Principle of compositionality
Encyclopedia
In mathematics
, semantics
, and 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 India
n philosophers of grammar such as Yāska
, and also in Plato
's work such as in Theaetetus
.
The principle of compositionality states that in a meaningful sentence, if the lexical parts are taken out of the sentence, what remains will be the rules of composition. Take, for example, the sentence "Socrates was a man". Once the meaningful lexical items are taken away"Socrates" and "man"what is left is the pseudo-sentence, "S was a M". The task becomes a matter of describing what the connection is between S and M.
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.
Scholars are also divided as to whether the principle should be regarded as a factual claim, open to empirical
testing; an analytic truth, obvious from the nature of language and meaning; or a methodological
principle to guide the development of theories of syntax and semantics. The principle has been attacked in all three spheres, although so far none of the criticisms brought against it have been generally regarded as compelling. Most proponents of the principle, however, make certain exceptions for idiomatic expressions in natural language.
Further, in the context of the philosophy of language, the principle of compositionality does not explain all of meaning. For example, you cannot infer sarcasm
purely on the basis of words and their composition, yet a phrase used sarcastically means something completely different from the same phrase uttered straightforwardly. The principle of compositionality, then, has to be revised to take into account linguistic and extralinguistic context
, which includes the tone of voice used, common ground between the speakers, the intentions of the speaker, and so on.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
, and philosophy of language
Philosophy of language
Philosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for analytic philosophers is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship between 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
Gottlob Frege
Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
is widely credited for the first modern formulation of it. However, the idea appears already among India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
n philosophers of grammar such as Yāska
Yaska
' ) was a Sanskrit grammarian who preceded Pāṇini , assumed to have been active in the 5th or 6th century BC.He is the author of the Nirukta, a technical treatise on etymology, lexical category and the semantics of words...
, and also in Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
's work such as in Theaetetus
Theaetetus (dialogue)
The Theaetetus is one of Plato's dialogues concerning the nature of knowledge. The framing of the dialogue begins when Euclides tells his friend Terpsion that he had written a book many years ago based on what Socrates had told him of a conversation he'd had with Theaetetus when Theaetetus was...
.
The principle of compositionality states that in a meaningful sentence, if the lexical parts are taken out of the sentence, what remains will be the rules of composition. Take, for example, the sentence "Socrates was a man". Once the meaningful lexical items are taken away"Socrates" and "man"what is left is the pseudo-sentence, "S was a M". The task becomes a matter of describing what the connection is between S and M.
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
Donald Davidson (philosopher)
Donald Herbert Davidson was an American philosopher born in Springfield, Massachusetts, who served as Slusser Professor of Philosophy at the University of California, Berkeley from 1981 to 2003 after having also held teaching appointments at Stanford University, Rockefeller University, Princeton...
, to mean that every construct of the syntax
Syntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....
should be associated by a clause of the T-schema
T-schema
The T-schema or truth schema is used to give an inductive definition of truth which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth...
with an operator in the semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
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
Montague grammar
Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on formal logic, especially higher order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models...
) this guideline is taken to mean that the interpretation of a language is essentially given by a homomorphism
Homomorphism
In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures . The word homomorphism comes from the Greek language: ὁμός meaning "same" and μορφή meaning "shape".- Definition :The definition of homomorphism depends on the type of algebraic structure under...
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.
Critiques
The principle of compositionality has been the subject of intense debate. Indeed, there is no general agreement as to how the principle is to be interpreted, although there have been several attempts to provide formal definitions of it.Scholars are also divided as to whether the principle should be regarded as a factual claim, open to empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....
testing; an analytic truth, obvious from the nature of language and meaning; or a methodological
Methodology
Methodology is generally a guideline for solving a problem, with specificcomponents such as phases, tasks, methods, techniques and tools . It can be defined also as follows:...
principle to guide the development of theories of syntax and semantics. The principle has been attacked in all three spheres, although so far none of the criticisms brought against it have been generally regarded as compelling. Most proponents of the principle, however, make certain exceptions for idiomatic expressions in natural language.
Further, in the context of the philosophy of language, the principle of compositionality does not explain all of meaning. For example, you cannot infer sarcasm
Sarcasm
Sarcasm is “a sharp, bitter, or cutting expression or remark; a bitter jibe or taunt.” Though irony and understatement is usually the immediate context, most authorities distinguish sarcasm from irony; however, others argue that sarcasm may or often does involve irony or employs...
purely on the basis of words and their composition, yet a phrase used sarcastically means something completely different from the same phrase uttered straightforwardly. The principle of compositionality, then, has to be revised to take into account linguistic and extralinguistic context
Context principle
In the philosophy of language, the context principle is a form of semantic holism holding that a philosopher should "never ... ask for the meaning of a word in isolation, but only in the context of a proposition"...
, which includes the tone of voice used, common ground between the speakers, the intentions of the speaker, and so on.
See also
- Componential analysisComponential analysisComponential analysis, also called feature analysis or contrast analysis, refers to the description of the meaning of words through structured sets of semantic features, which are given as “present”, “absent” or “indifferent with reference to feature”. The method thus departs from the principle of...
- Formal semantics (logic)
- Initial algebraInitial algebraIn mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F. The initiality provides a general framework for induction and recursion....
- Referential transparency (computer science)