[hist-analytic] Proving

jlsperanza at aol.com jlsperanza at aol.com
Sat Jan 9 08:58:59 EST 2010

The Oxford Texts, "Proof and Disproof in Formal Logic" has what I do have  
as "yields" (after Kleene, Metamathematics), i.e. Frege's assertion sign, to 
 read "proves", which is an interesting paradoxical one. For null set 
proves a  theorem, etc.
Another interesting feature of this is that as Grice uses the assertion  
operator (cfr. Grandy on quessertions), what we say is only theorematic, which 
 sounds good with me.
More on the Greek apres Jones:
He is indeed right about 'dialectic'. An online site on rhetoric has the  
"In Aristotle, dialectic is very similar, though for him, it represents  
something other than a path to Truth with a capital "T." Dialectic for 
Aristotle  uses cogent logic to reason from widely held or authoritative opinions. 
Its  conclusions are necessary even if its premises are not."
A good one is:

"enthymeme. (From Greek enthumēma, "thought,"  "reasoning," "argument.") In 
Aristotle, an enthymeme is a syllogism of a  particular type, namely, one 
whose premises are probable as opposed to obvious,  self-evident, or 
empirically confirmable. Thus it combines logic with to eikos,  proof by 
probability. For Aristotle, enthymemes are the basis of rhetorical  logic. Because 
rhetorical (rather than dialectical), they produce probable, not  necessary, 
which relates to Grice's implicit reasoning. Why he failed to use enthymema 
 for that -- knowing how he worshipped Greek escapes me)
The crucial one is:

"epideixis. Plural epideixeis, Greek for "demonstration," "proof"  
(epideiknunai, "to show")."
and here we may consult Mainetti, Theories of the Sign in Antiquity. He is  
a disciple of Eco, and he knows what he's writing about. Good chapters on  
Aristotle on this, as it relates to things like Grice's factive 'mean', and  
'show', etc.
For the assertion sign it's interesting that one meaning of 'logos' is  
indeed 'argument', as per online site referred to above:

logos. (Plur. logoi.) Account, story, speech, an individual speech; an  
argument. Also calculation, reason, rational thought, reasoned discourse, true  
story (versus myth), etc.
pisteis. The "proofs" section of a speech: where a speaker proves his  case.
--- this is an alphabetical site, hence my ordering. This pistis correlates 
 with the 'valid supplementation' referred to by Grice in his account of 
what a  prover does as he proves. Oddly, like "meaning", 'proving' is best 
used in the  past:
   Prover P has proved that p, iff P intended, ... and intended  that ... 
and the ... caused ... etc.
With 'provability' and 'probability' are cognate in English and Latin, that 
 was not the case for Greek, according to this online site:
Probability (to eikos), argument from. Considered a specialty of sophists  
like Gorgias, it seems to have been a fixture in the courtroom speeches of  
ancient Athens, due partly, perhaps, to the relative unavailability and  
unreliability of physical evidence. Perhaps the most famous / notorious use of  
argument from probability was by the sophist-professional 
speech-writer-oligarch  Antiphon. Accused of plotting the overthrow of democracy in 411 BCE, 
he pleaded  that a professional speech-writer like him (a logographer) could 
hardly be  expected to support oligarchy, a regime considered unfriendly to 
his line of  work. Thucydides, evidently, admired the speech highly. The 
jury, however,  didn't buy it: Antiphon was put to death.
Does 'reasoning' translate 'syllogism':

syllogism. A logical formula of Aristotle's devising, where two facts  
assumed to be true bear a relation to each other such that they imply a third  
fact necessarily true. Any given syllogism consists of a major premise, a 
minor  premise, and a conclusion, for instance:
MAJOR PREMISE. All human beings have souls. 
MINOR PREMISE. Socrates is  a human being. 
CONCLUSION. Socrates has a soul. 
If 1 and 2 above are  true, then perforce so is 3. Syllogisms figure in 
enthymemes, for Aristotle, the  basis of most persuasive speech.
My friend Graziella Chichi has dedicated her life to Aristotle's Topics.  
She would always try to convince me of the importance of this. Now from this  
online site I see what she meant:
topos. Or koinos topos, "common place" (plural koinoi topoi). Your  
Aristotle Rhetoric text translates the word as "topic." In Aristotle, it refers  to 
a widely applicable mode or scheme of argument, a logical "template" from  
which many different arguments, enthymemes, can be constructed. Given a  
particular thesis one seeks to prove or disprove, one will select a proper 
topos  to structure the right sort of proof or disproof. 
Underlying Aristotle's understanding of the word seems to be its earlier  
use by sophists, for whom it perhaps meant commonly available, 
"prefabricated"  or "ready-to-wear" verbal formulations (arguments, sentiments, topics, 
conceits  etc.) that could be "plugged-in" to a discourse as needed. In that 
sense (one  commonly used by critics today), a topos is like a cliché, only 
its appeal and  effectiveness actually lie in its familiarity: it expresses a 
speaker's  solidarity with attitudes endorsed by his/her audience.
That understanding of topos is not unrelated to Aristotle's use, as topoi  
in the Rhetoric clearly derive their plausibility in large part from the  
commonly accepted notions they deploy as arguments. 
Put differently, speakers/writers use topoi to "push" this or that  
audience-response "button," depending on need. Compare the topoi of funeral  
eulogies nowadays: 
"He was a good husband and a good father 
"He rose high but never forgot  where he came from" 
"He demanded much of his employees, but never more than  he did of himself"
Topoi of ancient coutroom oratory: 
"My friends are your [the audience's] friends; my enemies, your enemies"  
"My opponent tells you he 'loves' you, but his actions speak otherwise"  
"Excuse my lack of polish. This is my first time before a court" (I.e.,  
"Unlike my opponent, I'm just a regular Athenian who minds his own business")  
Topoi of political oratory: 
"Others will tell you want you want to hear, will resort to flattery  
[etc.]; I will tell you what you need to hear" 
"Whose interests will you  advance in your voting: those of your enemies 
abroad and of their lackeys here  in the city, or your own?" 

J. L. Speranza
   for the Grice Circle

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