-- by J. L. Speranza
---- for the Grice Club
THERE'S, as Jones notes, syntactic entailment, semantic entailment, and what I propose to call 'pirotic' or pragmatic entailment. Just kidding!
But seriously, consider Moore's obsession with Barbara. In symbols
(x)Hx --> Mx
Hs
---
Ms
All men are mortal
Socrates is a man
--
Socrates is a mortal.
(I love the antiquity of using 'a mortal' instead of 'mortal' in Moore. Surely Grice's prose is easier to digest).
----
Now, to Carnap. But first, an online source provided these illustrations (author: Wang):
I run fast
----
I run
(syntactic entailment). Grice was fascinated with this -- just to prove Davidson wrong:
"HMS Pinafore sank the Bismarck"
"HMS Pinafore sank"
----
Or
He bought some plastic flowers
---
He bought some flowers.
---
Wang constrasts this with semanatic entailment. His example:
He loves her
---
He likes her.
---
(Wang's points are so controversial they hurt, but one may recheck them, especially vis a vis the first 'syntactic' type to check what example HE uses).
Anyway, yes, now to Carnap:
All pirots karulise elatically
A is a pirot
--
A karulises elatically.
In symbols:
(x)Px --> Kx
Pa
--
Ka
(Carnap, Aufbau, tr. by this English lady).
So surely when Grice says, "this looks like entailment" he SHOULD know. Either a thing is an entailment or is not. (Granted, his was a subtle example, "Cook did not discover that the Pacific Islanders were interesting").
But in any case, since it makes a lot of sense to speak of 'entailment' when it comes to pirots (karulising elatically) I can't (or Kant) see what we improve by talking 'semantic'. Or not.
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(x)Hx --> Mx
ReplyDeleteHs
---
Ms
categorical syllogisms did not allow for the singular term, so the usual socrates example is not really BARBARA, but just Modus Ponens .
It would probably be like this:
All men are animals.
All animals are mortal.
All men are mortal.
Hypothetical syllogism isn't it
but weirder (and not sure Grice discusses this) is that the material implication means that the conditional is a disjunction, OR translated again, a denied conjunction --- so, translated--
(x)Hx --> Mx OR (x)~ Hx v Mx, OR via de morgan (x)~(Hx & ~Mx)
--which I suggest is really what the conditional means, in terms of ordinary language (rather than in terms of cause, where the conditional rarely works, except in colloquial sense); ie you can't have a human that is not mortal--
Great. I'll elaborate on J's point about the 'meaning' of 'if' as being given, 'colloquially' ("in terms of ordinary language" as J puts it) by 'or' and 'not' -- or 'and' are 'not'. Yes, Grice did discuss this in WoW:iv, I would think -- but will check out for actual collocation. For, for one, is one (thesis) I hold!
ReplyDelete-- (Talking of 'conjunction', 'conditional' and 'disjunction', rather than 'and', 'if', 'or' -- and, I'll add, 'not' -- seem to confuse issues in that: who cares how I call 'if'. If is if is if. I'm not legally BOUND to call it 'conditional'! (Less so 'material implication'!).
But the gem about Moore NOT KNOWING the first thing about Barbara is warming! (I'm all for Oxon., and despise this sense of superiority that Cantabs. has, as when Moore goes on in the same 1919 thing:
Words to the effect:
"Well, Mr. Russell said it, and I know a good many people who will follow suit, just because Mr. Russell said it".
Or the patronising,
"I hope I will be using Russell's sophisticated symbolisms in Principia Mathematica alright".
He does not care to say that Russell AND WHITEHEAD said things -- when he quotes from "Principia", p. 21, as being something RUSSELL said! Surely
"Russell and Whitehead said it"
does not REALLY ent
"Russell sad it".
(I actually think it does -- but because people, I'm just coining this now, DISentails.
entailment: whatever Moore thought it was.
implicature: whatever Grice thought it was.
disimplicature: a trick of a notion only cited by Grice in unpublished stuff. Read: scary notion.
disentailment: what people do with words after a few drinks. Or not.
OK, I agree "if" tends to confuse things, yet a truth table will show that that conditional..-->... IS logically equivalent via material implication to ~p v q, or the
ReplyDelete~(p & ~q). It's in Quine's Methods of Logic somewhere as well (for those who get through the nasty dot/. issues)...and vienna circle types were aware of it (and maybe St Ludwig of Tractatus, who more or less insisted that logic was merely formal-- tautologies, contradictions, etc-- and would not work with language).
I'm not surprised Moore didn't know much about logic (probably going to Russell for assistance--though I need to read Grice's essay on implicature again. I thought it was too much ordinary language a few years ago...
Thanks, J. I have now posted, due to your encouragement, and before your second commentary here (we could doublecheck dates!) on "Disimplicature and disentailment"! -- it's a rather hard thing to digest. The good source here is, expensive as it is, Chapman's book, "Grice" (Macmillan, 2006), where she quotes from unpublished material. In any case, I thought I said, 'conditional' confuses. "If" NEVER confuses!
ReplyDeleteAlthough, in Latin, "si" does confuse!
You are perfectly right about symbols. At the Grice Club we surely prefer the horseshoe for the 'material implication'
p)q
and then, in the WoW reprint of "Logic and Conversation" he uses, the
p/\q for conjunction (first paragraph)
and
p\/q for disjunction
and the squiggly (as Smith calls it in "Formal Logic" for the tilde
-p
So, indeed, it is the common fare and Quine SHOULD mention it in "Methods of Logic". It would be illegal if he didn't!
We could extend on your earlier point about the MPP (modus ponendo ponens) since this is the intro of the horseshoe in a System like Grice's System Q (which he elaborated for Quine, in Davidson/Hintikka) and which I, apres Myro, have titled, System G-HP, which is what is promoted at the club (to read: a hopefully plausible or highly powerful version of Myro's System G, "in gratitude to Paul Grice for the idea" -- his first name was "Herbert" hence the HIGHLY powerful.
--
Yes, Witters plays some role here. Jones has dropped a good diagram here at the club -- doing 'diagramme' in search engine should retrieve it --. Since Jones thinks it's all about Witters!
Re: MPP Jones has some VERY interseting things to say about it, so it does connect with 'if' indeed. MPP is our way to INTRODUCE our talk of 'if' if it echoes the horseshoe. Jones's point is about the analyticity involved here. By adding to the premisses the mere statement
"if premisse, conclusion", this renders all reasoning deductive in a rather otiose way -- which we do PROMOTE at the club.
(We follow Rogers Albritton that 'otiose' is NOT otiose, otiosely).
Grazi--you have some interesting material up (even the Chomster! There's some mysterious connection 'tween NC's syntactical analysis and anal.phil....and even the L-word (logick) that Im still attempting to fathom).
ReplyDeleteNote tilde on upper left hand corner of key-pad: ~ . Seems a bit superior, nugatorily speaking, to mere dash - , aka subtraction sign, but whatevs. Horseshoe, OK, Willard Quine still used it, but --> preferable in ways (and prefer Jeffrey and Boolos to Willard, really).
The Club appears to have fairly stringent criteria for membership and I'm more of a political hack but will scroll through
C'mon I was JOKING!
ReplyDeleteHow could you even THINK I was serious in asking you to use such outdated thing as a HORSESHOE!
And never mind System G-HP. It was my BEST joke todate!
I like your sense of humour. You amuse me. Keep dropping good puns. And thanks for the squiggley. I hadn't realised it was so close to (my) heart!
I may write a post to provoke you on Socrates not being a person, but something that Socratises.