On 4/22/2015 10:41 PM, LizR wrote:
On 23 April 2015 at 16:31, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>>
wrote:
On 4/22/2015 9:25 PM, LizR wrote:
On 23 April 2015 at 16:16, meekerdb <meeke...@verizon.net
<mailto:meeke...@verizon.net>> wrote:
On 4/22/2015 7:38 PM, PGC wrote:
"Both the records and the mathematical objects are human constructions
which
are brought into existence by exercises of human will; neither has any
transcendental existence. Both are static, not in the sense of existing
outside of time, but in the weak sense that, once they come to exist,
they
don’t change” (pp. 445-446)
The question they need to answer is /why/ these things don't change. Humans
can
change other things they make up - as already mentioned, the rules of chess
are one
example.
They can change things. Robinson arithmetic is a change of Peano's. But
we give it
a different name instead of saying we've changed arithmetic. It's just as
if we'd
kept the old version of chess around and given a different name to the new version.
It's a nominal distinction whether it's changed or it's a new thing.
As far as I know, we keep the old version. Surely the new one is an addition? Or are you
saying these changes could be made any which way, that there is no kicking back? That
2+2 can equal 5, as O'Brien claimed? That seems kind of unlikely, to be honest.
2+2=1 in mod 3 arithmetic. If you change the game you change what can be proven. You
can't keep the old version and assume its proofs apply to the new game.
Brent
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