ENTAILMENT, PRESUPPOSITION, AND IMPLICATURE

Entailment, as used by philosophers, is a term of art that, unlike logical consequence, lacks a precise definition that is consistently adhered to by those who employ it. Throughout much of the twentieth century, especially its early and middle years, many philosophers connected entailment with analyticity, requiring the material conditional ^┌A ⊃ B^┐ to be analytic when A entailed B. In later years, as conceptions of analyticity became less expansive, and philosophical uses of it more restricted, the presumption that entailment was to be understood in terms of analyticity waned. However, the relationship between entailment and necessity has remained robust. Standardly, when it is claimed that A entails B, B is taken to be a necessary consequence of A in the sense that it is impossible for A to be true without B's being true. Often, though not always, B is required to be apriori deducible from A, as well. The relata, A and B, are naturally thought of as propositions, or statements—in the sense of that which is stated by an assertive utterance of a sentence. However, sometimes theorists speak of sentences themselves as entailing other sentences. In such cases, it is natural to construe the relation holding between sentences as deriving from the primary entailment relation holding between the propositions they express.

A potentially more restrictive understanding of entailment requires that when A entails B, the falsity of A is a necessary consequence of the falsity of B. When entailment is understood in this way, it is sometimes contrasted with logical presupposition: A proposition A logically presupposes a proposition B if and only if the truth of B is a necessary condition for A's being either true or false. The most widely discussed (putative) examples of logical presuppositions are so-called existential presuppositions, corresponding to uses of singular terms. (These are also sometimes called referential presuppositions.) For example, according to a Fregean analysis of definite descriptions, the propositions expressed by (1a) and (1b) logically presuppose the proposition expressed by (1c).

1a. The person who proved Goldbach's conjecture is brilliant.

1b. The person who proved Goldbach's conjecture isn't brilliant.

1c. One and only one person proved Goldbach's conjecture.

For Frege, singular definite descriptions are complex singular terms, and the predicate is brilliant designates a function that assigns truth to some individuals and falsity to others. Because the sense of the person who proved Goldbach's conjecture fails to pick out any individual, the function designated by is brilliant has no argument to operate on, and (1a) is characterized as being neither true nor false. The same is true of (1b), which is taken to be the negation of (1a). Because, for Frege, the negation function—which assigns truth to falsity, and falsity to truth—has no argument to operate on in this case, proposition (1B) is not assigned any truth value. On this analysis, the truth of the logical presupposition, (1c), is a necessary condition for (1a) and (1b) to be either true or false.

The Semantics of Frege and Russell

Although the compositional semantics of Frege (1891, 1892a, and 1892b) produce elegant results in cases such as this, they run into trouble when fully generalized. For Frege, n -place truth-functional operators designate n -place truth functions, and the truth value of a truth-functional compound is the value of the relevant truth function at the n -tuple of truth values of its sentential constituents. Hence, the argument used to show that the negation of a proposition is truth valueless if and only if the proposition negated is truth valueless can be generalized to yield the conclusion that a truth functional compound is truth valueless if and only if one of its constituents is. This result is demonstrably incorrect, as is shown by (2a) and (2b)—based on an example given by Bertrand Russell in "On Denoting" (1905). (Read if, then, in (2a) as material implication.)

2a. If one and only one person proved Goldbach's conjecture, then the person who proved Goldbach's conjecture is brilliant.

2b. Either it is not the case that one and only one person proved Goldbach's conjecture, or the person who proved Goldbach's conjecture is brilliant.

Far from being truth valueless, these examples are made true because no one has proved Goldbach's conjecture.

This was one of the considerations that led Russell to analyze the examples in (1) differently from Frege. On his analysis, the logical form of (1a) is (R1a), while (1b) is ambiguous between (R1bw), in which the description is said to have wide scope, and (R1bn), in which it takes narrow scope.

R1a. ∃x [∀ y((y is a man & y proved Goldbach's conjecture) ↔ x = y) & x is brilliant]

R1bw. ∃x [∀ y((y is a man & y proved Goldbach's conjecture) ↔ x = y) & ∼ x is brilliant]

R1bn. ∼ ∃ x [∀ y((y is a man & y proved Goldbach's conjecture) ↔ x = y) & x is brilliant]

When (1c) is false, (R1a) and (R1bw) are also false, but (R1bn) is true. On this analysis, (1c) is a necessary consequence of (1a), and of the reading of (1b) represented by (R1bw). However, on this reading, (1b) is not the (logical) negation of (1a). Hence, for Russell, these examples are not instances of logical presupposition.

