A truth-conditional semantics for natural language?

The view that natural-language sentences typically do not encode a fully prepositional meaning raises the question of how their semantics is to be characterised. A dominant view is that, notwithstanding indexicality, vagueness and incompleteness, sentence meaning M UST be given in terms of truth conditions. I mentioned briefly in section 2.2 the way in which indexicality and ambiguity have been accommodated by truth-conditional approaches. So the T-sentence for T am happy now ’ is not (27a) but (27b):

(27) a. T am happy now’ is true iff I am happy now.

b. An utterance of T am happy now’ is true iff the speaker is happy at the time o f utterance.

This approach, which explicitly incorporates reference to elements of context (the speaker, the addressee, the time of utterance, the place of utterance, indicated objects, etc.) is generally known as "indexical semantics", though Montague referred to it as "pragmatics" (in a formal sense of the term, clearly different from the cognitive notion I am using). The assumption behind this is that the context-sentence pair will deliver the proposition expressed by the utterance (its truth-conditional content); that is, that for each indexical element of the sentence there is a rule or convention for picking out its referent in the context. An immediate and pressing issue is what such a formal notion of context amounts to and how it is to be delimited for particular sentences. Setting that aside for the moment, there is the remaining problem that the assumption does not seem justified for the main bulk of indexical terms. While it might seem reasonable for cases like T’ (the speaker), and ‘today’ (the day of utterance), it seems much less so for third person pronouns, demonstratives and definite descriptions. Consider an example taken from Blakemore (1987, 10):

(28) A: Have you heard Perahia’s recording of the ‘M oonlight Sonata’? B: Yes, it made me realize I’d never be able to play it.

Even supposing that both the entities referred to by ‘Perahia’s recording of the "Moonlight Sonata"’ and ‘the Moonlight Sonata’ are included among the contextual coordinates, there is no rule attached to the word ‘it’ that will determine which is the one referred to on each of the two uses. That is, the sentence-context pair alone does not determine the truth-conditional content of the sentence uttered by B.

However, Lewis (1979) builds into his truth-conditional account such cognitive features as the comparative salience of candidate referents and criteria for the evaluation of utterance interpretations such as plausibility and informativeness. So reference assignment to the first instance of ‘it’ in example (28) m ight be effected as a result of the greater comparative salience of the recording of the sonata than the sonata itself and to the second instance by considerations of the overall plausibility o f the interpretation. W hat he is proposing, in effect, is, in our terms, a combination semantic/pragmatic account on the basis of which a truth-theoretic account can be given ( ‘truth in a context’ as he repeatedly puts it). This is, of course, exactly w hat is needed, but for the purposes of a theory of the cognitive processes and representations involved in utterance interpretation this account ignores distinctions that are essential. Considerations of relative salience, context shift (what he calls ‘accom m odation’) and the overall plausibility and informativeness^^ of an interpretation are elements of the second (the pragmatic) phase of utterance understanding. The first phase, the automatic mapping of public linguistic forms onto mental structures (concepts or procedures), what relevance theorists call ‘decoding’, is a distinct type of cognitive activity effected by a distinct mental mechanism, the language faculty or module (following Fodor (1983)).

Higginbotham (1993,1994), an advocate of a Davidsonian style truth-conditional semantic theory, contends that a theory of meaning for a language has to distinguish those aspects of meaning that are strictly determined by linguistic form from those that involve the speaker’s choice, her free use of an expression to refer to a thing (given that there is always a range of expressions that could be used for this purpose). He refers to Kaplan (1977)’s argument that the sense of (an utterance of) a demonstrative, whatever it may be exactly, is irrelevant to the content o f what is said. This is a reflex of the famous character/content distinction (similar to Perry (1977)’s distinction between the ‘role’ of linguistic elements and the information they reveal on a given occasion of use). The character, the linguistic rule or procedure, which is provided by ‘this’, ‘that’,

‘it’, ‘he’, etc., does not enter into the truth-conditional content of an utterance of a sentence containing one of these elements; rather, the object referred to enters into the truth conditions and our knowledge that this is so is a feature of our semantic knowledge (competence). Higginbotham reiterates his earlier view (Higginbotham (1988)) that, since knowledge of sense is knowledge of conditions on truth and reference, what a person knows about a potential utterance of a sentence with demonstrative A can be captured by the conditional T-sentence schema (normal form) given in (29a). An instantiation of the schema is given in (29b):

(29) a. If u is an utterance of sentence S, and the speaker o f u refers with her utterance of A to x, then S is true iff P(x).

b. If the speaker of ‘this is green’ refers with the utterance of ‘this’ therein to X and to nothing else, then that utterance is true iff x is green.

