Principle of Compositionality

The principle of compositionality holds that the meaning of a complex expression is determined by the meanings of its constituents and the way they are combined.

Definition

Compositionality is the principle that the meaning of a complex expression is a function of the meanings of its parts and of the syntactic rules used to combine them.

Scope

This topic covers the formulation, motivation, and limits of the compositionality principle. It treats the arguments for compositionality from productivity and systematicity (our ability to understand and produce indefinitely many novel sentences), formal statements of the principle as a homomorphism from syntax to semantics, and apparent counterexamples such as idioms, propositional-attitude contexts, and quantifier scope that have prompted refinements of the principle.

Core questions

• What exactly does compositionality claim, and how can it be stated formally?
• What evidence (productivity, systematicity) supports it?
• Do idioms, attitude reports, or context-dependence threaten compositionality?
• Is compositionality an empirical hypothesis or a methodological assumption?

Key concepts

• productivity
• systematicity
• homomorphism (syntax to semantics)
• rule-by-rule interpretation
• idioms as challenges
• substitutivity

Key theories

Compositionality as syntax-to-semantics homomorphism

Compositionality is made precise by requiring the meaning assignment to be a homomorphism from the algebra of syntactic expressions to an algebra of meanings, so combination in syntax mirrors combination in semantics.

Productivity and systematicity arguments

Speakers understand indefinitely many novel sentences and exhibit systematic patterns of comprehension, which is best explained if meaning is built compositionally from a finite stock of word meanings and rules.

History

Compositionality is traditionally attributed to Frege, though its explicit attribution is debated. It became a guiding methodological principle of formal semantics through Montague's work and was given algebraic formulations by Partee and others, who also clarified how phenomena like idioms and attitude contexts can be accommodated without abandoning the principle.

Debates

Whether compositionality is substantive or trivial

Critics argue that, without constraints on meanings and rules, compositionality can always be satisfied and is therefore empirically empty; defenders argue that natural constraints make it a contentful and testable hypothesis.

Key figures

• Gottlob Frege
• Barbara Partee
• Zoltan Gendler Szabo

Seminal works

• partee1984
• szabosep2022

Frequently asked questions

Do idioms violate compositionality?

Idioms like 'kick the bucket' appear non-compositional because their meaning is not built from their parts, but they are usually treated as single lexical units whose meaning is stored as a whole, so they do not refute compositionality for the rest of the language.