[ExI] The "Unreasonable" Effectiveness of Mathematics in theNatural Sciences
Jef Allbright
jef at jefallbright.net
Sun Sep 28 19:40:13 UTC 2008
On Sat, Sep 27, 2008 at 10:09 AM, Lee Corbin <lcorbin at rawbw.com> wrote:
> TO WIT: The mathematical platonists say that intelligent minds have nothing
> whatsoever to do with math; that math was preexisting long before
> intelligence
> or subjectivity came into being (as most people take those terms), whereas
> the formalists insist that math is the study of relationships and requires
> students
> for its very existence. (Recall Jef's insistence on the importance of
> ***meaning***.)
My point all along is not to the ontological status of a hypothetical
entity referred to as "math", nor to the meaning of "math", but to the
deeper epistemological incoherence of blithely talking about the
status of X while unconcerned about the obvious lack of (even to the
extent of explicitly ruling out) any conceivable context for the
evaluation of X.
This reminds me of Gordon's (gts's) impassioned insistence some time
ago that there is something profoundly wrong with our inability to
answer the question of the dimensions of an average box (given a
distribution of actual boxes), as if "average box" must have an
intrinsic meaning despite lacking specification of a function in terms
of length, area, volume, mass, or otherwise.
This same epistemological confusion is common whenever discussion
ranges outside the bounds of present shared context while remaining in
the special-case mode of "what it is" rather than the generally
founded "what it looks like from here."
My interest is not in arriving at Truth, nor even in reaching
agreement on pragmatic truth (that which appears to work over
increasing scope), but in improving our processes improving our
modeling. Apply an increasingly effective instrumental model
promoting a /particular context/ of values and you get increasing
"good." Apply it to an /increasing context/ of increasingly coherent
values and you get increasing "good" in principle, or increasingly
"right."
I don't know of any more important project (in the bigger picture) than that.
- Jef
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