As he says himself of this sort of case, the speaker’s perspective on what she speaks about - the object x - is left out of the account, ‘so if we cannot be said to have understood the utterance without knowing that perspective then there will be aspects of understanding not covered by semantic rules’ (Higginbotham 1993, 2). Note that the talk of speaker perspective is not of some private ineffable take on the object, but concerns whatever ‘is involved in the speaker’s use of demonstrative A to refer to x ’ and this includes the rule (or convention or procedure) that is encoded by the linguistic (hence public) indexical expression the speaker chooses to use in her utterance. Apart from the obvious substitutions (of ‘that’ for ‘this’, etc.), the statement of truth conditions given in (29b) for ‘this is green’ would be exactly the same for ‘that is green’, ‘it is green’, ‘he is green’, etc. Higginbotham’s primary concern in this passage is to show how language effaces certain crucial distinctions amongst thoughts that we communicate. In the process he shows how this truth-conditional approach to natural language sentences effaces certain distinctions in linguistic meaning: our knowledge as native speakers of the differences in meaning among ‘this’, ‘that’, and ‘it’.

It is not just the meaning of demonstratives that falls outside a T-theory as construed here. Higginbotham (1994, 98) discusses the case of the ‘specific indefinite’,

‘a certain F ’, which he compares with the simple indefinite description ‘an F ’ in examples such as the following:

(30) a. A politician rang me yesterday.

b. A certain politician rang me yesterday.

While there seems to be no truth-conditional difference between (30a) and (30b), hence no difference in their T-sentence specifications, there clearly is one when the simple sentence is embedded:

(31) a. If a politician rings us today, tell him I ’m out.

b. If a certain politician rings us today, tell him I’m out.

Segal (1994, 112) points out that this situation arises for a range of cases of what have been called conventional implicature, that is, cases of encoded meaning that appear to make no difference to the truth conditions of simple sentences. In similar vein, Gazdar (1979, 166-67) pointed out that different patterns of contrastive stress, while truth- conditionally inert in simple sentences, make themselves felt in more complex sentences:^^

(32) a. JANE gave me the tickets. b. Jane gave ME the tickets. c. Jane gave me the TICKETS.

(33) a. Jane gave ME the tickets by mistake. b. Jane gave me the TICKETS by mistake.

Higginbotham (1994, 99-100) proposes the following move in order to pull these phenomena into the fold of his semantic theory: ‘Suppose that the theory o f knowledge of meaning gives us, not quite the truth conditions (or conditional truth conditions) of an utterance, but rather what a person who used the utterance to make an assertion would represent himself as believing.’ Very often, truth conditions and what a person

represents herself as believing coincide, but on occasion they do not; in the case of an assertion of (30b), a speaker would represent herself as believing of a specific person that he is a politician and that he rang her yesterday, that is, F(a) & G(a), as opposed to (Ex)[F(x) & G(x)], which is what a speaker o f (30a) would represent herself as believing. Although these are clearly distinct beliefs, the hearer gets the same information in the two cases about how things m ust be if the world is as the speaker says it is.

Higginbotham believes that this move will mop up most, perhaps all, cases of implicature and presupposition triggered by linguistic form. He does not specifically address the stress cases in (32), but I see no reason, in principle, why the idea shouldn’t extend to them as well. He concludes that nonetheless, despite this ‘concession’, truth conditions remain fundamental: ‘it remains true that only truth conditional semantics has the properties needed for systematic semantic theory’ (Higginbotham 1994, 100).

I won’t try to assess this interesting proposal here, since it lies beyond the limited point I am driving towards in this section, which concerns the sort of conception of linguistic semantics we need for an inferential processing account o f utterance interpretation. W hat the proposal highlights for me, though, is how distinct the two approaches to linguistic meaning are; the difference is at least one of explanatory levels - the one concerned with characterising a system of knowledge (a competence) in quite abstract terms, the other with finding a representational level (or levels) which an interpreter can use as input to his system for inferring the informative intentions behind utterances of the linguistic expressions. Higginbotham (1994) and Segal (1994) may well be right that ‘knowledge of conditions on reference and truth is the backbone of a theory of meaning’; if so, it follows that the relationship between our cognitive account of utterance interpretation and the theory of meaning is not a simple one; the components of neither one of them translate into or correlate with, in any direct way, the components of the other.

Segal (1994,1996) and Larson & Segal (1995) seem, however, to have a stronger Manguage orientation than Higginbotham, emphasising the place of the T-theory within a wider view of interacting mental systems. Segal (1994, 112) discusses the employment of the T-theory by other cognitive systems, which take the T-theorems as providing an interpretation of natural-language sentences and use this in such linguistic

performances as understanding utterances and making judgem ents of meaning. So he, unlike most truth-conditionalists, is claiming that the T-theory is a component in the performance theory of verbal comprehension. This is still at one remove from an account which will actually run, as it were, an account in terms of representations and processes (computations) and, as already mentioned, Segal does concede that there is semantic knowledge a speaker/hearer must have which is not captured by the T-theory (so-called conventional implicatures).