Semantics

• 1. Introduction

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  Semantics is the study of linguistic meaning, and it begins with a puzzle about the name Pegasus. Pegasus never existed, yet the name plainly means something. The same goes for Santa Claus. If a name meant only the thing it points to, these names would mean nothing at all. They clearly do mean something, so some other mechanism must be at work.

  That small paradox opens a field that thinkers have worked on since antiquity. Its answers matter far beyond the study of language.

  This documentary follows the questions the puzzle raises. What counts as meaning, and what does not? How does a sentence draw its meaning from its words? Why can two expressions for one object still differ? Which theories try to explain all of this, and who built them?

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• 2. Borders of the Field

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  The phrase "That's what I'm talking about" can mean many things, depending on who says it and in what situation. Semantics cares about the range of things such a phrase can and cannot mean in general. Pragmatics, its neighbor, asks which of those meanings applies on a given occasion. For this reason semantics is sometimes called the study of context-independent meaning. Pragmatics also covers meaning that is inferred without being spoken, such as what a speaker's silence on a topic implies.

  Semantics is a descriptive discipline. It tries to work out how meaning functions and does not dictate what people should mean by their words. It can focus on one language, such as English, or on meaning structures shared by all languages. It has an internal side, which links words to the ideas they evoke. It also has an external side, which asks how words refer to objects and when a sentence is true.

  Other neighbors claim different slices of language. Phonology deals with the sounds of a language and how they combine into words. Syntax deals with the rules for arranging words into sentences. The split is real, because a person can pronounce a word perfectly without knowing what it means. Semiotics is wider than semantics because it also covers non-verbal signs. Nodding to signal agreement, stripes on a uniform that mark rank, and vultures that point to a nearby carcass all count. The semiotician Charles W. Morris offered a compact way to keep the fields apart. Semantics links words to the world, pragmatics links words to their users, and syntax links words to other words.

  The name itself has a story. It comes from the Ancient Greek semantikos, meaning relating to signs, which derives from sēmeion, the word for a sign. At first it described medical symptoms, and only later did it widen to cover any sign, including linguistic ones. It reached English from the French sémantique, which the linguist Michel Bréal introduced at the end of the 19th century. Several related disciplines sit nearby. Etymology traces how words and their meanings changed through history, and hermeneutics concerns the interpretation of texts, especially scripture. Metasemantics goes deepest of all, asking where meaning comes from in the first place.

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• 3. Sense and Reference

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  A dictionary can define the word ram as adult male sheep. Semantics cares about public meaning of this kind, not the private associations of any one speaker. Someone who links the word needle with pain or drugs holds a speaker meaning that can drift away from the literal one.

  Meaning also lives at several levels. Word meaning, studied by lexical semantics, ties dog to the concept of a four-legged domestic animal. Sentence meaning is usually called a proposition, and different sentences can share one. The English "the tree is green" and the German "der Baum ist grün" express the same proposition. Utterance meaning belongs to pragmatics and covers an expression on one particular occasion. Irony shows how far sentence meaning and utterance meaning can come apart.

  The morning star and the evening star are the same planet, just as 2 + 2 and 3 + 1 are the same number. Yet each pair of expressions feels different. Analysts capture this with the pair sense and reference, also called intension and extension, or connotation and denotation. The referent is the object an expression points to. The sense is the way the expression points, or how the object is presented. Some semanticists weigh sense more heavily and some weigh reference. Full understanding usually requires both.

  The pair neatly explains identity statements. "The morning star is the evening star" is informative, because a listener can learn something from it. "The morning star is the morning star" teaches nothing. Its two expressions match in sense as well as in reference.

  The semiotic triangle, also called the triangle of meaning, pushes the point further. Its three corners are Symbol, Thought or Reference, and Referent. A dotted line joins symbol and referent to show that earlier two-part models were wrong to assume a direct link. The word apple is only a string of letters with no connection to a fruit. Seeing it calls up a mental image or concept, and that concept connects to the physical object. This works only if the reader has already learned the symbol. Convention decides the rest, so one symbol may name an object in one language, a different object in a second, and nothing in a third.

