[hist-analytic] Proving

Jlsperanza at aol.com Jlsperanza at aol.com
Sat Jan 9 16:36:21 EST 2010

In a message dated 1/8/2010 6:57:50 P.M. Eastern Standard Time,  
rbj at rbjones.com writes:

It is definitely dialectical.  I don't know where he introduces the  term, 
he uses it in the sense we are considering right at the beginning  of the 


Thanks  for the excellent references, as always. It's good to have a good 
Aristotelian  just a click away, and you may be interested to know that this 
online rhetoric  thing does have a thing about the 'dialectic' -- it's an 
alphabetic list, a bit  of a mixed bag (I cannot paste the html with this 
mailer I'm using, though) --  but I excerpted:
The online site goes:
"In Aristotle, dialectic is very similar,"
-- to Plato -- for recall Whitehead, all philosophy, metaphysics or what  
have you, is but footnotes to Plato!
"though for him, it represents  
something other than a path to  Truth with a capital "T." Dialectic for 
Aristotle  uses cogent logic to  reason from widely held or authoritative 
Its  conclusions are  necessary even if its premises are not."

I was thinking that there is such a slight distinction between Greek for  
'proof', epideiktikos, as it were (epideixis being the noun) and apodeiktic,  
which Kant uses versus problematic and a third term, that it hurts!

Jones adds:

"I might add on this topic that in modern  logic the distinction which 
attempts to draw between proof and  derivation is not sustainable.
It rests too heavily on the distinction  between an axiom and a rule, and 
exactly the same deductive system (i.e.  having the same theorems) can be 
presented entirely without rules, or  entirely without axioms or with a 
of the two.  For example, it  is not unusual for axioms to be treated as 
inference rules which require no  premises."
Yes, this is a good point. I'm slightly irritated by this author of "Proof  
and Disproof in Formal Logic" when he writes -- recall it's an Introduction 
for  Programmers rather than, pedants! -- 
  "Rain!" is not a claim, hence not provable.
--- A 'rule' is like a non-claim, then. And it is true that Gentzen seems  
to be having his cake and eating it too when he has the good old 'axiomata' 
of  Aristotle (for whom, as for Grice, axios, means 'valuable') turned into 
'rules'  of the game, which would then not be provable. While I'm not 
Kantian enough to  think that there is 'proof' in 'practical argument', I am 
Gricean enough to  think that something like a notion of 'consequentia' holds for 
both 'alethic'  and 'practica' arguments, to use Grice's jargon.
But the point you make is incredibly right.
"Furthermore, from a sceptical point of view, there is no better reason in  
general to trust an inference rule than an axiom, and so no basis for  
accepting derivations but denying that there can be proofs."
I see. On the other hand, I think I do understand D. Frederick's reluctance 
 with 'proving' (versus 'deriving'). I think Grice would probably agree 
with D.  Frederick. He has "Shropshire" proving the immortality of the soul, 
recall --  googlebooks, Aspects of Reason. Since it is so ridiculous to even 
think that the  soul is immortal (to me), I have to take Grice jocularly. As 
if saying that  Shropshire (and N. Allott, online, says that's a counterpart 
of Hampshire --  recall Grice, "I don't remember this fellow's name. All I 
remember is that his  surname was the name of an English county") 
  did prove 
that the soul is immortal. Based on his equally silly premises -- e.g. that 
 a chicken -- or chick as I prefer, since I use chicken only for the plural 
--  walks post-mortem, etc.
More later, I hope
J. L. Speranza
   for the Grice Club.

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