if and only if some swans are black. (ii) Specify the proposition that S expresses: S means (the proposition) that some swans are black. (iii) Specify S’s assertability conditions: S is assertable if and only if blackswan-sightings occur or black-swan-reports come in, etc. (iv) Translate S into that sentence of our language which has the same use as S or the same conceptual role.
Certain theories, especially those that specify meanings in ways (i) and (ii), take the compositionality of meaning as basic. Here is an elementary fact: a sentence’s meaning is a function of the meanings of its component words and constructions, and as a result we can utter and understand new sentences – old words and constructions, new sentences. Frege’s theory of Bedeutung or reference, especially his use of the notions of function and object, is about compositionality. In the Tractatus, Wittgenstein explains compositionality in his picture theory of meaning and theory of truth-functions. According to Wittgenstein, a sentence or proposition is a picture of a (possible) state of affairs; terms correspond to non-linguistic elements, and those terms’ arrangements in sentences have the same form as arrangements of elements in the states of affairs the sentences stand for.
The leading truth-conditional theory of meaning is the one advocated by Davidson, drawing on the work of Tarski. Tarski showed that, for certain formalized languages, we can construct a finite set of rules that entails, for each sentence S of the infinitely many sentences of such a language, something of the form ‘S is true if and only i. . .’. Those finitely statable rules, which taken together are sometimes called a truth theory of the language, might entail ‘ ‘(x) (Rx P Bx)’ is true if and only if every raven is black’. They would do this by having separately assigned interpretations to ‘R’, ‘B’, ‘P’, and ‘(x)’. Truth conditions are compositionally determined in analogous ways for sentences, however complex. Davidson proposes that Tarski’s device is applicable to natural languages and that it explains, moreover, what meaning is, given the following setting. Interpretation involves a principle of charity: interpreting a person N means making the best possible sense of N, and this means assigning meanings so as to maximize the overall truth of N’s utterances. A systematic interpretation of N’s language can be taken to be a Tarski-style truth theory that (roughly) maximizes the truth of N’s utterances. If such a truth theory implies that a sentence S is true in N’s language if and only if some swans are black, then that tells us the meaning of S in N’s language. A propositional theory of meaning would accommodate compositionality thus: a finite set of rules, which govern the terms and constructions of L, assigns (derivatively) a proposition (putting aside ambiguity) to each sentence S of L by virtue of S’s terms and constructions. If L contains indexicals, then such rules assign to each sentence not a fully specific proposition but a ‘character’ in the above sense. Propositions may be conceived in two ways: (a) as sets of possible circumstances or ‘worlds’ – then ‘Hesperus is hot’ in English is assigned the set of possible worlds in which Hesperus is hot; and (b) as structured combinations of elements – then ‘Hesperus is hot’ is assigned a certain ordered pair of elements ‹M1,M2(. There are two theories about M1 and M2. They may be the senses of ‘Hesperus’ and ‘(is) hot’, and then the ordered pair is a ‘Fregean’ proposition. They may be the references of ‘Hesperus’ and ‘(is) hot’, and then the ordered pair is a ‘Russellian’ proposition. This difference reflects a fundamental dispute in twentieth-century philosophy of language. The connotation or sense of a term is its ‘mode of presentation,’ the way it presents its denotation or reference. Terms with the same reference or denotation may present their references differently and so differ in sense or connotation. This is unproblematic for complex terms like ‘the capital of Italy’ and ‘the city on the Tiber’, which refer to Rome via different connotations. Controversy arises over simple terms, such as proper names and common nouns. Frege distinguished sense and reference for all expressions; the proper names ‘Phosphorus’ and ‘Hesperus’ express descriptive senses according to how we understand them – [that bright starlike object visible before dawn in the eastern sk. . .], [that bright starlike object visible after sunset in the western sk. . .]; and they refer to Venus by virtue of those senses. Russell held that ordinary proper names, such as ‘Romulus’, abbreviate definite descriptions, and in this respect his view resembles Frege’s. But Russell also held that, for those simple terms (not ‘Romulus’) into which statements are analyzable, sense and reference are not distinct, and meanings are ‘Russellian’ propositions. (But Russell’s view of their constituents differs from present-day views.)
