On 6/8/2015 4:16 PM, LizR wrote:
On 9 June 2015 at 05:31, meekerdb <[email protected] <mailto:[email protected]>> wrote:On 6/8/2015 1:03 AM, Bruno Marchal wrote:or that maths exists independently of mathematicians.That even just arithmetical truth is independent of mathematician. This is important because everyone agree with any axiomatic of the numbers, but that is not the case for analysis, real numbers, etc.Everyone agrees on ZFC in the same sense. So does that make set theory and its consequences real? Reality isn't defined by what everyone agrees on.
Tell it to Bruno, I was just following him.
What makes ZFC (or whatever) real, or not, is whether it kicks back.
Mathematics doesn't kick back - except metaphorically.
Is it something that was invented, and could equally well have been invented differently, or was it discovered as a result of following a chain of logical reasoning from certain axioms?
I'd say ZFC and arithmetic were both invented and then an axiomatization was invented for each of them. I'm not sure what "invented differently" means?...getting to the same axiomatization by a different historical path? Or inventing something similar, but not identical, as ZF is different from ZFC.
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