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 settheory and its consequences real? Reality isn't defined by what everyone agrees on. What makes ZFC (or whatever) real, or not, is whether it kicks back. 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?
Why do not those same arguments apply equally to arithmetic? What axioms led to arithmetic? Could one have chosen different axioms?
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