1 Zimmermann, Formal Semantics 1. Compositionality 1.1Frege’s Principle Any decent language, whether natural or artificial, contains more than just finitely many expressions. In order to learn and understand all these expressions, i.e. to associate a meaning with each of them, it does not suffice to learn just a vocabulary list: there must be some systematic way of associating meanings with forms – just like there is a systematic way of construing these forms, viz. syntactic rules. Indeed, it seems plausible to assume that there is some connection between the rules that govern what an expression is and those that say what it means. An initially plausible assumption on how this connection is made is a principle that has been attributed to Frege but which, for reasons of philological accuracy, should perhaps better be called by some neutral term like: The Principle of Compositionality The meaning of an expression is uniquely determined by the meanings of its parts and their mode of combination. Something should be said about the meanings of the expressions used in stating this principle. As it stands, the principle presupposes some part/whole relation among linguistic expressions. It should be clear that this must be provided by some syntactic account of the language in question. Thus, e.g., under a straightforward constituent analysis the sentence (1) contains (2), but certainly not (3) as a part, even though (1) does contain the former in some other, ‘physical’ sense: (1) Whenever Tom sees a lollipop he wants to eat it. (2) Tom sees a lollipop. (3) Tom sees a lollipop he wants to eat. More complicated part/whole relations may arise out of more involved syntactic descriptions. It may thus not be entirely implausible to engage some transformational analysis that partly reduces (1) to something like (4), which would then, in a sense, be a part of (1): (4) Tom wants to eat the lollipop. We do not seriously want to defend any such analysis but merely point out that the notion of a part of an expression is not as innocent and 2 Zimmermann, Formal Semantics straightforward as it may appear from the above formulation of Frege’s Principle. A second possible misunderstanding of the Principle of Compositionality concerns ambiguous expressions like the following two: (5) Linguists discovered a hidden ambiguity resolution method. (6) Not all rulers are straight. Since (5) has more than one meaning, we cannot expect ‘it’ to be (uniquely) determined by whatever the principle assumes. So we must either put the whole principle in the plural, or exclude ambiguous ex- pressions, or understand ‘expressions’ to refer to underlying (syntactic) structures which we may assume to be unambiguous. We take the third option, extending it even to clear cases of lexical ambiguity which we also assume to be resolved on some syntactic level at which, e.g., sub- scripts distinguish at least two different nouns ruler. A third source of possible unclarity is a meaning’s being uniquely de- termined by something else. In the present context, this should be taken in the weakest sense possible, viz. as functional dependence: the meaning of the whole is uniquely determined by the meanings of the parts if there is a function taking the meanings of the parts as its arguments and yielding the meanings of complex expressions as its values. Whether and in what sense this function is known to the language users and how complex it is (whether it is recursive etc.) will be of no concern to us here. If we know all parts of a complex expression and at the same time know how they combine, we know the expression itself. Given this reasoning, it might appear that the Principle of Compositionality applies vacuously: the parts of an expression and the way they are combined determine the expression which in turn determines its meaning in the weak sense that the latter is unique. However, Frege’s Principle is stronger than that. For it is not the parts themselves that we have to combine but their meanings. In order to see the exact meaning of this, consider two distinct expressions the corresponding parts of which have the same meanings: (7) My brother, who lives in Aachen, is an oculist. (8) My brother, who dwells in Aix-la-Chappelle, is an eye-doctor. Let us, for the purpose of this discussion, imagine that each word in (7) 3 Zimmermann, Formal Semantics has exactly the same meaning as the corresponding word in (8). Since the way the words are combined in these two sentences is obviously the same, the Principle of Compositionality immediately implies that (7) and (8) must have the same meaning. Clearly, this is a non-trivial claim. Not trivial, but not very exciting either; for all it says is that replacing one or more words (ultimate constituents) by synonyms results in a synonymous complex expression. And it is easily seen that this is the only kind of prediction one gets by literally applying Frege’s Principle. However, there is a different reading of the term parts that leads to a considerable strengthening of the principle: if by a part of an expression we mean an immediate part of it, we get slightly more substantial claims about synonymies. From the (assumed) synonymy of the noun phrases Tom and everyone who is identical with Tom we may, e.g., conclude that (9) and (10) must have the same meaning: (9) Tom is asleep. (10) Everyone who is identical with Tom is asleep. At least under a straightforward analysis, the immediate parts of (9) are the subject Tom and the predicate is asleep; those of (10) are the subject everyone who is identical with Tom and the same predicate as in (9). Since the subjects are supposed to be synonymous and the predicates are anyway, Frege’s Principle implies that so are the sentences. But it should be noted that this implication only holds under the strong read- ing of ‘part’ as ‘immediate part’; otherwise the internal combination of the lexical material in (9) and (10) would make the principle in- applicable. A generalization of this kind of argument reveals an important im- plication of Frege’s Principle, viz. the Substitutivity of Synonyms: re- placing one part of an expression by a synonymous one results in a synonymous expression. (9) vs. (10) is already an example and by em- bedding it we see the validity of the general principle: (11) Alain erroneously believes that Tom is asleep. (12) Alain erroneously believes that everyone who is identical with Tom is asleep. Having established the synonymy of (9) and (10) we can now go on like this: since (9) is an immediate part of that Tom is asleep and (10) is an immediate part of that everyone who is identical with Tom is asleep, the two that-clauses must be synonymous, again by the Principle of Com- positionality. Moreover, the complex verb erroneously believes is clearly 4 Zimmermann, Formal Semantics synonymous with itself and, once more, combining it with either that Tom is asleep or the synonymous that everyone who is identical with Tom is asleep must result in two synonymous verb phrases. One more step like that and we’re home; we leave it to the reader. The general con- clusion to be drawn from this is that the Principle of Compositionality implies: The Substitution Principle Synonymous parts may be substituted for each other without changing the meaning of the complex expression in which they occur. The Substitution Principle will prove to be helpful in evaluating Frege’s Principle. However, it must be kept in mind that any apparent counter- instance to the Substitution Principle does not necessarily constitute an argument against compositionality but may equally well serve as evidence against one of its underlying assumptions like, e.g., a certain syntactic analysis or the notion of meaning involved. Concerning the latter, we will gradually see that the Principle of Compositionality can be regarded as a restriction on what meanings are; some simplistic con- cepts of meaning are incompatible with Frege’s Principle. Before looking at specific examples and counter-examples, we must finally get clear about the status of the Principle of Compositionality: is it an empirical hypothesis, a methodological assumption, or what? This depends on how exactly we want to understand it. On one, rather strong reading the principle says that the only (empirically correct) way of assigning meanings to complex expressions is compositional. It turns out that this reading of the principle immediately leads to problems: as we will see in section 1.3, a very straightforward interpretation of predicate logic is non-compositional and it is not unlikely that the characteristic features responsible for this failure carry over to natural language. So we will not favour an empirical reading of Frege’s Principle but rather a weaker, methodological one: a compositional (and empirically correct) way of assigning meanings to expressions is to be preferred to its non-compositional rivals. Since it can be shown that, under reasonable assumptions, there is always some (empirically cor- rect) compositional way of assigning meanings to complex expressions, the Principle has a universal applicability. But why should we adopt it? Because it teaches us something about the complexity of meaning. This will best be understood from some standard examples to which we will now turn. 5 Zimmermann, Formal Semantics 1.2Compositional meaning assignments: some examples In order to get some feeling for the content of Frege’s Principle, let us first look at some cases in which it clearly applies. The easiest one is a traditional analysis of meanings in terms of semantic features or com- ponents.