Kripke rejected the ‘Frege-Russell’ view of ordinary proper names, arguing that the reference of a proper name is determined, not by a descriptive condition, but typically by a causal chain that links name and reference – in the case of ‘Hesperus’ a partially perceptual relation perhaps, in the case of ‘Aristotle’ a causal-historical relation. A proper name is rather a rigid designator: any sentence of the form ‘Aristotle i. . . ‘ expresses a proposition that is true in a given possible world (or set of circumstances) if and only if our (actual) Aristotle satisfies, in that world, the condition ‘ . . . ‘. The ‘Frege-Russell’ view by contrast incorporates in the proposition, not the actual referent, but a descriptive condition connotated by ‘Aristotle’ (the author of the Metaphysics, or the like), so that the name’s reference differs in different worlds even when the descriptive connotation is constant. (Someone else could have written the Metaphysics.)
Some recent philosophers have taken the rigid designator view to motivate the stark thesis that meanings are Russellian propositions (or characters that map contexts onto such propositions): in the above proposition/meaning ‹M1,M2(, M1 is simply the referent – the planet Venus – itself. This would be a referential theory of meaning, one that equates meaning with reference. But we must emphasize that the rigid designator view does not directly entail a referential theory of meaning.
What about the meanings of predicates? What sort of entity is M2 above? Putnam and Kripke also argue an anti-descriptive point about natural kind terms, predicates like ‘(is) gold’, ‘(is a) tiger’, ‘(is) hot’. These are not equivalent to descriptions – ‘gold’ does not mean ‘metal that is yellow, malleable, etc.’ – but are rigid designators of underlying natural kinds whose identities are discovered by science. On a referential theory of meanings as Russellian propositions, the meaning of ‘gold’ is then a natural kind. (A complication arises: the property or kind that ‘widow’ stands for seems a good candidate for being the sense or connotation of ‘widow’, for what one understands by it. The distinction between Russellian and Fregean propositions is not then firm at every point.) On the standard sense-theory of meanings as Fregean propositions, M1 and M2 are pure descriptive senses. But a certain ‘neo-Fregean’ view, suggested but not held by Gareth Evans, would count M1 and M2 as object-dependent senses. For example, ‘Hesperus’ and ‘Phosphorus’ would rigidly designate the same object but have distinct senses that cannot be specified without mention of that object. Note that, if proper names or natural kind terms have meanings of either sort, their meanings vary from speaker to speaker. A propositional account of meaning (or the corresponding account of ‘character’) may be part of a broader theory of meaning; for example: (a) a Grice-type theory involving implicit conventions; (b) a theory that meaning derives from an intimate connection of language and thought; (c) a theory that invokes a principle of charity or the like in interpreting an individual’s speech; (d) a social theory on which meaning cannot derive entirely from the independently constituted contents of individuals’ thoughts or uses. A central tradition in twentieth-century theory of meaning identifies meaning with factors other than propositions (in the foregoing senses) and truth-conditions. The meaning of a sentence is what one understands by it; and understanding a sentence is knowing how to use it – knowing how to verify it and when to assert it, or being able to think with it and to use it in inferences and practical reasoning. There are competing theories here. In the 1930s, proponents of logical positivism held a verification theory of meaning, whereby a sentence’s or statement’s meaning consists in the conditions under which it can be verified, certified as acceptable. This was motivated by the positivists’ empiricism together with their view of truth as a metaphysical or non-empirical notion. A descendant of verificationism is the thesis, influenced by the later Wittgenstein, that the meaning of a sentence consists in its assertability conditions, the circumstances under which one is justified in asserting the sentence. If justification and truth can diverge, as they appear to, then a sentence’s assertability conditions can be distinct from (what non-verificationists see as) its truth conditions. Dummett has argued that assertability conditions are the basis of meaning and that truth-conditional semantics rests on a mistake (and hence also propositional semantics in sense [a] above). A problem with assertability theories is that, as is generally acknowledged, compositional theories of the assertability conditions of sentences are not easily constructed.
A conceptual role theory of meaning (also called conceptual role semantics) typically presupposes that we think in a language of thought (an idea championed by Fodor), a system of internal states structured like a language that may or may not be closely related