From: Scott Roberts (jse885@earthlink.net)
Date: Wed Nov 17 2004 - 20:26:37 GMT
Simon,
> I recommend reading ZMM. In it you will find that Pirsig proposes, with
the
> help of Jules Henri Poincare, that the choice of conventions and axioms
from
> which mathematical truths are derived is made on the basis of
> preintellectual value. Mathematical truths are thus patterns of values.
> Value is phenomenal, it is sense experience. Therefore, mathematical
truths
> are verified by sense experience. Reason itself is a pattern of values.
[Scott:] Please tell me how sense experience verifies that no ratio of
integers is the square root of 2. I would also deny that value is a sense
experience. It rides along with all sense experience, and with reason. Nor
is it phenomenal. The point of the MOQ is that value precedes the
phenomenal/noumenal distinction.
I agree with Pirsig and Poincare, except to point out the following:
- I do not distinguish between convention and reality. By setting
conventions we create mathematical reality, and so, I claim, does Quality
create all reality. As such, it can also be called Reason. Pirsig keeps
saying (in Lila) that intellect, by making distinctions, covers up "pure
experience", while I am saying that making distinctions is how everything
is created.
- I see no justification on Pirsig's part for calling the basis for choice
among possible conventions "preintellectual". Better, I think, to call it
Creative Intellect, or something along those lines.
One other thing: You quoted:
> Poincaré concluded that the axioms of geometry are conventions, our
choice
> among all possible conventions is guided by experimental facts, but it
> remains free and is limited only by the necessity of avoiding all
> contradiction. Thus it is that the postulates can remain rigorously true
> even though the experimental laws that have determined their adoption are
> only approximative. The axioms of geometry, in other words, are merely
> disguised definitions.
From a mathematical point of view, there is no choice guided by
experimental facts. There is only choice guided by mathematical interest.
That is, we reject axioms that don't lead any where interesting, but accept
those that do. All geometries that don't immediately collapse into
triviality are equally valid. It is physics that chooses one over the other
based on experiment, not mathematics.
- Scott
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