[hist-analytic] A Priori/A Posteriori _Of What_?

[Jlsperanza at aol.com]

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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