I'm glad J enjoyed my Pietroski's precis on logical formations and deformations.
I am currenty checking this paradox, I saw online:
'the logical form of x is y'
This, Materna, and others were noting, involves a regress:
For what is the logical form of the logical form? So Griceians have to be careful as to what they think displays this or that logical form. It cannot yet be another sentence.
If we are working with a formal calculus, the topic is even more intriguing. Etc.
J notes:
"[The Petroski points] will require some review."
"One thing to note about the conditional, however-- p-> q to -p v q to -(p & -q), right?? material implication, to DeMorgans."
Yes, I'm always fascinated by the horseshoe, which I take to be the Megarian (Philonian) condition. It is odd, since Megara is close to the sea, and one would have expected he to stick with the 'fishhook' rather than the 'horseshoe' as representation of logical form for Greek conditionals. Another problem with Greek conditionals is that Greek grammar is complex enough without them
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J notes:
"So, in the last formation its a class membership thing,denied conjunction. felines-> mammals, ergo, there are no instances of felines which are not mammals (ie no (feline AND not-mammal, or non-mammal AND feline))."
Yes.
"In that case...the truth hinges on defining the terms, doesn't it."
Yes.
But note that the horseshoe is complex enough at the PROPOSITIONAL level:
"if p, q"
----
It is true that for the Square of Opposition, ")" (the horseshoe) features in some of the judgements:
A ---- E
I ---- O
and with Aristotle and Grice and Kant (and Kantotle) everyone should see quantificational logic as PRIOR to propositional logic. Logic teachers often misteach this, which does not make historical sense: Aristotle came before the Stoics!
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J goes on:
"The merely formal notation doesn't capture the semantic relations, or something (which is to say, logical formality runs into grammar...as well as meaning--at times the grammar/syntax cannot be adequately expressed, or something (tho thats not to approve of the chomkyites)"
According to Neale, online, "Logical form and LF", the Chomskyites don't know what they are talking about when they say "LF" -- if provoked, they say "ILF", interpreted logical form, an ambiguous mouthful!
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Grice used to say (to Strawson) when analysing the logical form of:
"She was pretty, and poor -- but she was honest".
"What is the logical form of a 'but' sentence?"
Grice thought it was:
"She is pretty AND she is honest".
Strawson disagreed. They also disagreed on the meaning of "and"
"Surely," Strawson would say, "you will not say that the logical form of "She got a baby and married" is "she got a baby AND THEN she married". "Why not?" answered the more liberal Grice.
When Strawson died, his obituarist wrote, in "The Times": "Sir Peter should have paid more notice to Grice's witty remark, "If you can't put it in formal symbols, don't say it".
---- But then it was too late.
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given material implication (ie, same truth table for p -> q AND -p v q and -(p & -q), right?) ...is there such a thing as a conditional? A true conditional's just another name for inclusion of a sort (not to bless set theory across the board)--ie, and yes Aristotle's square of opposition, mostly, with the (x) as universal and ∃x as particular. ("but" is usually read as "and")
ReplyDeleteBut....IIRC we also need to add...and the shit exists (which is to say, in real world situations, the ∃x relates to confirming premises, that is its worth caring about...Hubble searching for a bald King of France? Teapot? Jeezuss? or something)
What do syntactical types mean by logical form/LF ? Something like ,looks somewhat logical, and has a form, and helps out CHomsky's programmme