On 16 Feb 2011, at 22:36, Brent Meeker wrote:
On 2/16/2011 12:33 PM, Bruno Marchal wrote:
hat matter adds to a bundle of properties is existence. A non-
existent bundle of properties is a mere concept, a mere possibility.
Thus the concept of matter is very much tied to the idea of
contingency or "somethingism" -- the idea that only certain possible
things exist.
Only certain possible number relations exist. And relatively to a
number there is the provable relations, the consistent relations,
the true relation, and then the combination of those.
I don't understand that? A relation might imply a contradiction and
therefore be impossible.
Yes.
But I would suppose that all possible relations would exist in
Platonia.
Yes. I was perhaps unclear. "Only certain possible relation" =
"possible relation". It was an insistence type of use of "certain".
But "possible" in this context is "consistent for this or that machine
number". Possibility (consistency) applies to theories or machine or
number.
What non-contraditory relations would not exist?
I am glad you accept they all exist.
Sorry for having been unclear.
But even contradictory relation exists relatively to number/theory.
(PA is inconsistent) is consistent with PA, and "(PA + (PA is
inconsistent)" is true, that is, it belongs to arithmetical truth. and
"If PA is consistent then PA + provable('0=1') is consistent" is true
and provable by PA, etc.
Bruno
http://iridia.ulb.ac.be/~marchal/
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