Comp and sem

It has been more or less universally assumed in the philosophical/semantic literature, from the work of Frege onwards, that any semantic theory worth its salt must be compositional: to put it as neutrally as possible, the meaning of a sentence must be determined by the meanings of its component parts and their syntactic combination. But why make this assumption? After all, there are apparently many non-compositional interpretive semantic theories for any natural language. There are four inter-connected observations that are commonly advanced in support of compositionality as a constraint on semantic theory[1].

Firstly, lexical items seem to contribute systematically to the meanings of the sentences in which they appear. So, for instance, the sentences in (1) and (2):

seem to have a meaning-element in common, the element brought to their meaning by the lexical item ‘cats’. Equally, we would expect a speaker who was able to understand sentence (3) to be able to understand sentence (4) as well:

This can only be explained, so the compositionalist claims, on the assumption that each lexical item contributes to the meaning of sentence, in line with syntactic structure.

Secondly, as native speakers of a natural language, we’re able to understand an infinite number of sentences of that language. A non-compositional semantic theory, the argument goes, would be unable to account for this fact: we cannot store an infinite number of whole sentence meanings in a finite brain, so we must instead store a finite number of meaning atoms and a finite number of recursive rules for combining those atoms. The meaning of a sentence, therefore, must be compositional.

A very closely related argument rests on our ability to understand novel sentences of our native language. If we can understand a sentence we’ve never heard before, then that can only be because we know the meanings of that sentence’s component parts and the effect that their particular syntactic combination has on the meaning of the sentence.

And finally, another very closely related argument: compositionality offers the only hope we have of accounting for the language acquisition data. It would be impossible to acquire the meanings of all the sentences of a natural language if we had to learn them one-by-one; this problem vanishes, however, if we can work out the meanings of the sentences of our language by learning a finite set of atomic meanings and a finite set of compositional rules.

It seems, then, that there are good reasons to prefer compositional semantic theories to non-compositional theories. But, so far, we’ve been working with a version of the principle of compositionality which is neutral as between a range of different interpretations. I want now to pick some of those interpretations apart. It’s broadly accepted within both linguistic semantics and the philosophy of language that there are at least two distinct levels at which the meaning of an utterance of a sentence may be represented, levels which I shall call linguistic meaning and truth-conditional content. This distinction is motivated, if by nothing else, by the gap between Kaplanian character and content which demarcates the class of indexicals. This distinction between linguistic meaning and truth-conditional content immediately gives rise to a parallel distinction between two different versions of the principle of compositionality:

Compositionality_LM: The linguistic meaning of a sentence is determined by the linguistic meanings of its component parts and their syntactic combination

Compositionality_TC: The truth-conditional content of (an utterance of) a sentence is determined by the linguistic meanings of its component parts and their syntactic combination

But which of these versions of compositionality must a semantic theory respect? There is an assumption, held in common by otherwise widely differing approaches within the truth-conditional tradition, that a viable semantic theory must respect compositionality_TC. If we accept that, on the one hand, our semantic theory must be compositional and, on the other, that truth is the only tool we have for approaching the slippery notion of meaning, then a commitment to compositionality_TC seems to be forced upon us: in the absence of compositionality_TC, the truth-conditional programme begins to look somewhat shaky.

There are, however, some increasingly well-documented difficulties with this kind of story, most of which are mapped out by Carston (1988, forthcoming etc). Consider, for instance, sentences (5) and (6) (examples adapted from Carston (forthcoming)):

Under what conditions will an utterance of (5) be true? Roughly speaking, an utterance of (5) in Land’s End will be true iff it is raining in Land’s End, while an utterance of (5) in John O’Groats will be true iff it is raining in John O’Groats. It seems, in other words, that a particular element of context, in this case location, although entirely unrepresented in the overt syntax, is being built into truth-conditional content. And how about (6)? Again it seems that truth-conditional content is dependent upon context: uttered by the choirmistress to Mary’s mother, who is keen for Mary to join the choir, it will be true iff Mary is too young to join the choir; uttered, however, by the bouncer at the door of the bar, it will be true iff Mary is too young to enter the bar.

On the face of it, this kind of evidence seems to undermine the viability of compositionality_TC: if contextual elements unrepresented in the overt syntax can enter into truth-conditional content, then truth-conditional content cannot be determined by lexical semantics plus syntax. But maybe this is too strong a conclusion. Maybe all that examples like (5) and (6) tell us is that indexicality is a more pervasive feature of natural language than we had previously thought; maybe, in other words, the location element in (5) and the standard against which Mary’s age is judged in (6) correspond to indexical elements not in the overt syntax, but in the covert syntax of (5) and (6).

