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}John, List
I'm not convinced of the isolationist purity of mathematics. I
acknowledge that 'pure' mathematics focuses on a hypothesis without
acknowledgment of whether or not it corresponds to reality or not.
That can be said about many hypothetical formations. As John said -
this gives our system the full freedom of
imagination...aka..Firstness.
BUT, my point is that such an imaginary realm is not
self-sustaining and must, at some time, connect to reality, where it
will examine whether or not its Forms have any functionality. This
step might not be immediate; it might even take years.
But - without it, the imaginary realm would actually be
hollow...Firstness is fleeting..
And I'd also like to add that Gary F's very nice post on the
relationship between mathematics and phenomenology is exactly what I
have been arguing about for several weeks on this List - and have
been continuously chastised for doing so - I have rejected De
Tienne's 'Move On' exhortations to us, to Move On from Mathematics
and have instead opted for the synechistic interrelationship of these
two realms-of-science.
Edwina
On Sat 28/08/21 8:27 PM , "John F. Sowa" s...@bestweb.net sent:
Ediwina, Jon AS, Jeff JBD, List
I changed the subject line to clarify and emphasize the distinction.
ET: the distinction between pure and applied mathematics is very
fuzzy. I'd suspect it's the same in phenomenology. But I do
support
and agree with [Jeff's] agenda of using both mathematics and
phenomenology to function within a pragmatic interaction with the
world.
For both subjects, the distinction is precise. JAS highlighted
Peirce's distinction, which applies to both mathematics and
phenomenology:
JAS: It is incontrovertible that according to Peirce in CP 3.559
(and elsewhere), the mathematician frames a pure hypothesis without
inquiring or caring whether it agrees with the actual facts or not.
Yes, of course. That distinction is the greatest power of
mathematics: it is independent of whatever may exist in our
universe
or any other. It gives us the freedom to create new things that
never
existed before. The only constraints are physical, not mental.
That point is also true of phenomenology. For both fields, there is
no limitation on what anyone may imagine -- or on what anyone may
invent.
As an example, consider the game of chess. Before anyone carved
the wooden pieces, the rules of chess were the axioms of a pure
mathematical theory, for which there were no applicable facts.
But then, somebody (or perhaps a group of people) imagined a kind
of game that did not yet exist. They discussed the possibilities,
debated various options, and finally agreed to the axioms (rules)
and
the designs for physical boards and pieces. Before they played the
game, there were no facts that corresponded to the mathematical
theory
or to anybody's perceptions.
The tests of existence and accuracy are determined by the normative
sciences, especially methodeutic. For inventions, the only
limitations are the available physical resources to construct them.
JBD: For my part, I'd like to get clearer on how the pure
phenomenological theory is supposed to support and guide the applied
activities--such as the activities of identifying possible sources
of
observational error, correcting for those errors, framing productive
questions, exploring informal diagrammatic representations of the
problems, measuring the phenomena, formulating plausible hypotheses,
and generating formal mathematical models of the hypothetical
explanations.
Those issues depend on the normative sciences, especially
methodeutic.
The special sciences depend on phenomenology for the raw data and on
mathematics for forming hypotheses. Then they require the normative
sciences for testing and evaluating the hypotheses. In pure math,
the
variables do not refer to anything in actuality. In applied math,
one
or more of the variables are linked (via indexes) to something that
exists or may exist in actuality. Those indexes are derived and
tested by methodeutic.
John
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