SUO: Re: natural lite of reason
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| OGNA! (Oh God, Not Again, Factorial)
|
| In principial, all was formally void,
| and nothing at all was indispensable,
| The immanent question that would not
| go away is what can be dispenseed in
| practice, rendering the remainder to
| the status quotient of the practical
| indispensable. Ay, there's the rib.
MP = Mike Pool
MP: I'm not sure what you're saying here or in your "OGNA!" note has to
do with the discussion of naturalism and its ontological commitments.
I'd be much obliged if you would be so kind as to give me a plain-
English version free of puns, analogies, acronyms, metaphors.
Naturally.
I went through my first foundations of math anxiety in the late 1960's.
In my personal quest for certainty, I was sequentially a true believer
in all of the standard positions -- intuitionism, logicism, realism --
and quite a few non-standard ones. I sought advice from math and phil
professors, and got a variety of responses. Mostly my math professors
had been through their own "mathematical identity crises" -- that is a
direct quote that I still remember -- long ago, were burned out on the
topic, felt that more likely there was something wrong with the entire
metaphor of "foundation", didn't believe that all the fuss had much to
do with the actual practice of mathematics, and advised me not to talk
to phil profesors, or at least, only in moderation. As usual, I never
listened to their good advice. That is my vision of deja vu: "OGNA!".
Many people are aware that C.S. Peirce opted out of nominal thinking --
as a general rule I favor the adjective forms over speaking of -isms --
but fewer are aware -- and those "Peirceans" who are, are often just
a bit puzzled and even embarrassed by it -- that he always tried the
nominal heuristic first, like any expert problem solver would. When
the problems are simple, as they will tend to be at the inauguration
of one's career, the nominal strategy often satisfices, but when the
problems grow in complexity and subtlety, a realistic stance becomes
a practical necessity. All practitioners eventually understand this,
and it's such a mudane, "pragmatic" triviality that they hardly take
the time or the trouble to make a big point of it in "philosophical"
discussions, should they even take the time or the trouble to engage
in one. So the criterion that matters as far as doing the math goes
is what makes sense "in practice" -- it's just not an issue what may
be true "in principle", especially as argued from some unfalsifiable
universal principle. I know that many people think that mathematics
is all about that, but it is really more experimental, observational,
and even tangible than popular conception, which includes the lion's
share of philosophy of math, would have it.
The practical fact is that nominal thinking in mathematics fails for
exactly the same reason that nominal thinking in any other realistic
domain fails, for instance, the -ism that would reduce psychology to
behavior -- not because it's not possible in principle to design the
epicycles of circumlocution that would shore up this standpoint, but
because it's just not worth the candle in practice to maintain these
exorbitant centers and gyres of indirection.
End of the First Part of the Contention.
Jon Awbrey
| The natural thinker is one who believes
| that everything that happens is natural.
| Those who extract small truths from the
| roots of words will tell you that "be"
| and "physical" are co-derivatives of
| the same urpflanze. I am now, and
| always have been a natural thinker,
| and one who extracts small truths
| from the roots (stems, leaves,
| flowers, and seeds) of words.
| So what? A natural thinker
| says nothing of substance
| until claiming something
| about the form and the
| structure of what is.
| And that is what
| makes all the
| difference.
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