语言学

When compositionality does awry

In mathematics, semanticsand philosophy of language, The principle

of compositionality is the principle that the meaning of a complex

expression is determined by the meanings of its constituent expressions

and the rules used to combine them. This principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the idea appears already among Indian

Philosophers,of.grammar such as Yāska, and also in Plato's work.

Besides, the principle was never explicitly stated by Frege,and it was arguably already assumed by Boole decades before Frege’s work.

It is frequently taken to mean that every operation of the syntax should be associated with an operation of the semantics that acts on the meanings of the constituents combined by the syntactic operation. As a guideline for

constructing semantic theories, this is generally taken, as in the influential work on the philosophy of language by Donald Davidson, to mean that every construct of the syntax should be associated by a clause of the

T-schema with an operator in the semantics that specifies how the meaning of the whole expression is built from constituents combined by the

syntactic rule. In some general mathematical theories (especially those in

the tradition of Montague grammar), this guideline is taken to mean that

the interpretation of a language is essentially given by a homomorphism

between an algebra of syntactic representations and an algebra of

semantic objects.The principle of compositionality also exists in a similar form in the compositionality of programming languages.

Over the last few years, we have just aboutconvinced ourselves that

compositionality is the sovereign test fortheories of lexical meaning.So

hard is this test to pass, we think,that it filters out practically all of the

theories of lexical meaningthat are current in either philosophy or

cognitive science. Amongthe casualties are, for example, the theory that

lexical meaningsare statistical structures (like stereotypes); the theory that

themeaning of a word is its use; the theory that knowing the mean-ing of

(at least some) words requires having a recognitionalcapacity for (at least

some) of the things that it applies to; and thetheory that knowing the

meaning of a word requires knowingcriteria for applying it. Indeed, we think that only two theories ofthe lexicon survive the compositionality

constraint: viz., thetheory that all lexical meanings are primitive and the

theory thatsome lexical meanings are primitive and the rest are

definitions.So compositionality does a lot of work in lexical

semantics,according to our lights

Well, so imagine our consternation and surprise when, havingjust

about convinced ourselves of all this, we heard that PaulHorwich has on

offer a ‘deflationary’ account of compositionality,according to which, ‘. . .

the compositionality of meaning imposesno constraint at all on how the

meaning properties of words areconstituted’Surely, we thought, that

can’tbe right; surely compositionality must rule out at least some

theo-ries about what word meanings are; for example, the theory thatthey

are rocks, or that they are sparrows or chairs; for how couldthe meanings

of complex expressions be constructed from any ofthose? What, we

wondered, is going on here?.

We have arrived at a tentative diagnosis, which is thatHorwich fails

to enforce several distinctions that turn out to becrucial. For example,

sometimes he puts his main conclusion inthe way we quoted above: ‘the

compositionality of meaningimposes no constraint at all on how the

meaning properties ofwords are constituted’. But sometimes, even on the

followingpage, he puts it like this: ‘understanding one of one’s own

complex expressions (non-idiomatically) is, by definition, noth-ing over

and above understanding its parts and knowing howthey are combined’.

Now, prima facie, these wouldn’tseem to be at all the same theses.

Whereas the first purports toanswer a question about the metaphysics of

meaning, viz., ‘Whatlinguistic facts about a complex expression are the

superve-nience base for its meaning properties?’,the second purports

toanswer a question about the metaphysics of understanding, viz.,‘What

makes it true of a speaker that he understands an expres-sion in his

language?’

The point we want to emphasize, however, is not that the

reversecompositionality argument against stereotypes as lexical

meaningsis correct. Our point is that people who think itmatters to the

lexicon whether complex meanings are composi-tional have it in mind to