[FOM] Unreasonable effectiveness
steven at iase.us
Tue Nov 5 14:54:12 EST 2013
The acceptance of Einstein's general covariance as the basis of a logical
and mathematical construction of the world, in this structuralism,
recognizes limits of discovery. If nature may be fully described by its
generally covariant essential properties then the basis of these
distinctions, the essence of the subject, is inaccessible, except by our
direct experience of the world as its part.
The world is profoundly uniform, and this is indeed suggested by the
robustness of mathematical physics. The physical sciences depends in its
epistemology upon this uniformity and the exact discovery of these limits
and the effect of its approximation by mathematical means as indicators of
a requirement to modify its approach to enable new discovery.
If the world is not profoundly uniform in this way then the robustness of
mathematics in the physical sciences cannot be relied upon. This is the
answer to your question of how mathematics produces such robust tools. If
the tools did not demonstrate this robustness then we would need to rethink
the epistemology of science.
Our purely mathematical techniques improve and this process is somewhat
allied to its application in, and refinement of, the physical sciences.
I'll even go so far as to say that this structuralism provides us with a
conceivable certainty, so that, while keeping an open mind, our refinements
are such that they eventually provide a reliable account of the world, that
while still falsifiable, holds for all time.
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