Jlsperanza at aol.com
Jlsperanza at aol.com
Fri Jan 8 17:31:23 EST 2010
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
---- 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
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
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
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.
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.
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!).
J. L. Speranza
for the Grice Circle
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