Re: Article in the Chronicle of Higher Education

["Ian Murray" <seamus2001@xxxxxxxxx>]

----- Original Message -----
From: "pdavidso" <pdavidso@xxxxxxx>


> an axiom is accept as a universal truth underlying an exercise in logical
> deduction from axioms.

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"Now of the intellectual faculties that we use in the pursuit of truth
some are always true, whereas others -- opinion and calculation--
admit falsity; and no other kind of knowledge except intuition is more
accurate than scientific knowledge...It follows that there can be no
scientific knowledge of the first principles; and since nothing can be
more infallible than scientific knowledge except intuition, it must be
intuition that apprehends the first principles. This is also evident
not only from the foregoing considerations but also because the
starting point of a demonstration is not itself a demonstration, and
the starting point of scientific knowledge is not itself scientific
knowledge [Posterior Analytics II 19, 100]


If we are fallibilists, what is the difference between intuition and guess? And if we can
have no scientific knowledge of first principles without engaging in circular reasoning or
question begging, what does it mean to say they are universal truths? Everyone thought the
axioms of Euclid were universally true until Gauss, Bolyai, Lobachevsky and Reimann came
along.


Ian