Strawson's Theory of Presupposition

In "On Referring" (1950), Peter Strawson considered such cases, and presented his own analysis that included the following theses: (i) meaning is a property of expressions; referring, saying something, and being true or false are properties of uses of expressions in contexts; (ii) to give, or know, the meaning of a sentence S is to give, or know, a rule for determining the contexts in which S is used to say something true, and the contexts in which it is used to say something false; (iii) the primary referring use of a name, demonstrative pronoun, or singular definite description is one in which the term is used to refer to something that the rest of the sentence is used to say something about; the meaning of such a term, when used in this way, is a rule for determining its referents in different contexts; (iv) if a singular term b in a sentence ^┌Fb^┐ is used referringly in a context C, then ^┌Fb^┐ says something true (false) in C if and only if, in C, the referent of b has (does not have) the property that F is used to express; if b fails to refer to anything, then ^┌Fb^┐ fails to say anything true or false in C; (v) definition: S presupposes p relative to C if and only if the truth of p is a necessary condition for a use of S in C to say something true or false; and (vi) uses of ^┌The F is G^┐, ^┌All Fs are G^┐, ^┌Some F's are G^┐, ^┌No Fs are G^┐, and ^┌Some Fs are not G^┐ presuppose (in the sense of (v)) that expressed by ^┌(There is at least one F^┐.

Thesis (ii) is problematic. As it stands, it does not rule out, and may even seem to suggest, that the meaning of a sentence is a function from contexts of utterance to truth values. According to a better picture, presented by David Kaplan in "Demonstratives" (1989), the meaning of a sentence is a function from contexts to propositions, where the latter determine functions from circumstances of evaluation to truth values. When this view is substituted for (ii), corresponding changes must be made in theses (iii) and (iv). Strawson's emphasis on referring as the semantic function of a singular term, plus his tendency to treat referring uses of demonstratives as prime examples of this function, suggest a reformulation of (iii) and (iv) in which all referring uses of singular terms are, in Kaplan's words, directly referential. (iii_k) A referring use of a singular term b, as part of a sentence S, in a context C contributes the referent of b in C to the proposition expressed by S in C; the meaning of a singular term is a rule for determining the propositional constituents contributed by uses of b to the propositions expressed by sentences containing b in different contexts. (iv_k) If a referential use, in a context C, of a singular term b in a sentence ^┌Fb^┐ refers to o, and if F is used to express the property P, then ^┌Fb^┐ expresses a proposition in C that is true (false) in a possible circumstance w if and only if o has (doesn't have) P in w, if b fails to refer to anything in C, then there is no propositional constituent corresponding to b in C, and ^┌Fb^┐ fails to express a (complete) proposition in C.

The theory of presupposition that emerges from this reconstruction of Strawson's theses is a theory of what may be called expressive presupposition : A sentence S expressively presupposes a proposition p relative to a context C if and only if the truth of p is necessary for S to semantically express a (complete) proposition in C. This theory provides a plausible account of examples in which a pronoun, demonstrative, or demonstrative phrase is used referringly. However, the theory produces incorrect results when extended to the range of cases mentioned in thesis (vi). Such an extension also conflicts with Strawson's expressed intentions. In Introduction to Logical Theory (1952), he defines presupposition as follows: A statement (proposition) S presupposes a statement (proposition) S' if and only if the truth of S' is a necessary condition for S to be true or false. Because this is a definition of logical presupposition, Strawson's adoption of it belies any clear commitment to expressive presupposition, or any systematic analysis of the examples in (vi) along directly referential lines.

This suggests a second possible reconstruction of his position. On this interpretation, his theory of presupposition is substantially the same as Frege's, without the compositional semantics, but with the stipulation that statements involving certain generalized quantifiers bear existential presuppositions. This theory is broad in scope and has been historically influential. However, its leading ideas are not original with Strawson. As a historical point, it would be a mistake to attribute to him either an account of presupposition that is systematically Fregean (logical), or an account that is systematically expressive. His major discussions include elements of both, the conflict being masked by the flawed account of meaning given in thesis (ii), and the failure to articulate the more satisfactory picture later provided by Kaplan.

Pragmatic Presupposition and Conversational Dynamics

An important advance in the study of presupposition, signaled in Stalnaker (1973, 1974) and Lewis (1979), integrates presupposition into a broader theory of conversational dynamics. The crucial observation is that sentences are used in communication to contribute to an existing conversational record, which contains background assumptions shared by conversational participants. Because of this, it is natural for speakers to develop conventional means of indicating what assumptions they are making about the conversational record to which their utterances contribute. Pragmatic presuppositions may then be understood as requirements imposed on such records by utterances. Suppose, for example, that a use of S (e.g. "It wasn't Andrew who solved the problem") requires the set of background assumptions prior to the utterance to contain a specific proposition p (that someone has solved the problem). Imagine a conversation in which p is not already among the shared background assumptions prior to the utterance of S, but conversational participants are willing to accept p as uncontroversial. What response would be reasonable in such a case? The legalistic response would be to object to the speaker's remark on the grounds that p, which was required by the utterance of S, had not already been established. The speaker could then ask whether hearers were willing to accept p, and be told that they were. After adding p to the conversational record, the speaker could repeat the original remark, and continue.

