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.
Brent
I haven't read the whole thing, so perhaps they do have an explanation for why made up things can't be changed? If so, I'd be interested to know what it is (not having time, sadly, to read every paper published on this list).
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