On 19 Jan 2014, at 22:31, meekerdb wrote:

On 1/19/2014 9:45 AM, Bruno Marchal wrote:
But why should that imply *existence*.

It does not. Unless we believe in the axioms, which is the case for elementary arithmetic.

But what does "believe in the axioms" mean. Do we really believe we can *always* add one more? I find it doubtful. It's just a good model for most countable things. So I can believe the axioms imply the theorems and that "17 is prime" is a theorem, but I don't think that commits me to any existence in the normal sense of "THAT exists".

Because you are chosing the physicalist ostensive definition of what exists, like Aristotelians, but you beg the question here. The point is that, in that case, you should not say "yes" to the doctor.

Bruno




Brent



But then we believe in the existence of prime numbers, and in the many relative computational states.

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http://iridia.ulb.ac.be/~marchal/



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