[hist-analytic] Proving

[Jlsperanza at aol.com]

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.

Cheers,
 
J. L. Speranza
 
----
 
Appendix. From the Short/Lewis, Latin Dictionary, under 'probo', and should 
 find for the Greek 'cognate', Gk. for 'demonstratio' I assume  
(syllogismos?).
 
under probare:
 
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,  
1.—