`

`quodlibet) but mere consistency doesn't justify anything.`

Brent -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.