On 23 Apr 2015, at 08:37, meekerdb wrote:
On 4/22/2015 10:41 PM, LizR wrote:
On 23 April 2015 at 16:31, meekerdb <meeke...@verizon.net> wrote:
On 4/22/2015 9:25 PM, LizR wrote:
On 23 April 2015 at 16:16, meekerdb <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.
OK, but 2+2 is not equal to 1 in arithmetic. It is equal to 1 in
modular arithmetic, which is a way to assert that the rest of the
division by 3 of 2 + 2 is equal to 1 in arithmetic. Modular arithmetic
makes sense because we know already that 2+2= 4 in arithmetic. The
very existence of the many modular arithmetic is a consequence of
arithmetical laws. It confirms 2=2=4, without throwing any doubt on it.
Bruno
Brent
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