On 01 Mar 2014, at 22:30, meekerdb wrote:
On 3/1/2014 12:28 AM, Bruno Marchal wrote:
On 01 Mar 2014, at 07:04, meekerdb wrote:
On 2/28/2014 9:22 PM, LizR wrote:
Nevertheless, it does seem to be. That is, 17 is a prime number
regardless of whether anyone knows it is, or even knows what
numbers are, or indeed whether anyone is even alive (e.g. it was
prime in the first instants of the big bang - maths has been used
to work out what happened in the early universe, with observable
consequences now). There's a lot of hand waving going on to deny
this, but I haven't seen a knock down argument (or even a
suggestion of one) to indicate otherwise.
To deny what? That 17 is prime? That's a tautology. It's our
theory that the world consists of countable things - whether it
really is, is questionable.
Well, in the comp theory, there are no countable things, and non
mechanically countable things, etc. Both in the math, the physics,
the theology, etc.
Arithmetic doesn't include countable things, aka "numbers". I think
you're slipping into mysticism, Bruno.
Arithmetical truth, notably with comp, can explain the epistemological
existence of non mechanically countable object. It is math. I don't
see what is mystic here. I don't understand your remark. I did not say
"arithmetic", but comp, and this does use only the "mystical" idea
that I can remain conscious with a relative digital brain. This leads
to taking into account the internal points of view of the machine in
arithmetic, which can have beliefs extending a lot arithmetic. The
existence of ZF and its proofs is a theorem of arithmetic (even
Robinson Arithmetic).
Bruno
Brent
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