Michael Johnson

1

Compositionality

Michael Johnson

Lingnan University

1. Introduction

A symbolic system is compositional if the meaning of every complex expression E in that systemdepends on (and depends only on) (i) E’s syntactic structure and (ii) the meanings of E’s simple parts. If a language is compositional, then the meaning of a sentence S in that language cannot depend on the prior discourse, speaker intentions, salient objects and events in the environment, or the non-semantic character of S’s simple parts, such as their shape or sound. It can only depend on the meanings of the words composing S, and the way those words are syntactically related to one another.

Several arguments purport to show that not only is natural language compositional, but that it must be, since we could not have the linguistic abilities we in fact do have, unless the languages we speak are compositional. A commitment to compositionality has driven a large amount of research in the philosophy of language and in linguistics, since it appears to be very difficult to provide adequate compositional treatments of commonplace linguistic constructions, especially propositional attitude ascriptions. On the other hand, some philosophers have argued that natural language is not compositional, or that compositionality induces no substantive restriction on possible theories of meaning.

This article addresses the different ways compositionality has been understood by philosophers and linguists, and surveys the arguments that natural language is, must be, or should be compositional, as well as the arguments that it isn’t or needn’t be.

2. Interpretations of Compositionality for Natural Language

2.1 Syntactic Structure

In natural languages (like English, Cantonese, Kalaallisut, etc.), the smallest meaningful symbols are called “morphemes.” For highly analytic languages like English, there is a large overlap between morphemes and words: words are largely the smallest meaningful units. (English does have a number of morphemes that are not words, however, like the plural ending –sfor nouns, the possessive ending –’sfor noun phrases, and the 3rd person singular ending –s for verbs. These are “bound” morphemes, in that they cannot grammatically occur on their own.) In other, more synthetic languages (like Kalaallisut), single words can be made of many meaningful parts. For example, the word atuartariaqalirpuq (“he began to have to study”) contains six morphemes, and can be used by itself as a sentence. [Example from Bittner 1995.]

‘Morphology’ is the set of rules governing how morphemes are combined to form words; ‘syntax’ is the set of rules governing how words are combined to form phrases and, ultimately, sentences. These rules describe (among other things) how smaller parts are put together to form larger units called “constituents.” The syntactic rules that formed an expression can affect its meaning. Consider the expression ‘large horse painting’: it can either mean painting of a large horse or large painting of a horse, depending on whether ‘large’ is modifying ‘horse painting’ or just ‘horse.’

The principal claim regarding compositionality that philosophers have been concerned with is the claim that all actual and possible natural languages are compositional. A natural language is a language that humans learn to speak naturally, as part of their development, as opposed to an artificial language like computer languages. In this context, the claim that natural languages are compositional amounts to the claim that the meanings of complex (multi-morphemic) expressions are determined by and only by (i) the ways their morphemes are put together by the morphosyntactic rules of the language and (ii) the meanings of those morphemes.

This may seem like a clear statement of a single thesis, but unfortunately there is wide philosophical disagreement concerning (a) what meanings are and (b) how we should understand ‘dependence’ in the statement of compositionality. We turn now to these two issues.

2.2 Meaning

There are two ways in which there are a wide variety of meanings of ‘meaning.’ First, many different philosophers will use the word ‘meaning’ and understand by it various distinct things. Some will think meanings are conceptual roles; others that they are set theoretic objects and functions. Second, one and the same philosopher may recognize several types or dimensions of meaning. She may think, for example, that connotations are meanings in one sense, and that denotations are meanings in a different sense. In discussing compositionality, a reasonable stance is to consider all proposed types of meanings as bona fide meanings and therefore understand that there are numerous compositionality theses. For example:

Compositionality of stereotype: the stereotype associated with a complex expression E in a natural language is determined by (and only by) (i) E’s morphosyntactic structure and (ii) the stereotypes associated with E’s morphemes.

Compositionality of semantic features: the semantic features (e.g. [+male] or [+animate], as they attach to ‘he’ and ‘who,’ respectively) of a complex expression E in a natural language is determined by (and only by) (i) E’s morphosyntactic structure and (ii) the semantic features of E’s morphemes.

And so on, for each possible type or dimension of meaning. The philosophical question is which, if any, of these theses is true. Any argument for or against compositionality should make it clear what conception of meaning it takes to be or not to be compositional. It is quite possible that there are several legitimate conceptions of meaning, each deserving the name ‘meaning,’ where on some of those conceptions, natural languages are compositional, and on other of those conceptions, they are not.

The question that has perhaps most concerned philosophers interested in compositionality is whether the truth-conditions of a sentence depend on (and only on) its syntax and the meanings of its simple parts. The truth-conditions of a sentence are simply the conditions under which the sentence is true. The truth-conditions of a sentence do not depend only on its syntax and the meanings of its simple parts if some sentences with the same syntax and the same meanings assigned to their parts are true, and other sentences with the same syntax and the same meanings assigned to their parts are false. For example, we will later consider sentences like ‘It is midnight.’ Sometimes this sentence is true, but other times—apparently without a change in the meanings of the words or in the way they are combined—it is false. This is an apparent violation of the compositionality of truth-conditions.

