On 27 May 2012, at 20:59, meekerdb wrote:

## Advertising

On 5/27/2012 5:02 AM, Bruno Marchal wrote:As Bruno said, "Provable is always relative to some axioms andrules of inference. It is quite independent of "true ofreality". Which is why I'm highly suspicious of ideas likederiving all of reality from arithmetic, which we know only fromaxioms and inferences.We don't give axioms and inference rule when teaching arithmetic inhigh school. We start from simple examples, like fingers, days ofthe week, candies in a bag, etc. Children understand "anniversary"before "successor", and the finite/infinite distinction is as oldas humanity.In fact it can be shown that the intuition of numbers, addition andmultiplication included, is *needed* to even understand what axiomsand inference can be, making arithmetic necessarily known beforeany formal machinery is posited.But only a small finite part of arithmetic.

`I don't think so. Our arithmetical intuition is already not`

`formalizable. If it was, we would be able to capture it by a finite`

`number of principle, but then we would be persuade that such finite`

`theory is consistent, and that intuition is not in the theory.`

`I suspect that our intuition is full second order arithmetic, which is`

`not axiomatizable. In fact it is the very distinction between finite`

`and infinite that we cannot formalize. Like consciousness, we know`

`very well what finite/infinite means, but we cannot defined it,`

`without using implicitly that distinction. The natural numbers are`

`*the* mystery, and it has to be like that: no machine will ever been`

`able to define what they are. Assuming comp, neither will we.`

`Arithmetical truth per se, as no corresponding complete TOE. It is`

`inexhaustible.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.