{"id":1279,"date":"2024-12-03T14:18:36","date_gmt":"2024-12-03T12:18:36","guid":{"rendered":"https:\/\/linguistica.info\/b\/lei\/?page_id=1279"},"modified":"2025-06-26T11:32:38","modified_gmt":"2025-06-26T09:32:38","slug":"6-3-from-extension-to-intension","status":"publish","type":"page","link":"https:\/\/linguistica.info\/b\/leiwp\/toc\/6-lexical-semantics\/6-3-from-extension-to-intension\/","title":{"rendered":"6.3 From extension to intension"},"content":{"rendered":"

Can we use the extension of a word to define its meaning? Intuitively, it may seem so: when interacting with a child acquiring its first language, or an adult learning a foreign language, we might point at a blue rubber ball and say This is a ball<\/em>, thinking that we have thereby defined it for the child or foreign-language learner. But first, this is not, of course, an extensional definition<\/strong> \u2014 we have pointed out a single referent from the extension of the word ball<\/em>, not the extension itself. Pointing out an entity exemplifying the extension of a word is called giving an ostentative definition<\/strong>. This may be a useful way of informing a learner of the meaning of a word, but it relies on the learner to do most of the work: they have to recognize which properties of the example are relevant and generalize them to arrive at the potentially infinite extension of the word. For ball<\/em>, these properties might include \u201cis an artificial object\u201d, \u201cis round\u201d, \u201cis used to play\u201d, but not \u201cis blue\u201d or \u201cis made of rubber\u201d.<\/p>\n

We can observe children slowly moving towards the actual extension of a word during language acquisition. When learning the word ball<\/em>, they might, for example, apply it to roundish things in general for a while \u2014 apples and oranges, balloons, a globe, a lightbulb, the moon \u2014, before discovering which properties distinguish balls from other round objects. In doing so, they are identifying the features that determine<\/em> the extension of the word \u2014 the properties that make an entity a potential referent of the word. In other words, they are discovering the sense of the word \u2014 the mental concept associated with the word.<\/p>\n

The content of a word\u2019s sense is called its intension<\/strong>, the description of a word\u2019s meaning in terms of its intension is called an intensional definition<\/strong>. It is the intension of a word that allows us to determine its extension in the first place. The intension of the word TREE encompasses properties like \u2018is a plant\u2019, \u2018is perennial\u2019, \u2018is made of wood\u2019, \u2018has a single trunk\u2019, \u2018has branches\u2019, \u2018has leaves\u2019, etc. When deciding whether an entity can truthfully be referred to as a tree<\/em>, we project this intension onto the entity to see if there is a match. Again, we have to remind ourselves that language is not limited to talking about the particular possible world we call reality. Take the word unicorn again: its intension encompasses properties like \u2018is an animal\u2019, \u2018has four legs\u2019. \u2018has hooves\u2019, \u2018has a mane\u2019, \u2018has a tail\u2019, and \u2018has a single horn on its forehead\u2019. It is this intension that allows us to make the statement that there are no unicorns in reality: the set of entities identified by this intension is empty. It is also this intension that allows us to identify an entity as a unicorn in a possible world where the extension of the word is not empty \u2014 for example, in Ponyland \u2014, and to distinguish it from similar entities, such as pegasusses (which have wings, but no horn) or regular ponies (which have neither wings nor a horn).<\/p>\n

As linguists, we are primarily interested in intension and intensional definitions, first, because they are primary in that they are part of the linguistic sign and allow speakers to determine extensions in the first place, and second, because extensional definitions are typically impossible to give (this would require listing all members of the extension). However, before we focus on intension, note that there are cases where intensional definitions are difficult or even impossible to give, while extensional definitions are relatively straightforward.<\/p>\n

Consider the word weekday<\/em>. How would you define it? Dictionaries will typically give you a definition like \u2018any day of the week except Saturday and Sunday\u2019. This is actually an extensional definition: it requires you to know the set of days of the week, i.e., {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday} (the curly braces do not signal morpheme status here, they are the standard way of representing sets in mathematics), and then specify what part of that set falls into the extension of the word weekday<\/em>. What would an intensional definition look like? Perhaps something like \u2018a day when most people work and most shops, educational institutions and government agencies are open\u2019. The interesting question is which of these definitions \u2014 the extensional one or the intensional one \u2014 is more relevant to our understanding of the word weekday<\/em>. It is difficult to tell, as the days of the week are a closed and very small set, so that it seems natural to use an extensional definition, and on the other hand, we have very strong cultural associations between work and some days of the week, so we probably use this association to make sense of the distinction between weekdays and the weekend, even if we happen to belong to a group of people who work on weekends. We have to apply the word in other possible worlds to see which of the definitions is ultimately the one on which we base our use of the word.<\/p>\n

(a) Imagine a law was passed mandating that from now on, Wednesday through Sunday will be the days when people are generally expected to work and institutions are expected to be open, and Monday and Tuesday will be the days that people are generally expected to use for leisure and institutions will be closed. Would this change your definition of the words weekday<\/em> and weekend<\/em>? (b) After the French revolution, a ten-day week was established, with the following days of the week: primidi<\/em> (first day), duodi<\/em> (second day), tridi<\/em> (third day), quartidi<\/em>, quintidi<\/em>, sextidi<\/em>, septidi<\/em>, octidi<\/em>, nonidi<\/em> and d\u00e9cadi<\/em>. People had to work primdi through nonidi, and were allowed to rest on d\u00e9cadi. How do you use the intensional or extensional definition of weekday<\/em> to determine which of these were weekdays?<\/div>\n

It seems that, ultimately, it is always the intensional definition that is more important, but there are cases where the extension of a word also figures very prominently in the way we think of the meaning of words. Other examples are: capital city<\/em>, nation<\/em>, continent<\/em>, planet<\/em> \u2014 all of them having finite, relatively small extensions.<\/p>\n

 <\/p>\n

\u2190<\/span> Previous section<\/a><\/span> Next section \u2192<\/span><\/a><\/span><\/p>\n

CC-BY-NC-SA 4.0, Written by Anatol Stefanowitsch<\/p>\n","protected":false},"excerpt":{"rendered":"

Can we use the extension of a word to define its meaning? Intuitively, it may seem so: when interacting with a child acquiring its first language, or an adult learning a foreign language, we might point at a blue rubber ball and say This is a ball, thinking that we have thereby defined it for […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1268,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1279","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages\/1279","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/comments?post=1279"}],"version-history":[{"count":10,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages\/1279\/revisions"}],"predecessor-version":[{"id":2022,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages\/1279\/revisions\/2022"}],"up":[{"embeddable":true,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages\/1268"}],"wp:attachment":[{"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/media?parent=1279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}