Jlsperanza at aol.com
Jlsperanza at aol.com
Thu Jan 7 22:08:00 EST 2010
Some further points, as I google 'proof' and 'disproof' as titles in
advanced search for amazon.
1. There's that delightful, and originally, I expect, legalese (cfr.
Dickens, the law's an ass) "onus probandi", which I never really understood.
2. There are a few books on "idiot-proof" (as used by R. Carston in her
"Thoughts and Utterances"). Cfr. fool-proof. This may relate to a point that
sort of interests me. There seems to be this idea, by Grice et alii, that
the shortest proof is the best. This must be a corollary of Ockham, Do not
multiply steps in a proof beyond necessity. And it may relate to Euclid's
(and wasn't he based on Aristotle) on axiomata as, per definition,
'unprovable'. As Zeleny has noted elsewhere, the idea that an ass does not need to
_prove_ that the straight line is the shortest distance between two points.
3. Books on "Goedel's proof", so called. This book in the Oxford Test
Series (on proof and disproof in formal logic) seems to be very good: it has a
chapter on Goedel 'blowing up the stadium', after Russell hits Frege in the
knee -- with the Greeks inventing the game and Frege wickedly changing the
rules for it!
4. As the "Oxford Texts" book, there is J. Barwise, _Proof_ book, which
seems to have been popular as a Logic course in American universities (but
they keep changing textbooks every term, for commercial reasons).
5. I found a book by Berg on the "Disproof of the existence of God". I
thought about it, and came to the conclusion that as a healthy sceptic, I'm
not convinced. To me, a disproof of the existence of God seems as unrealistic
as a proof of the existence of God. (And I need not agree with Bayne that
a world with a God is more interesting than a God without one).
6. "Disproof in Formal Logic" (Oxford Texts) --. This seems like a very
good book. Contents available online. I could follow most of the Table of
Contents in any case. Very neat and tidy: starting with 'negation',
'conjunction', disjunction, material implication, turning to predicate logic, good
chapter on the empty class. It even has a section on 'proof' in science
(title of another google book -- and cfr. proof in mathematics as used by
Lakatos). Apparently, the author takes 'proof' as 'go by the rules' and
'disproof' by 'counterexample'.
7. Revising the online Latin Dictionary (Lewis/Short, Oxford) I note the
use of 'probare', to mean something like 'show': "my paternal fear shows that
I am your father" ("et patrio pater esse metu probor", Ovid.
Metamorphosis, 2, 91. Which is of course a loose use of 'proof', for the fear may be due
to the utterer's _false_ belief that he is the addressee's father, of
course. I'm not even DNA testing, which Ovid could not have dreamed of, proves
anything of that sort, either.
8. There are a couple of hits for 'prove' and B-raising verbs ("I will
prove it that Mary is the culprit" as ill-formed) and Kiparsky and Kiparsky.
Also on the asymmetry of proof and disproof for Popper and Lakatos.
Apparently, in Chinese, Lakatos, Proofs and refutations" comes out as "Proofs and
disproofs" which has a nice ring to it. A google hit notes that 'prove' is
_NOT_ a factive, but possibly a 'veridical'.
9. It should be pointed out the similarities between "Meaning" (1948) by
Grice and "Proving". While 'factive' (with 'counterfactive' of disproof, and
nonfactive) is a new invention, Hart was already citing Grice (1948) -- in
"Words and Signs" (Philosophical Quarterly, 1952) on the 'entailment' bit
re: the 'natural' use of "mean" -- and indeed the Oxford Texts book has a
section on "No smoke without fire?" which may relate.
10. Grice mentions 'epagogic' vs. 'diagogic' sort of 'proofs' (Reply to
Richards), and he seems to have viewed 'proof' as a value-oriented concept
(like 'reasoning' and 'sentence'). I.e. while 'sentence' entails, possibly,
'good, well-formed sentence', ditto for 'proof'. Another google hit mentions
that 'prove' possibly entails the sequencing of steps. Etc.
J. L. Speranza
Appendix. From the Short/Lewis, Latin Dictionary, under 'probo', and should
find for the Greek 'cognate', Gk. for 'demonstratio' I assume
B. In partic., to make a thing credible, to show, prove [very helpful,
this. :). JLS], demonstrate: “crimen,” Cic. Fl. 37, 93: “his ego judicibus non
probabo, C. Verrem contra leges pecunias cepisse?” Cic. Verr. 2, 1, 4, §
10: “causam paucis verbis,” id. Balb. 21, 49: “se memorem probare,”
grateful, id. Fam. 10, 24, 1: “perfacile factu esse illis probat, conata
perficere,” Caes. B. G. 1, 3: “hoc difficile est probatu,” Cic. Tusc. 5, 1, 1: “
et patrio pater esse metu probor,”
my paternal fear shows that I am your father, Ov. M. 2, 91: “sicut
Thrasvmachi probat exitus,” Juv. 7, 204.—With se: malo praesens observantiā,
indulgentiā, assiduitate memorem me tibi probare, Planc. ap. Cic. Fam. 10, 24,
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