A clear and concise description of how people are using a word.

When one word has a certain type of relationship to another word. For example, several words can have about the same definition. They’re synonyms, like “happy” and “glad” and “joyful.” Two words can also have the opposite definition. They’re antonyms, like “inside” and “outside.”

One word can refer to a specific member of a broader category, such as “red,” which is a type of “color,” or “rabbit,” a type of “animal”. The specific word, like red and rabbit, is a hyponym. The broader word, like color and animal, is a hypernym.

A word which is a hyponym of one word can be a hypernym of another: snowshoes are one type of rabbit, and a rabbit is a type of animal.

Semantic relationships, like synonyms, antonyms, hyponyms, and hypernyms, are found across many languages, but not all languages draw semantic lines in the same place For example, English has the one word “know,” while Polish splits this up. It has wiem for ‘I know a fact’ and znam for ‘I know a person’. In contrast, Portuguese fazer is used where English has both “to do” and “to make”. If you look up a word in a bilingual dictionary, you’ll often find more than one possible translation, and you need to know further context about how a language carves up the semantic space in order to know which translation to use.

Definitions are also useful for describing how words shift their meanings over time. For example, words can become broader in their meaning. “Thing” used to refer to a council or assembly in English, but now it can be used to refer to ay thing. Words can also become narrower in their meaning. For example “girl,” used to mean “child,” and now it’s more specific.

Words can change meaning all together. “Nice” used to mean “ignorant,” and then “silly,” then “fussy,” and now, well, “nice.” What a journey. One driver of this language change is taboo. We use words as euphemisms to avoid saying ruder words. But then the euphemisms start getting associated with the original meaning, and so another euphemism is needed, and so on. For example, the word “toilet” originally meant a cloth, and then a cloth used on a dressing table. Then it meant the items associated with a dressing table (like a mirror and hairbrush),and then a room containing a dressing table with a lavatory attached. Finally, people used this word to refer to the porcelain plumbing item and the room it’s in, because it sounded more polite than, I dunno, craphouse? pooproom? Now, the word “toilet” is a bit too direct in some people’s minds, and they use another euphemism for “toilet”, such as a bathroom or loo. Or maybe bathroom even feels like a little too much for you, and you use a different euphemism, like “I’m just gonna go wash my hands”. The euphemism cycle continues.

Even as words change, their definitions can still be straightforward. But definitions don’t always work so easily. For example, the same sequence of sounds can have multiple meanings, like “bank,” which can be the side of a river or a place where people store money. This is known as polysemy. And it only gets trickier from there. The sandwich we would choose if we were going to draw an unremarkable, sandwich-y sandwich. We might consider the type of bread — white? Whole wheat? Square loaf or something more rustic? And we’ll probably imagine a filling. Maybe you went with a PB&J, or something with meat, cheese, and lettuce like in the emoji sandwich. A sandwich can be served on a roll, and wraps and pitas are on a lot of sandwich menus, so maybe a sandwich is “a filling between two somewhat bread-like pieces?” Okay, so our sandwich definition isn’t really working that well, and we probably need to figure out definitions for “filling” and…”somewhat bread-like pieces.” Oh no. We are, to use a sandwich figure of speech, in a bit of a pickle.

Anyway, any definition, if we think about it hard enough, starts to break down with exceptions and edge cases. How do we know whether something is a cup? Whether a dress is blue and black, or white and gold? And that’s not even getting into social constructs like genders and emotions. Maybe nothing means anything, ever! And yet, somehow, we do manage to go through the world and communicate with each other reasonably well, most of the time. If I ask you to think of a sandwich, or a chair, or a bird, you do think of something. So maybe the problem isn’t with words, it’s with trying to use definitions to express their meaning.

Psychology professor Eleanor Rosch came up with a different idea. Rather than imagining we have dictionary-style, clear-cut definitions of things in our brain ,Rosch argued that instead we have prototypes or exemplars, the most typical representatives of a category. Then we can also have other category members that are more or less central depending on how similar they are to the exemplar.

For example, an exemplar of a chair probably has four legs, a rigid back, and seats one human, but that doesn’t mean that a chair can’t have three legs, or be extra tall, or be an adjustable desk chair. Most people’s exemplars of a bird are small, feathery ones like sparrows or robins, but that doesn’t mean that less-central category members like emus or penguins aren’t still birds.

Rosch’s prototype theory offers us an escape hatch from definitions. We don’t need to pin down an exact set of criteria for sandwich-hood or chair-ness. Instead, we can recognize that some examples are really obvious, prototypical members of their category, and other examples are more loosely related. Both kinds of meaning are totally okay.

Prototype theory works well with content words, words with meanings that we could point to, describe, or draw a picture of. It even works okay when the ideas are abstract, like happiness and democracy. But not every word has a prototype. Take words like “the”, “of”, “is”, “or”, “if”, and “every.” It doesn’t make much sense to ask what a “the” looks like, or to try to think of the most prototypical example of an “of”. These little words that help a sentence fit together grammatically are called function words. They can only really be described based on their relationship to the words they’re used with — their function in the sentence. We can express the relationships between words in mathematical, symbolic terms, using predicate calculus. This concept also comes up in mathematics, computer science, or philosophy, where it can also go by the names first-order logic, quantificational logic, and first-order predicate calculus.

Predicate calculus is a branch of formal semantics — that’s formal as in “using formulas”, not as in the semantics . At the heart of formal semantics is one assumption: to understand what a sentence means, we have to know when that sentence is true or not. Predicate calculus helps us find the meanings of certain words in those true sentences. There’s an extensive set of notation we can use to explore other function words, and some are still being figured out! That said, like prototype theory, predicate calculus also doesn’t work for everything — these methods are just two ways to do semantics. Other approaches to semantics specialize in still more kinds of meanings, such as Binary Feature Analysis, which is useful for precisely describing words that are part of a taxonomy, like words for family members. There’s Natural Semantic Metalanguage, where words can be broken down into other, more basic units of meaning, and Cognitive Semantics, where metaphors draw connections between abstract concepts like time and concrete concepts like physical location. Some aspects of semantics highlight similarities between different, unrelated languages; other aspects highlight meanings that are more specific to a particular language or language family.

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