FOM: Shpmn/Mchovr: A distinction.
Robert S Tragesser
RTragesser at compuserve.com
Tue Dec 16 18:09:34 EST 1997
ABSTRACT: There are countless sufficiently proven
theorems to count as abiding, even eternal. "fact".
What is at issue is the big picture of which they
are a proper part. Of those countless theorems,
Lakatos cannot raise a single legitimate doubt.
What he can raise a doubt about is whether in any
single case we have found the proper and final
theoretical setting for it. Shipman is confusing
the second situation with the first.
With possibly one exception, all the propostions
in Euclid's Elements are adequately proved in this sense:
Anyone who has doubts about any of the propositions
doesn't understand it(them).
Take, for example, Proposition 1, Book 1. I'd say:
There is no hidden and unproved assumption there;
there is only adequate understanding.
Is the p!+1 proof of the infinitude of
primes dubious in the least?
Anyone who thinks so will look very much like someone
who doesn't understand the theorem.
I want now to make a distinction that might
help things out.
A THEORY in the orginal sense is something by which
"parts" are perfectly understood by exhibiting how
they stand in relation to a self-contained whole to
which they most properly belong.
The FACT of the existence of infinitely many primes, or
the FACT of the Pytharorean Theorem are beyond any power
of doubting that is not itself dubious.
What is at issue is their theoretical setting:
How are they to be understood, what is the big
It is the mark of the tradition of episteme (Plato, Aristotle,
Neoplatonists. . .) that there is a unique and self-
contained such theory, such a big picture.
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