--- by J. L. Speranza
------ for the Grice Club.
GRICE WOULD OFTEN AMUSE me, and others -- his contemporaries -- with stuff. E.g. his use of 'implicature'. Isn't that word _funny_? Note also 'entailment'. Isn't that word 'also' funny? It is. Grice would play on 'entailment' versus 'implicature'. In "Entailment" he addresses the monster. It was created by Austin's man ("Some like Witters, but Moore's MY man"). Back in the day, Austin's man had said -- and the thing to reprinted in the Proceedings of the Aristotelian Society for 1919 -- as follows.
Moore writes:
"Let us express the relation which we assert to hold
between a particular proposition p,
and a particular proposition q, when we say that in
this sense q "follows from" or "is deducible from" p, by
the symbol "ent"; which I have chosen to express it, because
it may be used as an abbreviation for "entails," and
because "p entails q" is a natural expression
for "q follows from p," i.e., "entails" can naturally be used as
the converse of "follows from.""
The source of this 'naturalness' is NOT clear. Surely 'entails' is NOT an Italian common verb! What Moore should have done is choose a term of 'Latinate' pedigree. There were plenty AROUND. By choosing something that only holds water in English, he did a great dishonour to Cambridge philosophy that Grice (who was, even, Oxford) tried to remedy by using 'implicat', instead.
Moore goes on:
"(We cannot unambiguously
use the phrase "p implies q" as equivalent to "q follows
from p," though it is in fact often so used,
because, especially in consequence of Mr. Russell's writings,
"implies" has come to be used as a name for a totally
different relation: we might perhaps use
"p logically implies q2" or
"p formally implies q," though Mr. Russell has also
given a different meaning to "formal" implication)."
So -- just because this Lord is playing games with the
English language, we need a new coinage!? Give me a break!
Note that, come to grits, Russell's only
heritage in the history of logic is due to his association
with Alfred North Whitehead -- who KNEW. What is of value in
Russell's writings springs from this joint collaboration. This is
called "Principia Mathematica" and it IS an extended volume -- in
fact a few of them. It was first published in toto in 1913, and
only in connection with that monumental work does Russell's opinion
on this or that holds water.
Whitehead was more careful with the Engish way of words than Russell was. Russell was a rebel. (The painting of the man in the film, "Tom and Viv" did not help).
Moore continues:
""p ent q" will then assert that there
holds between p and q that relation which holds, for
instance, between the two premisses of a syllogism in Barbara,
taken as one conjunctive proposition, and the conclusion, equally
whether the premisses be true or false; and which does not hold, for
instance, between the proposition "Socrates was a man" and
the proposition "Socrates was a mortal," even though
it be in fact true that all men are rnortal."
Grice preferred, on the whole, "logical implication" (rather than what Moore also mentions in connection with this: Russell's "FORMAL implication"). Note that it all boils down to
phi /- psi
phi /= psi
---
i.e. we don't really NEED a way to 'pronounce' those symbols, do we? For Grice, there are VARIOUS things to consider here. In "Retrospective Epilogue" (1987), now in WoW, he distinguishes (Strand 6)
a) logical inference
b) pragmatic inference
within logical inference we have logical implication -- what Moore thinks he is being witty by using 'entail' instead. The point of KEEPING 'implication' is to mark the connection between what Grice and Thompson and many others call "if". "If" is called "material implication"
if p, q.
---- The meaning of this is given by the truth-table.
p ) q
1 1 1
0 1 1
1 0 0
0 1 0
In a premise-conclusion display, 'if' STILL holds
premise (phi, in metalogical parlance)
--------------
conclusion (psi, in metalogical parlance)
If Premise, Conclusion. The point, made by Grice, and many others -- in fact, the STANDARD way of seeing things, as in Myro et al, "Rudiments of Logic" -- is what wiki has as the method of the "associated" 'if' or associated conditional.
In a valid syllogism, it become TAUTOLOGOUS that if premise, conclusion. Talk of entailment can only confuse. Plus, he (Moore) wasn't really being
SO original. Many people had used 'entail' before him, and I don't know what
they are talking when they said he coined anything!
At least Grice did coin "implicature" -- in English. It had been used in
Latin, 'implicatura' by Sidonius, but his usage did not quite stick (for some reason). (My acknowledgment to R. Paul, of Reed).
Moore, G. E. (1920). External and Internal Realations, Proceedings of the Aristotelian Society (New Series), 20 (1920), pp. 40-62.
Subscribe to:
Post Comments (Atom)
Posts
In the usage with which I am accustomed, the term "entails" expresses a semantic relationship, and is parallel to the syntactic notion "is derivable from".
ReplyDeleteWhether this is always the case, or whether some philosophers have used the term either for the syntactic relationship, or for either, or in ignorance of the distinction, I do not know, but it is often the case that explanations of the idea are ambiguous as to whether the intended relationship is semantic or syntactic.
This seems to apply even to the origin of the term, which I understand is held to be in Moore.
When the term is explained through the syllogism, which is the first formal deductive system, it is natural to construe the concept syntactically, but we may still doubt that this is what was intended by Moore.
The distinction is that between the syntactic "|-" for derivability and the semantic "|=" for entailment, and though you mention these, you do not draw the distinction or connect it with the other terminology.
