On 11/09/2016 21:30, Sven R. Kunze wrote:
On 10.09.2016 15:00, Chris Angelico wrote:
Some things are absolute hard facts. There is no way in which 1 will
ever be greater than 2, ergo "1 is less than 2" is strictly true, and
not a matter of opinion. If you hear someone trying to claim
otherwise, would you let him have his opinion, or would you treat it
as incorrect?
I don't know exactly if it's clear that one would need to make a distinction
between real/physical-world facts and pure-logic facts.
"1 < 2" is by definition "true" (construction of natural numbers) not by
real-world evidence. IIRC, the quote is about real-world matters.
as I understand it, the universe is said by some to be a long lived random
fluctuation of nothing and it is said that observers make a real difference to
reality. The existence of arithmetic etc is somewhat moot under such assumptions.
Also presumably there are other constructions of 'our' familiar arithmetic.
Perhaps someone could probably make an arithmetic where most of standard ZF is
true except for 1<2. Gödel definitely says there are holes in arithmetic :)
-possibly non-existently yrs-
Robin Becker
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