H. P. Grice, “Paradoxes of Entailment”

 Entailment. Grice thought that we probably did need an entailment. The symposium was held in New York with Dana Scott and R. K. Meyer. The notion had been mis-introduced (according to Strawson) in the philosophical literature by Moore. Grice is especially interested in the entailment + implicatum pair. A philosophical expression may be said to be co-related to an entailment (which is rendered in terms of a reductive analysis).  However, the use of the expression may co-relate to this or that implicatum which is rendered reasonable in the light of the addressees assumption that the utterer is ultimately abiding by a principle of conversational helfpulness. Grice thinks many philosophers take an implicatum as an entailment when they surely shouldnt! Grice was more interested than Strawson was in Moores coinage of entailment for logical consequence. As an analyst, Grice knew that a true conceptual analysis needs to be reductive (if not reductionist). The prongs the analyst lists are thus entailments of the concept in question. Philosophers, however, may misidentify what is an entailment for an implicature, or vice versa. Initially, Grice was interested in the second family of cases. With his coinage of disimplicature, Grice expands his interest to cover the first family of cases, too. Grice remains a philosophical methodologist. He is not so much concerned with any area or discipline or philosophical concept per se (unless its rationality), but with the misuses of some tools in the philosophy of language as committed by some of his colleagues at Oxford. While entailment, was, for Strawson mis-introduced in the philosophical literature by Moore, entailment seems to be less involved in paradoxes than if is. Grice connects the two, as indeed his tutee Strawson did! As it happens, Strawsons Necessary propositions and entailment statements is his very first published essay, with Mind, a re-write of an unpublication unwritten elsewhere, and which Grice read. The relation of consequence may be considered a meta-conditional, where paradoxes arise. Grices Bootstrap is a principle designed to impoverish the metalanguage so that the philosopher can succeed in the business of pulling himself up by his own! Grice then takes a look at Strawsons very first publication (an unpublication he had written elsewhere). Grice finds Strawson thought he could provide a simple solution to the so-called paradoxes of entailment. At the time, Grice and Strawson were pretty sure that nobody then accepted, if indeed anyone ever did and did make, the identification of the relation symbolised by the horseshoe with the relation which Moore calls entailment, p⊃q, i. e. ~(pΛ~q) is rejected as an analysis of p entails q because it involves this or that allegedly paradoxical implicatum, as that any false proposition entails any proposition and any true proposition is entailed by any proposition. It is a commonplace that Lewiss amendment had consequences scarcely less paradoxical in terms of the implicata. For if p is impossible, i.e. self-contradictory, it is impossible that p and ~q. And if q is necessary, ~q is impossible and it is impossible that p and ~q; i. e., if p entails q means it is impossible that p and ~q any necessary proposition is entailed by any proposition and any self-contradictory proposition entails any proposition. On the other hand, Lewiss definition of entailment (i.e. of the relation which holds from p to q whenever q is deducible from p) obviously commends itself in some respects. Now, it is clear that the emphasis laid on the expression-mentioning character of the intensional contingent statement by writing pΛ~q is impossible instead of It is impossible that p and ~q does not avoid the alleged paradoxes of entailment. But it is equally clear that the addition of some provision does avoid them. One may proposes that one should use  entails  such that no necessary statement and no negation of a necessary statement can significantly be said to entail or be entailed by any statement; i. e. the function p entails q cannot take necessary or self-contradictory statements as arguments. The expression p entails q is to be used to mean p⊃q is necessary, and neither p nor q is either necessary or self-contradictory, or pΛ~q is impossible and neither p nor q, nor either of their contradictories, is necessary. Thus, the paradoxes are avoided. For let us assume that p1 expresses a contingent, and q1 a necessary, proposition. p1 and ~q1 is now impossible because ~q1 is impossible. But q1 is necessary. So, by that provision, p1 does not entail q1. We may avoid the paradoxical assertion that p1 entails q2 as merely falling into the equally paradoxical assertion that p1 entails q1 is necessary. For: If q is necessary, q is necessary is, though true, not necessary, but a contingent intensional (Latinate) statement. This becomes part of the philosophers lexicon: intensĭo, f. intendo, which L and S render as a stretching out, straining, effort. E. g. oculorum, Scrib. Comp. 255. Also an intensifying, increase. Calorem suum (sol) intensionibus ac remissionibus temperando fovet,” Sen. Q. N. 7, 1, 3. The tune: “gravis, media, acuta,” Censor. 12. Hence:~(q is necessary) is, though false, possible. Hence p1Λ~(q1 is necessary) is, though false, possible. Hence p1 does NOT entail q1 is necessary. Thus, by adopting the view that an entailment statement, and other intensional statements, are non-necessary, and that no necessary statement or its contradictory can entail or be entailed by any statement, Strawson thinks he can avoid the paradox that a necessary proposition is entailed by any proposition, and indeed all the other associated paradoxes of entailment. Grice objected that Strawsons cure was worse than Moores disease! The denial that a necessary proposition can entail or be entailed by any proposition, and, therefore, that necessary propositions can be related to each other by the entailment-relation, is too high a price to pay for the solution of the paradoxes. And here is where Grices implicature is meant to do the trick! Or not! When Levinson proposed + for conversationally implicature, he is thinking of contrasting it with ⊢.  But things aint that easy. Even the grammar is more complicated: By uttering He is an adult, U explicitly conveys that he is an adult. What U explicitly conveys entails that he is not a child. What U implies is that he should be treated accordingly.