[hist-analytic] A Priori/A Posteriori _Of What_?
Jlsperanza at aol.com
Jlsperanza at aol.com
Fri Feb 6 18:01:46 EST 2009
In a message dated 2/6/2009 4:54:04 P.M. Eastern Standard Time,
rbj at rbjones.com writes:
We are not really talking about the analytic/synthetic
distinction, but the a priori/a posteriori distinction,
-----
I guess I missed the earlier bits of this conversation; but I'm too
fascinated by the a priori/a posteriori. I recall Kripke's showing us (i.e. showing
my teacher, who showed _me_) how there's more to philosophy than a two-entry
diagramme of the type Kant conceived:
justification
end/bit
A priori a posteriori
subject/ synthetic analytic
predicate
considerations
a priori a posteriori
analytic synthetic
It seems philosophers realised that 'a priori analytic' is possibly
redundant; ditto for 'a posteriori synthetic'. A posteriori-analytic God knows what
it amounts to (perhaps Mill on numbers), and a priori-synthetic was, to use
Strawson's phrase*, Kant's nightmare.
-- this is _not_ P. F. Strawson.
--- The word to use for "of what" cannot be 'experience' (Gk. empereia). It
_should_ have to do with 'justification'; but Danny Frederick has recently
started to convince me, "There's no justification" (for anything) so I'm less
sure it's about, or _should_ be about 'justification', then.
I agree with R. B. Jones that mathematicians cared a fig (Fig. No. 1 -- in
Eddington's parlance) about the _physical_ world; mind, most _physicists_
*I*'ve talked to seemed also to care the same fig (Fig. No. 2 -- let's concede
Eddington) about the physical world, or its nature (to use the title of
Eddington's Gifford Lectures in Natural Theology).
Eddington says, perhaps trying to amuse, that there's no beauty or purpose
with Figs No. 2 -- but of course I disagree.
He goes on to say that to describe Fig No. 2 we should need powerful
mathematical symbolisms, and that to inquire too much about them is misguided.
On the other hand, the mathematicians I've talked to (who followed Burbaki)
are _very_ much into *beauty*. I mean, if what they are going to say is per
se analytic, and let's say a priori too, I can't see why at least they should
not have fun in inventing _nice_ theories.
There's _beauty_, as I think Roger Jones will agree, about Riemann spaces,
etc., and of course mathematicians (applied mathematicians) will have fun in
finding postulates, theorems, and corollaries for these, too.
I once thought that it was _Cartesius's_ discovery that arithmetics and pure
mathematical geometry _agree_: but of course, for the Greeks they never
diverged in the first place. Ivor Thomas's two volumes for the Loeb Classical
Library make for some fascinating reading there. Especially as he manages to
combine how much (or how little at parts) of the mathematical terminology comes
from Philosophy and vice versa.
Surely mathematics predates Philosophy; so it's very possible that
philosophical reflections on the analytic, the 'a priori', etc. -- as in Aristotle,
say -- (his views on axioms, first principles, proof, etc.) are modelled after
what he saw successfully being used (for fun) by Pythagoras, Thales and all
the Old Sages.
And recall Plato's motto to his Academy, "You better be accountable for your
mathematics before you _enter_ here".
Cheers,
J. L.
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