Am 03.05.2024 21:42:56 Ross Finlayson schrieb:

On 05/03/2024 07:06 AM, Tom Bola wrote:

Am 03.05.2024 15:41:24 WM drivels:

Le 02/05/2024 à 01:32, Tom Bola a écrit :

I think that WM has a very fixed idea of the
"world of math" which is fixed by nature and
not a creation of culture in the mind of men

I don't know whether actual infinity is true.

Being true IN MIND is all the Mathematicians want and need.

That there is a "theory of truth" has two schools:
"idealists" are "platonists" who agree mathematics is discovered, "nominalists" are "figurists" who each say mathematics is invented.

So, "logical positivism" is usually that in a rejection
of any metaphysics, it's axiomatics and formalism, that
arrives at the formalism and constructivism.

Yet, a "stronger logical positivism" can arrive back at
a "strong mathematical platonism", because the objects
of mathematics that are central and primary, are ubiquitous.

So, mathematicians vary, yet, over time over history,
most have at some point been mathematical platonists,
and agree that truths of mathematics, are discovered,
not invented.

Its not only between discovery and invention. I mean, take
simple geometry - it works wherever to one looks, also on
the moon, so it cannot be invented, with the the values of
pi or e. Then, folks are able to invent their own models
with math and find out in which of their axioms are showing
contradictions, what they can proof and what not. So it is
both, discovery and invention. Anyway, both, to work with
and the discovery of (new) math takes always place is in
the mind of somebody and there is no way to find out, for
instance, by experiment whether there is one last integer
before w. On the other hand, what must be discovered (pi)
was already there before in the "Platonic space" which
clearly is of mental nature and which can only be found
out in the same way on other milky ways. Furthermore,
the "laws" of math clearly work in the mental space
alone, that is you don't need to draw rectangles to find
out whatever is required to do triangulation and geometry.
...

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