On 09 Jun 2015, at 04:00, meekerdb wrote:
On 6/8/2015 4:16 PM, LizR wrote:
On 9 June 2015 at 05:31, meekerdb <meeke...@verizon.net> 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.
I don't define "reality" at all, but I do show that with comp,
arithmetical truth is enough, ontologically.
What makes ZFC (or whatever) real, or not, is whether it kicks back.
Mathematics doesn't kick back - except metaphorically.
Well, then it is an open problem if physics kick back in any non
metaphorical sense.
With computationalism, math kick back by leading mathematical entity
toi believe in non mathematical kicking back stuff.
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.
There is only one standard model of arithmetic. There are no well
defined standard models of ZF. The notion is controversial.
You said all computations explain too much, which is NOT the case (it
leads may be to a too much big problem). But set theory explains too
much, and flatten the higher order notion too strongly.
Bruno
Brent
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