But there would be no point to this. Because hearers are ready to accept p anyway, they may as well add it to the background, and let the speaker go on without objection. In short, the most efficient response is to accommodate the speaker by updating the conversational record so that it meets the requirements of the utterance. Knowing that hearers can work this out on their own, the speaker can exploit this strategy of accommodation by uttering sentences the presuppositional requirements of which are not already satisfied by the conversational record—provided the requirements are both recognizable and uncontroversial. One virtue of this pragmatic approach is its eclecticism regarding different factors that may give rise to presuppositional requirements. As indicated in Soames (1989), logical presupposition, expressive presupposition, conventional implicature, constraints on the interpretation of anaphora, and non-conventional pragmatic facts have all been suggested as sources of pragmatic presuppositions. Further developments are found in Heim (1982, 1983) and Beaver (2001).

Conversational and Conventional Implicatures

Closely related to pragmatic presuppositions, are conversational and conventional implicatures, introduced in Grice (1989) (originally delivered as the William James Lectures at Harvard in 1967). For conversational implicatures, the key insight is that the efficient and rational exchange of information by cooperative speakers is governed by maxims that include: (i) don't make your conversational contribution too weak (or too strong); (ii) don't say that which you believe to be false, or that for which you lack adequate evidence; (iii) be relevant; and (iv) avoid obscurity and ambiguity; be brief and be orderly.

Conversational implicatures are propositions that a speaker is committed to, above and beyond that which is said or asserted, by virtue of the presumption that the conversational maxims are being obeyed. According to Grice, a speaker s conversationally implicates q by saying p if and only if (a) s is presumed to be observing the conversational maxims, (b) the supposition that s believes q is required in order to make s's saying p consistent with that presumption, and (iii) s assumes that the hearers can recognize both this requirement and that s is assuming this. For example, if s assertively utters a disjunction ^┌A or B^┐, then standardly s conversationally implicates that there are non-truth-functional grounds for the assertion (because if s's grounds were truth-functional, and hence sufficient for asserting either disjunct alone, then s's utterance of the disjunction would be too weak, and hence violate maxim (i)). This shows that the simple truth-functional semantics for disjunction do not have to be complicated in order to explain why assertive utterances of disjunctive sentences standardly convey non-truth-functional information.

Another example of some philosophical significance involves the observation in Austin (1964) that it would be an abuse of language for a man who can see that there is a pig in front of him—without having to make any special investigation or to infer the presence of the pig from other propositions—to assert merely that it seems to him as if a pig is present, or that he has evidence of the presence of a pig. From this Austin concludes that such assertions would be false, and that, in a case such as the one imagined, a person can have empirical knowledge without having evidence for the proposition known. However, as pointed out in Ayer (1967), Austin's observation does not support his conclusion. Because the speaker in the imagined situation is in a position to make the stronger claim that a pig is present, the decision to make the weaker statement instead violates Grice's maxim (i). The abuse of language here is not that of stating a falsehood, but of conversationally implicating one.

Like conversational implicatures, Gricean conventional implicatures are propositions to which the speaker is committed, despite their not being parts of what is said by the speaker's utterance. The difference between the two is that the former arise from the conversational maxims, whereas the latter are due to aspects of meaning. For example, an utterance of "She is poor but honest" conventionally implicates—in virtue of the nonassertive meaning of "but"—that there is some contrast between poverty and honesty, an utterance of "He is an Englishman, and therefore, brave" conventionally implicates—in virtue of the nonassertive meaning of "therefore"—that being brave is an expected consequence of being an Englishman, an utterance of "Mary hasn't arrived yet" conventionally implicates—in virtue of the nonassertive meaning of "yet"—that Mary's arrival is expected, and an utterance of "It wasn't Andrew who solved the problem" conventionally implicates—in virtue of the nonassertive meaning attached to the construction "It was (wasn't) NP who VPed"—that someone solved the problem. (Contrast this with "Andrew didn't solve the problem.") A significant point, developed in Karttunen and Peters (1979), is that conventional implicatures such as these may plausibly be regarded as pragmatic presuppositions. This suggests that the nonassertive meaning that generates them may be presuppositional in nature.

See also Analyticity; Austin, John Langshaw; Ayer, Alfred Jules; Frege, Gottlob; Grice, Herbert Paul; Kaplan, David; Lewis, David; Presupposition; Propositions; Russell, Bertrand Arthur William; Semantics; Strawson, Peter Frederick.

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Scott Soames (2005)