By J. L. Speranza
--- for the Grice Club
I REFER TO JONES's commentary on "Grice, "Entailment"", this blog, vis a vis the important distinction between
p ⊢ q
and
p ⊨ q
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Distinctions apart, one wonders that the person who first created the second symbol, "⊨", must have had in mind the first one, "⊢". I wonder if he (or she if it was Ruth Barcan Marcus, :)) cared to name the extra stroke. For "⊢" (or turnstile), introduced by Frege features the context stroke, '-', and the judgement stroke, '|'.
From
http://psivision.objectis.net/SemanticSyntacticEntailment
I copy:
"(a) Semantic entailment is the same as the implication that we have seen earlier. If all truth assignments that satisfy a set of forumulae S also satisfy A, then S semantically entails A. That is, S -> A; (b) Syntactic entailment is slighly different. If A can be derived from S using a finite application of the propositional inference rules, then S syntactically entails A."
--- which does not seem is a distinction which Grice would make. Why he does use 'semantic', or 'semantics' pretty freely, I don't think he uses 'syntax' much, less so 'syntactic'.
Then again I read from
http://www.physicsforums.com/archive/index.php/t-71508.html
"We have semantic entailment and syntactic entailment. Semantic entailment
is associated with a decision procedure, say truth tables, and theorems. Syntactic entailment is associated with a proof procedure (axioms, inference rules), say natural deduction, and proofs. For soundess, syntactic entailment (there is a proof of P in L) implies semantic entailment (P is a theorem of L). For
completeness, semantic entailment (P is a theorem of L) implies syntactic
entailment (There is a proof of P in L). ... So, basically, personally, when I have something I want to check, I think semantic; When I want something I need to construct, I think syntactic."
And when I need to deconstruct I think pragmatically!
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This differs from my own commentary in that I took entailment to be exclusively semantic and used other terminology for what is here called "syntactic entailment" (derivability).
ReplyDeleteEvidently there is sufficient currency in the latter that I should stop using entailment unqualified for the semantic notion and make the semantic explicit.
Thus most of my commentary is nullified.
I would now have to go back and rework the commentary pointing out where the ambiguity in using "entailment" unqualified is significant. Which is probably not that far from what I was doing.
It is the incompleteness results which drives a wedge between the extensions of these (intensionally distinct) concepts.
RBJ
Thanks. I did not mean my comment as a hint for you to rework a minute in the proceedings (of the club!). I love the word 'minute' -- it does not mean a unit of measure, here (as Jones is discussing with Bayne elsewhere) but something different!
ReplyDelete-----
No. Perhaps 'semantic' is NOT necessary. But one has to be slightly careful. I recall when I was doing the OED2 -- or OED3 -- on this (NOT NOW) that I was overwhelmed, flabbergasted, or what have you, by the ZILLION uses of 'entail' in ALL the literature. The OED credits Moore, but surely 'entail' had been used zillion times before 1919 to mean perhaps what HE meant. (Else why would he just propose THAT term?).
(cfr. Grice on 'implicate' to do duty as term of art for 'imply', WoW:iii).
In "Pirotic Entailment" I refer to the idea of exploring this vis a vis Moore's "Barbara" example as interpreted by Carnap: Pirots karulise elatically, A is a pirot; A karulises elatically". It seems a lot can be said about 'entailment' here -- but the fact that 'pirot', 'karulise' and 'elatically' mean NOTHING should be qualified -- for 'entailment' would be hypothetical if it's just 'on the assumption' that "pirot", etc., means something.
(This, incidentally, relates to Grice's pet notion of the 'vacuous' concept, name, or description!). Or not!