[hist-analytic] Proving

[Jlsperanza at aol.com]

In a message dated 1/8/2010 6:55:33 A.M. Eastern Standard Time,  
rbj at rbjones.com writes:
yet another attempt by [Frederick] to impose his own  standards on 
others.  Yet another attempt to render useless a part of  our normal 
vocabulary.
 
---- Mmm. I see [what you mean]. Oddly, I was reading 'proof' in wiki and  
they say Thales proved a few (theorems). It's odd that this is not what made 
him  a philosopher, anyways (sic)!
 
Anyway, I read the article, and also bits from this Oxford Series texts  
("Proof and disproof in formal theory") -- which perhaps is too much on the  
comical side, "Who wants to be formal?" the author wonders. This reminds me 
of  Grice when he confesses that it was "of all People, Putnam, who said I 
was _too_  formal".
 
In any case, I started to search for 'psychology of proof' and got the  
reference of this Lips author whose book came out in 1994, "Psychology of 
Proof"  and manages to quote from Grice, "Aspects of Reason", as they still 
unpublished  were.
 
I find the online relevant bit of "Reply to Richards" as a googlebook, --  
it's page 81. He refers to a 'revised version' of the "Aspects of reason"  
lectures, which alas, he never found the time to complete. So perhaps the 
"Reply  to Richards" _is_ the last word by Grice on this. Paraphrasing him a 
bit, he  seems to be saying (I use double quotes when it's his exact wording):
 
Prover P "intends that there should be some 
               valid supplementation"
of the explicitly present material 
"which would justify the 'conclusion'" (of the proof)
 
"together perhaps with a further intention
that the first intention should be causally
efficacious in the generation of the [prover]'s
belief in the afore-mentioned conclusion".

Must say I love that, however, psychologically implausible -- I recall  
sharing the quote with S. Stich, the Pope of Cognitive Psychology for  
Philosophers, and he said, 'preposterous!' -- but he is a slightly rude man,  Stich 
is. 
 
In any case, the idea by Grice of referring to the prover's intentions  
seems very good, and of course we are accustomed to the sort of 
cross-textuality  of the intentions from his work on 'meaning'. The idea of the 'causal' 
role  seems appropriate.
 
Apparently, Lakatos is into something similar in his "Proofs and Disproofs" 
 as I prefer to title his book. He has students considering Euler's proofs 
and  "failed proofs". Lakatos notes that a counterexample to a proof should 
be  distinguished from the less local, more global, counterexample to a 
conjecture.  These are important points that would have appealed Grice.
 
The author of this "introduction for programmers" seems to minimise proofs  
by saying it's all computers can do. But they don't have intentions, so 
Grice's  analysis would seem futile -- and I wouldn't think he would object. He 
treasured  the reply by Bergman on being invited to one of Austin's 
kindergartens  (so-called because they all had to be, by axiomata, Austin's 
juniors), "And  waste my time with the English futilitarians? No way!"
 
Still looking for Good Greek vocabulary on this. "Syllogismos", no doubt,  
for proof. Latin 'demonstratio', based on 'monstratio' is an interesting 
concept  too. "monstrare" is to show. This incidentally has a funny linguistic  
consequence. Consider Kuhn's obsession with the Copernican Revolution:
 
1. Copernicus discovered that the earth turns around the sun, rather than,  
as Ptolemy had previously believed, the other way round.
 
Now, 'discover' has this negative particle (which I wonder how Grice, in  
his considerations of 'know' as factive, can -- as per my previous quote from 
 WoW, Presupposition and Conversational Implicature) even colloquially 
think it  has no maximal scope), 'dis'. So a disproof is a proof that not-p.  
Etc.
 
Now, 'discover' then is cover that non-p. For surely Ptolemy was _covering_ 
 things, only to have Copernicus DIScovering them for posterity. And to 
cover and  discover are thus factive. For if Joan Rivers covers that she is 
seventy-three  years old, she is that age -- as a paparazzo should discover. 
Etc.
 
What R. B. Jones or D. Frederick may have to say about Grice's idea of  
providing some sort of analysis in terms of sufficient and necessary conditions 
 remains to be seen...
 
What I don't like about much of the psychology of proof, unless practiced  
by a first-rate philosophical psychologist as Grice was, is that it becomes 
so  mentalistic it _hurts_... (e.g. Johnson-Laird mental models, Wason, 
Lipps, and  the rest of them!).
 
Cheers,
 
J. L. Speranza
   for the Grice Circle