On Mon, Jan 12, 2004 at 03:50:42PM +0100, Bruno Marchal wrote:
> What I mean is that their arithmetical property are independent > of us. Do you think those people believe that the proposition > "17 is prime" is meaningless without a human in the neighborhood?
Of course it is meaningless. Natural numbers are representation clusters by infoprocessing systems: currently machines or animals. Pebbles can't count themselves, obviously.
Natural numbers are not representation. They are the one represented, for exemples by infosystems, or pebbles, animals etc. It seems to me you confuse the thing abstract immaterial numbers, and the things which represent them. Pebbles can't count themselves, obviously. But it is not because pebbles can't count that two pebbles give an even number of pebbles. Electron cannot solve schroedinger equation (only a physicist can do that), nevertheless electron cannot not follow it (supposing QM).
No realization without representation.
It depends of the level of description. It depends of your favorite primitive act of faith.
I have no trouble seeing the universe as artifact from some production system (but that metalayer be transcendent by definition), but assuming universe exists because numbers "exist" does strike me as a yet another faith.
That numbers exists independently of us is based on a act of faith I agree. But all theories are based on some act of faith. That the universes follows from numbers is not an act of faith, but a consequence of comp. See my thesis for that, or links to explanations in this list: all that in my url below.
PS there is a missing word in my answer to Jesse. Just to be clearer:
Godel's theorem: self-consistency is not provable by consistent machine
Tarski's theorem: truth (and knowledge) is not even expressible by the consistent