[hist-analytic] Proving

Jlsperanza at aol.com Jlsperanza at aol.com
Wed Jan 6 21:42:42 EST 2010


I should revise the bibliography on this, but I am still interested, sort  
of, into the 'logic' (as ordinary language philosophers would have it) of  
'prove' _qua_ (alla Kiparskys) 'factive'.
 
It seems that Grice was onto something (good or bad) when he emphasised how 
 much of our ordinary talk is about 'deeming' this to be x or y (his idea 
of  sublunary 'knowledge', e.g. in "Meaning Revisited", now in WoW). 

Ditto his emphasis on _implicit_ reasoning, as exegisised (?) by Warner in  
his intro to Grice's Aspects of Reason. The idea indeed that, say, if you 
want  to _prove_ A from A (say), to use an example, alla R. B. Jones, of, 
technically,  a 'formal proof', we have a two step proof.
 
1. A (Ass)
2. Therefore A (Concl).
 
There are, of course, longer proofs for other things, but the logic of  
'proving' (or the _grammar_ of 'proving' as other language philosophers would  
have it) would remain the same.
 
Grice makes various points on this. On the one hand, there is what the OED2 
 has as "woman's reason" (I like it because I like it). This Grice relabels 
(in a  way, since he does not use "woman's reason), 'trivial' reasoning, or 
(sometimes)  'irrelevant' reasoning. For who would like to prove "A" out of 
"A"? (other than  an OED2 'woman' that is).
 
If 'factive' is taking seriously, though, unless the complete steps of a  
'formal proof' are made explicit, perhaps we wouldn't like to say that an 
agent  (say) has "proved" that p.
 
Popper, alas, though he did write a book on "Proofs and Refutations" would, 
 as D. Frederick would, have cared less, or would _not_ have cared less, 
about  the ordinary logic or grammar of 'proving'. Indeed, if I understand 
Popper or D.  Frederick aright, there's a lot of 'deeming' going on, since, 
well, each alleged  'proof' is just that until _refuted_. 
 
As a historian of analytic philosophy of sorts, I am forever  interested in 
the historical sources of this. And should start with the  Philosopher's 
Index with essays featuring 'proving' in the title (for there's  something of 
an abstract-noun quality which Toulmin calls a 'non-logical goat'  in his 
Uses of Argument) that keeps me slightly apart from grandiose talk of  'proof' 
as such.
 
Cheers,
 
J. L. Speranza
    for the Grice Club, etc.
 
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