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• 4. Parts and Wholes

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  Consider the sentence "Zuzana owns a dog." A listener understands it by knowing what Zuzana, owns, a and dog mean, plus how they are joined. This is compositionality, the idea that the meaning of a complex expression is a function of the meanings of its parts. Single words work differently. Nobody can deduce a word's meaning from its letters, so a dictionary is needed.

  The principle explains something remarkable. Words and cognitive resources are finite, yet people produce and grasp an almost endless range of meanings. Many sentences a person reads are brand new to them, and they understand them anyway.

  In its strong form, the principle says the parts and their arrangement fully determine the meaning, not merely influence it. Whether that is true is controversial. Context may shape meaning, and an idiom such as "kick the bucket" carries a figurative sense that cannot be read off its individual words.

  The sentence "it is raining outside" shows a second tool, the truth condition. This is the way the world must be for a sentence to be true, and here it means raindrops are falling from the sky. The sentence is true whenever those conditions are met. Understanding a statement usually means grasping its truth conditions, even without knowing whether they hold. Some theories of meaning rest on truth conditions alone.

  In "the boy kicked the ball," the boy is the agent who performs an action. The ball is the theme or patient, involved in the action without acting itself. One entity can fill both roles, as when someone cuts themselves. The knife used for cutting is an instrument. When a girl sees a bird, no action occurs but an experience does, and she is the experiencer. Further roles include location, source, goal, beneficiary and stimulus.

  Phrasal semantics puts these tools to work on whole sentences. In "Mary hit the ball," Mary is the subject, hit is the predicate, and the ball is an argument that completes the predicate. Verbs usually act as predicates and link expressions together. In "Beethoven likes Schubert," the verb connects a liker to the one liked. Other words modify instead of linking. The adjective red, for instance, alters the color of a car in "red car." Variable binding handles reference, because the closing clause of "the woman who likes Beethoven" says which woman is meant. Parse trees can display the hierarchy by which the parts combine. Even grammatical devices such as the gerund form add meaning, a topic known as grammatical semantics.

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• 5. The Web of Words

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  Car and automobile, buy and purchase: such pairs are synonyms, words sharing the same or a very similar meaning. Antonyms are opposites, like alive and dead or fast and slow. Hyponymy describes inclusion, so ant is a hyponym of insect. A prototype is a hyponym that has the characteristic features of its type. Meronymy describes part and whole, and wheel is a meronym of car.

  Sound and spelling add tangles. Flour and flower are homophones, sharing a pronunciation. Homonyms share a spelling, as with the bank of a river and a bank as a financial institution. An expression is ambiguous when it has more than one possible meaning, and it can sometimes be disambiguated to find the intended one. Polysemy is the gentler case, where the meanings are closely related. The word head can mean the topmost part of the human body or the top-ranking person in an organization.

  The word horse carries the semantic feature animate but lacks the feature human. Meanings can often be broken into such components, though listing every feature may still fail to rebuild a word's full meaning. Words also cluster into semantic fields. The field of cooking includes bake, boil, spice and pan. Lexical semanticists use features and fields to build taxonomies of lexical knowledge. These separate physical from abstract entities and split physical ones into stuff and individuated entities.

  Lexical semantics runs in two directions. Semasiology starts with a word and asks what it means, including whether it has one meaning or several. Onomasiology starts with a concept and asks what names it has in a given language. Units smaller and larger than words also count. Being under the weather has a non-literal meaning that works as one unit. Prefixes such as in- and dis- change meaning, as in inanimate and dishonest.

  The expressions here and she show why context matters. Context means the time, location, speaker and audience of an expression, plus the passages that come before and after it. Context also governs whether expressions can be swapped. Take the sentence "the number 8 is even." Replace "the number 8" with "the number of planets in the Solar System" and it stays true. That makes the environment extensional, or transparent. In "Paco believes that the number 8 is even," the swap may fail. Paco may not know that the number of planets is 8. That environment is intensional, or opaque.

  A last distinction concerns the language of the researcher. Semanticists call the language under study the object language and the language used to describe it the metalanguage. Suppose a professor uses Japanese to teach a student the language of first-order logic. Logic is then the object language and Japanese is the metalanguage. One language can play both parts at once, as in a monolingual English dictionary, where the entry word and its definition are both English.