2.3 Dependence

Dependence and determination are common and vital notions in philosophy, though they are in many ways ambiguous. Sometimes dependence is a functional notion, as in: “the signs of two numbers determine the sign of their product (the sign of their product depends on their signs).” Dependence can also be a causal notion, as in: “the success of our movie depended on our advertising campaign.” It can be a constitutive notion, as in: “whether I win depends on whether I get a card lower than 4.” There are many ways the notion of dependence has been understood with regard to the compositionality thesis.

2.3.1 Functional Dependence

One way of understanding the sense in which the meaning of the whole, according to compositionality, “depends on” the meanings of the parts, and the way those parts are combined, is reading “depends on” as “is a function of.” That is, a symbolic system is compositional if, and only if, the meaning of each complex expression E in that system is a function of (a) E’s syntactic structure and (b) the meanings of E’s simple parts.

Let the meaning function be designated M. The functional conception of compositionality says that M’s outputs only differ when M’s arguments differ in either (a) their syntactic structure or (b) the meanings of their simple parts. Thus M(E) and M(E*) will be identical whenever E and E* differ only in the substitution of simple parts that are synonymous. (For example, “Fred sweats” and “Fred perspires” must be assigned the same meanings if “sweats” and “perspires” are assigned the same meanings.) The functional conception of compositionality is equivalent to the substitutional conception of compositionality: a symbolic system is compositional if, and only if, for any two complex expressions E and E* in that system, where E contains simple part P and E* is identical to E except in containing simple part P* where E contains P: if P and P* have the same meanings, then E and E* have the same meanings.

While the functional conception of compositionality is easy to characterize and understand, it fails to capture the full force of the constraint many philosophers have thought compositionality imposes upon semantic theories for natural languages. This is because many semantic theories which are not compositional intuitively are compositional in the functional sense.

One way to see this is by noting that any symbolic system that contains no synonyms is compositional in the functional sense. If a symbolic system contains no synonyms, the meaning function for that language can’t treat two expressions differing only in the substitution of synonyms differently (because there are no such expressions). Thus for any expression E of S, there is a function F that takes E’s syntactic structure and the meanings of E’s parts as inputs and returns the meaning of E as output. This entails that a non-compositional language could be made compositional solely by removing a few redundant expressions (synonyms of other expressions in the language).

Second, the functional conception of compositionality does not demand any particular relatedness among the meanings of related expressions. The functional conception requires only that the meaning function not assign different meanings to expressions that differ only in the substitution of synonyms. It does not require that the meanings it does assign to complex expressions be in any natural way related to the meanings of their parts, or to the meanings of other complex expressions composed of similar parts.

For example, consider these meaning assignments:

Le chien aboie.The dog barks.

Le chat aboie.The cat dances.

Le chat pue. The skunk eats.

Sentences (1) and (2) share a verb, but nothing about their assigned meanings are similar; (2) and (3) share a noun phrase, but again nothing about their assigned meanings is similar. Nevertheless, there exists a function that takes the syntax, and the meanings of the morphemes, of each expression on the left, and maps it to the meaning on the right: it’s displayed in (1)-(3). In fact, any random, unsystematic assignment of meanings to sentences is compatible with the functional conception of compositionality, provided that either there are no synonyms or that sentences that differ only in the substitution of synonyms are assigned the same meaning. This is ‘dependence’ only in the weakest sense of that word.

2.3.2 Dependence as Computability

As we shall see, the principal historical reason for the belief that natural languages are compositional is that only compositionality can explain how we can figure out the meanings of a potential infinitude of expressions given our finite memories and capacities. Compositionality, on this conception, says that if you know the syntactic structure of an expression E, and you know the meanings of E’s simple parts, this suffices for you to “work out” the meaning of E: there exists a procedure that you can use, which after a finite number of steps, tells you the meaning of E itself. In other words, the meaning of any expression E is computable from (a) E’s syntactic structure and (b) the meanings of E’s simple parts.

If the meaning of any expression E is computable from E’s syntactic structure and the meanings of E’s simple parts, then it is a function of E’s syntactic structure and the meanings of E’s simple parts. But the converse is not true, for not every function is computable.

While computability imposes some standard of systematicity in meaning assignments, it nevertheless allows more freedom than we might wish. Consider how different programs running on your computer produce wildly different outputs, even given the same sequence of keystrokes. The outputs of the programs are computed from the keystrokes, but they process that information in radically different ways, and produce outputs of radically different characters. The keys I used to type the previous sentence in a word processer might result in a complicated series of moves if typed in a fantasy role-playing game. The computability conception of compositionality says that the transition from the syntax of a complex expression and the meanings of its parts to the meaning of that expression must be a function of the syntax and the meanings of the parts, and that it must be rule-governed; but it doesn’t say anything about what the rules are or can be, except that they can be carried out in a finite number of steps.