Where does this idea leave us? It still undermines a strict reading of compositionality_TC, on which every element of full truth-conditional content must be determined compositionally. But maybe we can save the spirit of compositionality_TC by introducing a level of representation intermediate between linguistic meaning and truth-conditional content, a level at which compositionality can hold. Following a comment by Neale (1999), I shall call this level propositional form and character. Corresponding to this level of representation is a further version of the principle of compositionality:

Compositionality_FC: the form and character of the proposition expressed by (an utterance of) a sentence is determined by the linguistic meanings of its component parts and their syntactic combination.

It seems to me that this version of the principle of compositionality is, either tacitly or overtly, gaining increasing acceptance within the truth-conditional tradition. However, there is a certain amount of convincing evidence that even this version of compositionality is too strong. To take one example, Carston (forthcoming) has shown that the temporal, causal and other elements standardly associated with ‘and’-conjunction appear in truth-conditional content, although apparently unrepresented at any syntactic level, overt or covert. Consider the following sentences:

In (7), ‘and’ seems to be operating truth-functionally: so long as each conjunct is true, the whole sentence will be true. In (8), however, there is something else going on: both temporal sequencing and causation appear in what is communicated by an utterance of (8): what is communicated is something like Mary put a blanket over Tom’s face and then, because Mary put a blanket over his face, Tom died of suffocation. But do these elements appear in the truth-conditional content of an utterance of (8), or is the truth-conditional content restricted to a straightforwardly truth-functional conjunction, with the temporal and causal elements appearing merely in some further, implicated proposition? We can deploy a now familiar test, first used by Cohen (1971), to show that they are, in fact, truth-conditional. Consider (9) and (10):

(9) If Mary put a blanket over Tom’s face and Tom died of suffocation, then Mary will go to prison.

(10) If Tom died of suffocation and Mary put a blanket over Tom’s face, then Mary will go to prison.

If the conjunction in (8) were indeed truth-functional, then (9) and (10) would have to share a truth value, since the only difference between them is that the order of the conjuncts has been reversed. But that isn’t so: it’s possible to imagine situations in which (9) and (10) would have different truth-values. And the only explanation for this is that temporal and causal elements are entering into the truth-conditional content.

But maybe this is just more of the same; maybe, in other words, part of the meaning of ‘and’ is a covert indexical element, over and above its truth-functional meaning. There are good reasons to think this can’t be right. One of the characteristic properties, for instance, of overt indexicals, is that a hearer who fails to assign reference to an overt indexical fails to grasp full propositional content. But consider the example in (7): no reference has been assigned to the covert indexical, if there is one, and yet what is expressed by an utterance of (7) will be fully propositional.

It seems, then, that, in the case of ‘and’-conjunction, pragmatic inference can alter the form and character of truth-conditional content: it can make the difference between the truth-functional A & B, and something more like A, and, because of A, B, propositions which are surely not of the same form and character. This evidence, amongst much else that there is not the space to go into here, seems strongly to suggest that compositionality_FC is also too strong a formulation of the principle of compositionality: even the form and character of the proposition expressed by an utterance is not fully determined by lexical semantics plus syntax.

We are left, then, with only one level at which compositionality can hold, the level of linguistic meaning. This conclusion immediately gives rise to three questions: firstly, is it plausible that linguistic meaning is indeed compositional? Secondly, if so, what kind of picture of language and meaning does it suggest? And thirdly, is compositionality_LM enough? Does it satisfy the data with which we initially motivated compositionality as a constraint on semantic theory?

I don’t intend to spend much time answering the first of these questions: I’m sure not many would doubt the compositionality of linguistic meaning. The problem for the truth-conditionalist is not that it is wrong to say that linguistic meaning is compositional, but rather that it is not enough. If compositionality_LM is the only version of compositionality which holds, then the project of tackling linguistic meaning via truth conditions is undermined, since the structure of the proposition which constitutes the interpretation of an utterance of a sentence, and which is the real bearer of truth, no longer need mirror the structure of the sentence itself.

I’m not sure how worried we should be by this conclusion: the conception of meaning which it gives rise to offers some interesting analyses of traditionally problematic semantic phenomena. But what conception is that? The story that I would advocate looks something like this: the linguistic meaning of a sentence, which is compositionally determined by the lexical items in the sentence and their syntactic combination, falls far short of determining the proposition which will be expressed by an utterance of the sentence in a particular context. The gap between linguistic meaning and truth-conditional content is bridged by inference, inference which is guided by a combination of context and pragmatic principles. On this picture an account of linguistic meaning cannot be directly given via the notion of truth conditions; instead, the relation between language and world must crucially be viewed as a chain with two links. Let me give just one illustration of why this is so.