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• 6. Rival Theories

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  The name George Washington means, on the simplest view, the person who bore it. Referential theories hold that the meaning of an expression is the part of reality it points to. A general term like cat points to the set of all cats. Verbs usually refer to classes of actions or events, and adjectives to properties of individuals and events.

  The name Santa Claus exposes the weakness of this view, since it has meaning though no such person exists. Roger Bannister and the first man to run a four-minute mile name the same person but do not mean quite the same thing. That matters for beliefs, since someone may understand both phrases without knowing they match. Context-bound words such as here and I raise a third problem.

  Repairs exist. Some theorists tie meaning to functions that pick out objects, so the same word can point to different things in different contexts. The word here depends on where it is spoken. Possible world semantics goes further and lets expressions point to entities in other possible worlds. Under it, the first man to run a four-minute mile may name a different person in a different world. Possibility becomes truth in some worlds, and necessity becomes truth in all of them.

  John Locke gave the most influential version of the ideational, or mentalist, view. The meaning of the word dog is the idea people hold of dogs. Language moves ideas between minds. Once speaker and audience have learned the same meanings, a sign shaped by one person's idea evokes the same idea in the other.

  Paul Grice shifted the focus to intentions. People usually speak to provoke a reaction, and he held that an expression's meaning is the intended reaction. Imagine someone looking for petrol who is told "there is a garage around the corner." The remark means petrol can be had there, because the speaker intends to help. The literal words never mention petrol.

  Shouting "Fire!" illustrates behaviorist semantics, also called stimulus-response theory. Meaning is the situation that prompts the speaker plus the response in the audience: an uncontrolled fire, and attempts to control it or reach safety. Behaviorists see language learning as the adoption of stimulus-response patterns. They also wish to avoid private mental entities and define meaning through observable behavior.

  Saul Kripke supplied another causal account, for names. A naming event, like a baptism, forms the first link in a chain that all later uses of the name join. The name Plato refers to an ancient Greek philosopher because he was named that way and people kept using it. Kripke aimed the view at names only, but others extended it to other kinds of speech.

  The sentence "Hillary Clinton won the 2016 American presidential election" is false in the actual world, yet true in some possible worlds. Truth-conditional semantics builds on that: to understand a sentence is to know what the world must be like for it to be true. A sentence's extension is its truth value, and its intension is the set of all possible worlds where it is true. Verificationist theories add that a verification procedure should exist. Meaning lies in the method of checking, or the circumstances that justify the sentence. Scientific claims often make predictions that observation can confirm or disconfirm. By this standard, a sentence that can be neither verified nor falsified is meaningless.

  Ludwig Wittgenstein introduced the use theory, which sees language as a collection of language games. Inside a game, an expression has the meaning its use gives it, and one expression can mean different things in different games. Some versions identify meaning with patterns of regular use. Others add social norms and conventions, asking whether a use counts as appropriate in a society.

  From "x is a male sibling" one can infer "x is a brother." From "x is a brother" one can infer "x has parents." Inferentialist semantics, also called conceptual role semantics, holds that an expression's meaning is the role it plays in the premises and conclusions of good inferences. On this view, the meaning of brother is fixed by these inferences and all similar ones.

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• 7. Thinkers Across Centuries

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  Plato (427-347 BCE) staged a debate about names in his dialogue Cratylus. One side, naturalism, held that things have their names by nature. The other, conventionalism, held that names attach to referents through custom and agreement among speakers. Aristotle (384-322 BCE) wrote On Interpretation, whose distinctions shaped later semantics. He sketched an early semantic triangle. Spoken and written words evoke mental concepts, and the concepts relate to external things by resembling them. For him, concepts are the same for every human, while words are conventional. The Stoics built a complex theory of language through logic. They separated names, common nouns and verbs by their roles, and they distinguished statements, commands and prohibitions.

