At 06:43 1/22/02, Andrew Fildes, wishing to explore "deep thought" more wrote:
Weltansicht and Euclid in one sentence - well done! If axioms are in
themselves debateable, then you are demanding proof which in its turn
requires a preceding logical process. The problem is that you can then
never prove anything because each proof is built on a preceding proof and
so on retrospectively ad infinitum - the main problem with primitive
skepticism. Whatever you build, you build on sand unless you have some a
priori. As I remember, Aristotle demanded that we accept that the real
world exists as we experience it, in contradiction to Plato, in order that
he could move forward.
No, not a demand, but strict recognition of the difference between the
"induced" and the "deduced." To demand a deductive standard of the induced
would require exactly the primitive skepticism you cite, ad infinitum, ad
nauseum. One must be willing to accept a priori assumptions, but must also
keep them highlighted as such with the validity of *all* of them equally
reexamined when incongruous contradiction occurs.
The danger in confusing the two is strongly exemplified by the collision of
Maxwell's Wave Theory with Sir Isaac Newton's [formerly immutable] Laws of
Motion during the 19th Century. The Physics Weltansicht was turned upside
down by the unmitigated audicity of a lowly patent office clerk, Albert
Einstein. His brilliance was absurdly simple. Einstein recognized
"Newton's Laws" for what they were, induced axioms, and questioned their
validity with the "Mind of a Child." He dispensed the necessity for the
horridly ugly Lorentz Transform "kluge" to make the two fit. The rest of
The World held Newtonian Mechanics as sacrosanct until their noses were
rubbed in it with such ferocity that Einstein's Special Theory of
Relativity could no longer be ignored.
I am a Formalist, not a Platonist; id est "concepts" such as Euclidean
Geometry do not exist outside the human mind. It is a construct created
[invented] by and residing within the human mind. OTOH a pure Platonist
would cite it exists with or without the human mind and is therefore
discovered, not invented.
Psychologically humans tend to cling most tenaciously to the induced a
priori axioms [First Principles] from which all else is deduced. This
exacerbates the danger of not highlighting the induced as such. Why? One
flaw in them brings down *all* of the deduction that followed from them
until they can be reconstructed. It cuts to the very core and rends the
existing Weltansicht with a "massive earthquake."
-- John
P.S.
More on your other remarks later . . . "My brain hurts" [with apologies to
Monty Python's Flying Circus]
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