On 9/27/2018 6:05 PM, Jerry LR Chandler wrote:
it is not possible to fully respond to your beliefs about the
relationships between Peircian realism, modern mathematics and
science. Our disagreements are sharp and well defined.
My beliefs are based on Peirce and the overwhelming majority
of modern mathematicians and scientists.
The scope of pure mathematics, as Peirce defined it, is infinitely
larger than whatever was or ever will be discovered, taught, or
applied by anyone anywhere. That includes all intelligent aliens
in any galaxy anywhere in the universe.
Wow! Wow! Wow!
That is pure Peirce and consistent with the mainstream of modern math.
Mathematicians are frequently inspired by what empirical scientists
discover, but they are not constrained in any way by observations.
For more, Peirce's CP has 49 instances of "pure mathematics".
In CP 1.636, for example, he says that the goal of pure mathematics
is to discover pure possibilities: "that real potential world" of
which actual existence is "nothing but an arbitrary locus”:
Really? ... Of course, if one ignores the methods mother nature uses
to count objects, you can ignore my objectification and objection.
Mother nature does not count anything. People invent representations,
which they apply, as appropriate, to what they observe in nature.
The word 'variable', as used in mathematics, is a metalevel term
about the notation. It just means that letters like x, y, z may
be used to refer to different things on different occasions. If
you use x to refer to something, that does not imply that the
thing you designate by x would vary.
Many mathematical texts disagree with this view
Please quote any text that seems to be inconsistent with what I said.
And I'd be happy to show how that statement correctly describes
what is meant.
John
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