  In ancient India, the Nyaya school held that all names refer to real objects. It studied how words lead to an understanding of the thing meant. Mīmāṃsā philosophers debated whether individual words or full sentences are more basic. Bhartṛhari (4th-5th century CE) wrote the Vākyapadīya, which sorted types of words and showed how use changes their meanings. In ancient China, the Mohists argued that names help make the distinctions that guide moral behavior. They inspired the School of Names, which studied how names identify and judge entities.

  Augustine of Hippo (354-430) defined signs as entities that stand for other entities and convey them to the intellect. He was first to separate natural from linguistic signs as two types of one genus. Boethius (480-528) translated Aristotle's On Interpretation and commented on it, which spread its ideas and prompted scholastic reflection. Peter Abelard (1079-1142) turned attention to propositions, the meanings of sentences, rather than single words. He treated universals as semantic phenomena of common names, produced by mental abstraction and referring to no entities. In the Arabic tradition, Ibn Faris (920-1004) equated meaning with a speaker's intention. Abu Mansur al-Azhari (895-980) placed meaning in speech itself, to be extracted through interpretation.

  Late medieval thinkers split terms into two kinds. Categorematic terms, like horse and Socrates, have independent meaning and refer to part of reality. Syncategorematic terms, like some, not and necessarily, lack independent meaning and modify or quantify other expressions. Roger Bacon (c. 1219/20 - c. 1292) proposed an early causal theory, saying things receive names much as people do, through an initial baptism. His ideas inspired the speculative grammarians, who argued that all languages share universal structures. They reasoned by analogy between modes of signification in language, modes of understanding in mind, and modes of being in reality.

  Thomas Hobbes (1588-1679) separated marks, used privately to recall one's own thoughts, from signs, used publicly to tell others. Antoine Arnauld (1612-1694) and Pierre Nicole (1625-1695) wrote the Port-Royal Logic, an early precursor of the distinction between intension and extension. John Locke (1632-1704) wrote the Essay Concerning Human Understanding. Gottfried Wilhelm Leibniz (1646-1716) saw language as the mirror of thought and sketched a universal formal language for scientific and philosophical truths. That attempt inspired Christian Wolff (1679-1754), Georg Bernhard Bilfinger (1693-1750) and Johann Heinrich Lambert (1728-1777) to propose a general science of sign systems. Étienne Bonnot de Condillac (1715-1780) developed Leibniz's idea that thought is linguistic. Against Locke, he argued that language helps create ideas rather than merely carrying them.

  In the 19th century, semantics solidified as an independent field. Christian Karl Reisig (1792-1829) is sometimes called its father for clarifying its scope and key ideas. Michel Bréal (1832-1915) followed with a similarly broad conception. John Stuart Mill (1806-1873) stressed the role of names in referring to things, separated connotation from denotation, and held that propositions combine names. Charles Sanders Peirce (1839-1914) imagined semiotics as a general theory of signs with several subdisciplines. Charles W. Morris (1901-1979) later labeled them syntactics, semantics and pragmatics. Peirce's pragmatist approach held that a conception's meaning is the entirety of its practical consequences.

  Gottlob Frege (1848-1925) contributed on many levels. He first introduced the distinction between sense and reference. His predicate logic and the principle of compositionality became foundations for later formal semantics. Edmund Husserl (1859-1938) approached meaning through phenomenology, looking at the mental acts that give expressions meaning. He held that meaning always implies reference to an object, so expressions lacking a referent, like "green is or," are meaningless.

  Alfred Tarski (1901-1983) defined truth in formal languages with his semantic theory of truth. Donald Davidson (1917-2003) drew on it to develop truth-conditional semantics. Tarski's student Richard Montague (1930-1971) built a complex formal framework for the semantics of English, which established formal semantics as a major area of research. Structural semantics took inspiration from Ferdinand de Saussure (1857-1913) and treats language as a network of relations. A word's meaning then depends on its position in that network. Alfred Korzybski (1879-1950) developed general semantics to ask how language represents reality and shapes thought. George Lakoff, born in 1941, and Ronald Langacker, born in 1942, laid the foundation for cognitive semantics. Charles J. Fillmore (1929-2014) developed frame semantics within it. Ray Jackendoff, born in 1945, inaugurated the related field of conceptual semantics.