A further point may be made concerning the connection betweem entailment and material implication.
The notation A => B may be paraphrased that A materially implies B. What this means is captured by the truth table for material implication.
This is not the same as saying that A entails B in the semantic sense.
A entails B only if A => B is analytic, not if it is contingently true.
How this connects with Grice I do not know.
Can we be assured that in his discussion of "entailment" Grice was talking about the semantic relationship of which I have spoken, or is it possibly that he had some other in mind?
In Moore, and in any philosopher before Goedel, it is possible that, like Hilbert, it has not occurred to them that there may be a difference of extension between "derivable from" and "entailed by".
This may contribute to their not thinking the distinction important, or not noticing it at all.
Explicit research on semantics is a very modern thing.
RBJ
Thanks, Roger.
ReplyDeleteYes, sorry about that. I should have been explicit as to the
p |- q
vs.
p |= q
which we have discussed elsewhere in this blog -- and where I used even a different symbolism where it comes as one thing -- rather as composed, if you get what I mean.
Nothing important, but in fact, Jones makes a big point, which I follow, that the sign is composite in Frege: content first, judgement second.
----
Indeed, 'entail' should be restricted to 'semantic', and the thought occurs to me that perhaps in popularisations of Carnap's views, this is indeed what transpires behind his idea of the 'meaning postulate'. Never mind 'postulate' -- but if he was talking 'meaning' (at some stage) HE is the person to rely on for the syntactic-semantic distinction at the point.
I expect Grice was pretty familiar with all this. A good locus classicus for me here is WoW:279, where he writes:
"... I can say that some explorer went off to someplace expecting to discover that the natives were very interesting in certain respects, but he did not discover that because they were not. So we have a case where there is logical implication on the part of affirmative, but not on the part of its denial. (That loks like a case of entailment)."
---
Note that he is using 'implication' -- in the collocation "logical implication" versus "entailment". Or rather he IS _equating_ 'logical implication' with 'entailment' which is Moore's point in commenting on Russell (in Moore 1919). At this point I suppose all we need to know about Russell is as per "On denoting" which he supplied for Mind in 1901 and that Grice cites on the opening page of the essay to which WoW:279 refers to.
This essay by Grice is dated 1970 (of the first version), and the "Entailment" symposium must have echoed in him at the time. It would be good to find more about that symposium -- not that it would help, but just out of curiosity. (Not all proceedings of the APA were published -- and this, alas, is one such case).
----
So, I would like your point about -- "before and after Goedel". I would think that indeed, before the Goedelian era", people COULD overlook 'syntactics' and 'semantics' like that (when you see an author uses 'syntactics' you know he is being serious about Morris, about whom one NEED to be serious, on occasion).
In Grice's System Q, which becomes Myro's System G (and which becomes my -- and L. Horn's -- System G-HP), there is a pretty easy way to give an answer to the point.
Note that in System Q, and G -- and indeed G-HP, even 1-correlation and 0-correlation (the truth-tables) are meant -- "in Z" --, in an interpretation. I should come back to this soon, I hope. And thanks for your points.
Incidentally, in relation to "|=" there is, early in the historical material I referred to in Carnap Corner by Awodey and Reck a description of some additional related uses of this symbol.
ReplyDeleteWe have:
"p |= q"
as p entails q
with the special case:
"|= q"
as q is analytic
Another use is:
"M |= q"
as q is true in M, where M is some interpretation (model) of the language of q.
and
"M,N,...|= q"
as q is true in every interpretation on the left.
My reading above involving the notion of analyticity (which is also implicitly interdefinable with entailment) will possibly look odd to a mathematical logician, since it is usual in that context to think in terms of a narrower notion of logical truth which depends on the logic in question.
We are then talking about first order entailment, or second order entailment, for example, and first or second order "validity" (logical truth).
RBJ
Thanks. That is very interesting. Will elaborate on your first-order and second-order, since I understand it's an interest of yours: to see how much of metalogic has informed logic, or related matters.
ReplyDelete----
The idea of 'analytic' as
|= p
is very good. And I am amused by thinking that, for Grice/Strawson it's
|= My neighbour's three-year old is NOT an adult
(the only example -- a variant -- of an analytic sentence in "Defense of a dogma".
One should also connect this with the first part of Strawson's "Introduction to Logical Theory". I wouldn't be surprised if it's ALL about 'entail'. Strawson, like later Grice, was interested in the use of 'therefore', which I think is a good thing to be (interested in thus). To use Moore's example, we would have in Barbara
A
A
---
Therefore A.
For Strawson, 'therefore' is the mark that relates to 'entails', too. Strawson's polemic with Grice can be thus seen as to the analysis of 'therefore'. Strawson favours an analysis of 'therefore' in terms of conventional implicature, which Grice actually endorses. But they disagree as to the analysis of the 'if'. Strawson assimilates the 'if' with the 'so' and the 'therefore'. The 'therefore' marks a reasoning in ASSERTED contexts (I assert A, I assert A; therefore, I assert A -- for Barbara). For Strawson, the 'if' marks something like the SAME reasoning in UNasserted contexts (if p, q).
To consider. Or not!