jlsperanza at aol.com
jlsperanza at aol.com
Thu Jan 7 14:48:08 EST 2010
"When people talk of ‘proof’ they normally mean ‘derivation;’ ifthey
don’t, they are just mistaken."
I think you are very right on a couple of points.
1) I do like your distinguishing ¨deriving¨ from "proving". Indeed,
Christopher Columbus only derived that the Earth was round. (Recall I´m
only interested in proving-that, rather than proving-how).
2) Husserl was possibly wrong when he thought he could derive from
Aristotle and beyond that there is such a thing as a
¨presuppositionless philosophy". We do need a datum, or data, and these
are called "Ass." by B. Mates (in his Elementary Logic) and Grice (in
Vacuous Names, in the Quine Festschrift).
3) I suppose the old mathematicians -- but R. B. Jones should know
better -- were pretty confused about things. And I _include_ Euclid. (I
do own the two-volume Thomas edited Greek Mathematics in the Loeb
Series so should be able to check this out). When the scholastics (to
think that ´schole´ for the Greeks was "otium" is a joke seeing that
monks were and really _are_ into ´converting´ people) talked of
Q. E. D.
-- i.e. quod erat demonstrandum, this is possibly empty flatus vocis,
for what we need is a phrase like ¨quod erat probandum". I should
revise the Latin for this. And also the Greek for "proving".
4) Interestingly, the proof of the pudding is, indeed, in the
derivation (of the pudding) or should at least refer to the derivation.
Without derivation, no proof.
5) I suppose we could speak (but I won´t) of ¨conditional proof¨, i.e.
assuming the premises are true, then the derivation is an assumed
6) I like your idea of a "idle waste of time" in providing step-by-step
in MATHEMATICAL (which is only analytic anyway) formal proof. "Only
that it CAN be done is what matters" as you write. This relates to B.
Aune´s recent considerations on the ¨CAN¨ (and ¨CANNOT¨) of things like
¨Nothing CAN be red and green all over". I would think Popper -- in his
Conjectures and Refutations -- but mostly his ´disciple´ Lakatos in the
Popper-inspired (and applied to mathematics), ¨Proofs and Refutations"
-- were possibly right in that while "proving" tends to assume "loose"
usages (e.g. Peter proved me wrong), "disproving" seems a better choice
of a verb. Wouldn´t Popper say that only when "p" has been falsified
(disproved) that we can witness some sort of growth in our objective
knowledge of things?
J. L. Speranza
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