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• 8. Branches and Neighbors

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  Montague semantics uses higher-order logic, lambda calculus and type theory to show how expressions of different syntactic categories combine into meaning. It belongs to formal semantics, which draws on logic and mathematics to give precise accounts of how expressions relate to what they denote. A common picture has words refer to individual objects or groups of objects, while sentences relate to events and states. Ontological models let the theory map expressions to entities, and each sentence receives a truth value according to whether it matches the model. The field also models quantification, intensionality, noun phrases, plurals, mass terms, tense and modality. Dynamic semantics studies how information grows over time. Its slogan is "meaning is context change potential." A sentence's meaning is the change it brings to a context, not the information it holds.

  The word hypotenuse profiles a straight line against a base that is a right-angled triangle. Cognitive semantics, part of cognitive linguistics, uses this profile and base contrast to describe knowledge structure. The profile is the aspect an expression brings to the foreground. The base is the background that gives it context. Cognitive semanticists see no sharp line between linguistic knowledge and knowledge of the world. They study how language and cognition shape concepts in broad domains such as space, time, causation and action. They compare conceptual patterns across languages, asking how far human conceptual structures are universal. They also study categorization, a heuristic that avoids information overload by treating different entities alike, and embodiment, the effect of bodily experience on meaning. Frame semantics holds that terms depend on conceptual structures. Words like bride, groom and honeymoon evoke the frame of marriage.

  Conceptual semantics also takes a psychological view but separates meaning from syntax strictly and uses formal devices. It holds that meaning concerns the cognitive structure of concepts linking thought, perception and action, not the objects expressions refer to. Computational semantics asks how computers can represent and process meaning. It borrows from formal semantics and tackles problems such as computing the meaning of complex expressions from their parts and handling ambiguity, vagueness and context-dependence. It also feeds extracted information into automatic reasoning. Its applications include machine learning and machine translation.

  Spanish tu and usted, or German du and Sie, encode politeness and social hierarchy, whereas English uses you for both. Cultural semantics studies such links between meaning and culture, including how politics, religion and customs change meanings over time. Pragmatic semantics treats communicative meaning as context-sensitive, dependent on the participants, their shared information, intentions and background assumptions. Some theorists place those topics inside semantics and others in pragmatics.

  To say "Bertie is a dog" in first-order logic, one writes D(b). Here b is an individual constant for Bertie and D is a predicate for dog. A semantics for a formal language is a set of rules, usually a mathematical function, that assigns meanings to its expressions. Classical model-theoretic semantics uses an interpretation function that maps b to Bertie and D to the set of all dogs. The sentence is then true if Bertie belongs to that set and false otherwise. The same machinery defines validity. Syntactic entailment applies rules of inference to logical form alone and ignores meaning. Semantic entailment holds when every interpretation that makes the premises true also makes the conclusion true.

  In JavaScript, the commands i += 1 and i = i + 1 look different but both raise the variable i by one. That gap is the one between syntax and semantics in computer science. A program's semantics is how it behaves when a computer runs it. Different programming languages use different syntax yet can produce the same behavior. Static semantics covers aspects that affect compilation, such as catching type errors, for instance a numerical function handed a string instead of a number. Dynamic semantics covers run time behavior through three main approaches. Denotational semantics uses mathematical formalisms to describe the effects of each code element. Axiomatic semantics uses deductive logic to analyze the conditions before and after execution. Operational semantics treats execution as a series of steps, each moving from one state to another.

  Psychological semantics asks how meaning is represented in the mind and what mental processes underlie understanding and producing language. It studies how people learn new words and relate them to familiar things. It also studies how they infer the meaning of compound expressions they have never heard, resolve ambiguity, and misread sentences because of semantic illusions. Semantic memory holds general knowledge of language, concepts and facts. It contrasts with episodic memory, which records events a person lived through. A common view says word meanings are stored by semantic features. The feature comparison model says "a robin is a bird" is checked by comparing the features of robin and bird. The check is fast when the example is a prototype of its category. For "a penguin is a bird," the overlap is smaller and the process is significantly slower.

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