Much attention has been given within the philosophy of language, in particular over the last thirty-five years or so, to the interpretation of definite descriptions. Do descriptions have two uses, the so-called referential and attributive uses of Donnellan (1966)? If so, are these uses truth-conditional? And, if they are, does that entail that definite descriptions are lexically ambiguous? I believe there is much evidence in favour of the claim that referential and attributive uses are truth-conditionally distinct; interestingly Stephen Neale, one of the staunchest opponents of this view[2], has recently come to accept that there is a truth-conditional distinction[3]. But surely there is also good evidence to suggest that definite descriptions are not lexically ambiguous: they would, for instance, given referential uses, attributive uses, generic uses, functional uses, specific uses and so on, have to be many-ways ambiguous; and, in addition, the same purported ambiguity seems to carry over into languages other than English, at least an unusual state of affairs for a genuine semantic ambiguity.

If, however, we accept, as I believe we must given the evidence above, that pragmatic inference plays a crucial part in determining the truth-conditional content of an utterance, then a natural account of the referential-attributive distinction emerges. Definite descriptions are indeed univocal, encoding a constraint on the hearer’s interpretive process; in very rough terms, ‘the F’ will constrain interpretation to an individual conceptual representation, specifically to an individual conceptual representation associated in the appropriate way with the concept ‘F’, what I shall call an ‘F’-concept. Which ‘F’-concept the hearer will access will be a matter of context and pragmatic inference. Given, however, the different kinds of relations that can hold between individual conceptual representations and the world, the ‘F’-concept retrieved may make a number of different kinds of contribution to truth-conditional content. It may, for instance, be causally linked to the object that falls within its denotation in the way appropriate for de re thought, or it may simply represent its denotation descriptively. If the hearer is intended to access an ‘F’-concept of the former sort, then the utterance will have a singular truth condition; if he’s intended to access a concept of the latter sort, then it will have a general truth condition. On this type of account, although the truth-conditional content of an utterance of a description sentence may differ according to context, the encoded meaning of a definite description is entirely blind to this difference.

Finally, I want to answer the third of the questions I set earlier: is compositionality_LM enough? Does it satisfy the considerations which led us initially to accept compositionality as a necessary constraint on semantic theory? The first of those considerations concerned the systematic contribution made by lexical items to the meanings of the sentences in which they appear. On the account sketched above, lexical items do, indeed, make a systematic contribution to sentence meaning, although not necessarily to propositional content. But would we want them to do so? Consider the following two sentences, the latter a standard example of metonymy:

While we are certainly going to want to say that the description ‘the mushroom omelette’ has the same meaning in both contexts, this intuition must operate at the level of linguistic meaning rather than truth-conditional content: we certainly don’t want to say that ‘the mushroom omelette’ makes the same contribution to truth conditions in both contexts.

Since the remaining considerations which led us to accept compositionality are so closely related, I propose to address them together. Without compositionality, so the argument went, it would be impossible to explain how native speakers of a natural language can learn and understand the meanings of an infinite number of novel sentences of their language. Will compositionality_LM account for this data? It has no difficulty in so doing: on the picture I have painted, grasping the truth-conditional content of an utterance of a sentence involves two processes: linguistic decoding and pragmatic inference. The process of decoding involves compositionally building up the linguistic meaning of a sentence from the linguistic meanings of its parts and their syntactic combination, and is thus, given the recursive nature of syntactic and combinatorial rules, able to deliver an infinite number of novel semantic representations. Once this is done, the rest is down to a pragmatic machinery, which is antecedently motivated by, among other phenomena, the retrieval of implicatures. Compositionality_LM thus does all the work we need from the principle of compositionality.

Carston, R. 1988. Implicature, Explicature and truth-Theoretic Semantics. In R. Kempson (ed.) Mental Representations: the interface between language and reality. 155-181. Cambridge: Cambridge University Press.

Carston, R. (forthcoming). Thoughts and Utterances: The Pragmatics of Explicit Communication. Oxford: Blackwell.

Cohen, L.J. 1971. Some remarks on Grice’s views about the logical particles of natural language. In Y. Bar-Hillel (ed.) Pragmatics of Natural Language. Dordrecht: Reidel

Donnellan, K. 1966. Reference and Definite Description. The Philosophical Review 75, 281-304.

Larson, R and G. Segal. 1995. Knowledge of Meaning: An Introduction to Semantic Theory. Cambridge: MIT Press.

Miller, A. 1997. Tacit Knowledge. In Hale, B. and C. Wright (eds.) A Companion to the Philosophy of Language. Oxford: Blackwell.

Neale, S. 1999. Coloring and Composition. In K. Murasugi and R. Stainton (eds.), Philosophy and Linguistics, 35-82. Boulder: Westview.

[1] See, for instance, Larson and Segal (1995), Wright (1986) and Miller (1997) for different presentations of these ideas.

[2] See Neale (1990).

[3] See Neale (1999).