2.3.3 Dependence as Supervenience

Suppose language L1 contains a complex expression E1 and language L2 contains a complex expression E2. E1 and E2 are similar in the following way: each expression in E1 has a counterpart in E2 that means the same thing, and those expressions are combined in exactly the same way in E1 as they are in E2. The supervenience conception of compositionality says that in any such situation E1 and E2 must have the same meaning.

For example, the supervenience conception would say: if the French words ‘le,’ ‘chien,’ and ‘aboie’ have the same meanings as the English words ‘the,’ ‘dog,’ and ‘barks,’ and the French sentence ‘Le chien aboie’ has the same syntax as the English sentence ‘The dog barks, then ‘Le chien aboie’ and ‘The dog barks’ must have the same meaning.

The thesis that the meaning of a complex expression E supervenes on its syntax and the meanings of its simple parts entails the thesis that E’s meaning is a function of its syntax and the meanings of its simple parts, but not the thesis that E’s meaning is computable from its syntax and the meanings of its simple parts. However, the supervenience thesis is consistent with the computability thesis, and they may well both be true.

Whether supervenience is an adequate characterization of dependence for the purposes of compositionality is unclear. It allows non-computable meaning functions, and it allows unsystematic meaning assignments—provided every language has the same unsystematic assignments. Computability and systematicity are properties that many philosophers believe natural languages satisfy, but perhaps they are independent of compositionality.

2.3.4Dependence as Mereology

The functional and computational conceptions of dependence, with regard to the thesis that natural languages are compositional, are seemingly weaker than the pre-theoretical conception of dependence that occurs in the thesis itself. There is another conception of dependence in the literature that can reasonably characterized as too strong (though it is not necessarily false that languages are compositional in this sense).

On this conception, the meanings of the parts of a complex expression are literally part of the meaning of that expression. To see how this could be, consider the view that the meaning of a sentence is a structured proposition. The French sentence [[le chien] aboie]—where bracketing indicates syntactic structure—means a structured proposition like <the dogbarks>-- where the italicized words stand here for the meanings of ‘le,’ ‘chien,’ and ‘aboie,’ respectively. On this view, the meaning of ‘chien,’ for example, is literally a part of the meaning of ‘le chien aboie.’

This notion of dependence is quite strong: the meaning of a complex expression is made out of its syntactic structure and the meanings of its parts. And while many theories of the meanings of complex expressions, like the structured propositions theory, validate the principle of compositionality as interpreted with the mereological conception of dependence, it should be clear that this is more than what philosophers normally mean when they say natural languages are compositional.

2.3.5 The Empirical Conception of Dependence

Finally, it’s possible to define compositionality in terms of the role that it plays in explaining certain of our linguistic abilities. In particular, many philosophers have thought that unless the meanings of complex expressions in natural languages depend on (and depend only on) (a) the syntax of those expressions and (b) the meanings of those expressions’ parts, we would not be able to learn and understand the languages we in fact learn and understand. Thus we can understand “dependence” here as whatever relation in fact obtains between the meaning of a complex expression and that expression’s syntax and the meanings of its parts that in fact explains our ability to learn and understand a language containing an infinitude of such expressions. We know that language is compositional, but it is an empirical question as to just what compositionality consists in.

The empirical conception of compositionality need not be thought of as a competitor to the alternative conceptions considered above. Instead, it provides a methodological backdrop against which we can evaluate various proposals regarding the sense of “dependence” at the heart of compositionality. As we saw, the functional conception of dependence is ill-favored precisely because it fails to explain our abilities to learn and understand the natural languages we speak. Any proposed account of compositionality not only has to meet certain internal criteria, like clarity and consistency, but it also has to (a) actually be true of the languages we speak and (b) actually explain our abilities to learn and understand those languages.

There is of course the possibility that no dependence relation that obtains only between the meanings of complex natural language expressions and their syntax and the meanings of their simple parts plays a discernible role in our linguistic abilities. Perhaps the meanings of complex expressions are partly determined by prior discourse, speaker intentions, salient objects and events in the environment, or the non-semantic character of those expressions’ simple parts, such as their shape or sound. In such an event, it might turn out not just that natural languages are not compositional, but that “compositionality” is without application, its introduction having rested on a false presupposition.

3. Compositionality and Thought

According to the language of thought hypothesis (LOT), mental representations have a syntactic structure comparable to natural language expressions and expressions of artificial computing languages. In particular, according to LOT, there is a distinct category of simple mental representations (containing no meaningful parts), and these simple representations are combined in rule-governed hierarchical structures to form complex mental representations. We can thus ask whether thought is compositional, that is, whether the meanings of complex mental representations depend on (and only on) (a) their syntactic structures and (b) the meanings of the simple mental representations that are their parts.