On 5/27/2012 5:02 AM, Bruno Marchal wrote:

`As Bruno said, "Provable is always relative to some axioms and rules of inference. It
``is quite independent of "true of reality". Which is why I'm highly suspicious of
``ideas like deriving all of reality from arithmetic, which we know only from axioms and
``inferences.
`

`We don't give axioms and inference rule when teaching arithmetic in high school. We
``start from simple examples, like fingers, days of the week, candies in a bag, etc.
``Children understand "anniversary" before "successor", and the finite/infinite
``distinction is as old as humanity.
``In fact it can be shown that the intuition of numbers, addition and multiplication
``included, is *needed* to even understand what axioms and inference can be, making
``arithmetic necessarily known before any formal machinery is posited.
`

But only a small finite part of arithmetic.
Brent
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