Intension
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In any of several fields of study that treat the use of signs—for example, in
linguistics Linguistics is the scientific study of language. The areas of linguistic analysis are syntax (rules governing the structure of sentences), semantics (meaning), Morphology (linguistics), morphology (structure of words), phonetics (speech sounds ...
,
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
,
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
,
semantics Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...
,
semiotics Semiotics ( ) is the systematic study of sign processes and the communication of meaning. In semiotics, a sign is defined as anything that communicates intentional and unintentional meaning or feelings to the sign's interpreter. Semiosis is a ...
, and
philosophy of language Philosophy of language refers to the philosophical study of the nature of language. It investigates the relationship between language, language users, and the world. Investigations may include inquiry into the nature of Meaning (philosophy), me ...
—an intension is any
property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, re ...
or
quality Quality may refer to: Concepts *Quality (business), the ''non-inferiority'' or ''superiority'' of something *Quality (philosophy), an attribute or a property *Quality (physics), in response theory *Energy quality, used in various science discipli ...
connoted by a
word A word is a basic element of language that carries semantics, meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no consensus among linguist ...
,
phrase In grammar, a phrasecalled expression in some contextsis a group of words or singular word acting as a grammatical unit. For instance, the English language, English expression "the very happy squirrel" is a noun phrase which contains the adject ...
, or another symbol. In the case of a word, the word's
definition A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitio ...
often implies an intension. For instance, the intensions of the word ''
plant Plants are the eukaryotes that form the Kingdom (biology), kingdom Plantae; they are predominantly Photosynthesis, photosynthetic. This means that they obtain their energy from sunlight, using chloroplasts derived from endosymbiosis with c ...
'' include properties such as "being composed of
cellulose Cellulose is an organic compound with the chemical formula, formula , a polysaccharide consisting of a linear chain of several hundred to many thousands of glycosidic bond, β(1→4) linked glucose, D-glucose units. Cellulose is an important s ...
(not always true)", "alive", and "organism", among others. A '' comprehension'' is the collection of all such intensions.


Overview

The meaning of a word can be thought of as the bond between the ''idea the word means'' and the ''physical form of the word''. Swiss linguist Ferdinand de Saussure (1857–1913) contrasts three concepts: # the ''signifier'' – the "sound image" or the string of letters on a page that one recognizes as the form of a sign # the ''signified'' – the meaning, the
concept A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs. Concepts play an important role in all aspects of cognition. As such, concepts are studied within such disciplines as linguistics, ...
or
idea In philosophy and in common usage, an idea (from the Greek word: ἰδέα (idea), meaning 'a form, or a pattern') is the results of thought. Also in philosophy, ideas can also be mental representational images of some object. Many philosophe ...
that a sign expresses or evokes # the ''referent'' – the actual thing or set of things a sign refers to. See '' Dyadic signs'' and '' Reference (semantics)''. Without intension of some sort, a word has no meaning. For instance, the terms ''rantans'' or '' brillig'' have no intension and hence no meaning. Such terms may be suggestive, but a term can be ''suggestive'' without being meaningful. For instance, ''ran tan'' is an archaic onomatopoeia for chaotic noise or din and may suggest to English speakers a din or meaningless noise, and ''brillig'' though made up by
Lewis Carroll Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet, mathematician, photographer and reluctant Anglicanism, Anglican deacon. His most notable works are ''Alice ...
may be suggestive of 'brilliant' or 'frigid'. Such terms, it may be argued, are always intensional since they connote the property 'meaningless term', but this is only an apparent paradox and does not constitute a counterexample to the claim that without intension a word has no meaning. Part of its intension is that it has no extension. Intension is analogous to the signified in the Saussurean system, extension to the referent. In philosophical arguments about dualism versus
monism Monism attributes oneness or singleness () to a concept, such as to existence. Various kinds of monism can be distinguished: * Priority monism states that all existing things go back to a source that is distinct from them; e.g., in Neoplatonis ...
, it is noted that thoughts have intensionality and physical objects do not (S. E. Palmer, 1999), but rather have extension in space and time.


Statement forms

A statement-form is simply a form obtained by putting blanks into a sentence where one or more expressions with extensions occur—for instance, "The quick brown ___ jumped over the lazy ___'s back." An instance of the form is a statement obtained by filling the blanks in.


Intensional statement form

An ''intensional statement-form'' is a statement-form with at least one instance such that substituting co-extensive expressions into it does not always preserve
logical value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in c ...
. An ''intensional statement'' is a statement that is an instance of an intensional statement-form. Here co-extensive expressions are expressions with the same extension. That is, a statement-form is intensional if it has, as one of its instances, a statement for which there are two co-extensive expressions (in the relevant language) such that one of them occurs in the statement, and if the other one is put in its place (uniformly, so that it replaces the former expression wherever it occurs in the statement), the result is a (different) statement with a different logical value. An intensional statement, then, is an instance of such a form; it has the same form as a statement in which substitution of co-extensive terms fails to preserve logical value.


Examples

#Everyone who has read '' Huckleberry Finn'' knows that
Mark Twain Samuel Langhorne Clemens (November 30, 1835 – April 21, 1910), known by the pen name Mark Twain, was an American writer, humorist, and essayist. He was praised as the "greatest humorist the United States has produced," with William Fau ...
wrote it. #
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
often remarked that he enjoyed stargazing. The first example has a different logical value if the term "Mark Twain" is replaced with the co-extensive term "The author of '' Corn-pone Opinions''", since not everyone who has read ''Huckleberry Finn'' knows that the same author also wrote ''Corn-pone Opinions''. The second example has a different logical value if the term "stargazing" is replaced with the co-extensive term "looking at luminous
spheroids A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface (mathematics), surface obtained by Surface of revolution, rotating an ellipse about one of its principal axes; in other words, an ellipsoid with t ...
of plasma held together by self-gravity", since Aristotle would not have been aware of this definition of the term "star", and therefore would not have used it in a remark. The intensional statements above feature expressions like "knows", "possible", and "pleased". Such expressions always, or nearly always, produce intensional statements when added (in some intelligible manner) to an extensional statement, and thus they (or more complex expressions like "It is possible that") are sometimes called ''intensional operators''. A large class of intensional statements, but by no means all, can be spotted from the fact that they contain intensional operators.


Extensional statement form

An ''extensional'' statement is a non-intensional statement. Substitution of co-extensive expressions into it always preserves logical value. A language is intensional if it contains intensional statements, and extensional otherwise. All natural languages are intensional. The only extensional languages are artificially constructed languages used in
mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
or for other special purposes and small fragments of natural languages.


Examples

#Mark Twain wrote ''Huckleberry Finn''. #Aristotle enjoyed stargazing. Note that if " Samuel Clemens" is put into (1) in place of "Mark Twain", the result is as true as the original statement. It should be clear that no matter what is put for "Mark Twain", so long as it is a singular term picking out the same man, the statement remains true. Likewise, we can put in place of the predicate any other predicate belonging to Mark Twain and only to Mark Twain, without changing the logical value. For (2), the term "stargazing" can now be substituted with "looking at luminous spheroids of plasma held together by self-gravity", since Aristotle personally being aware of the two terms being co-extensive is no longer relevant to the logical value of the sentence.


See also

* Description logic * Connotation *
Extension (predicate logic) The extension of a predicatea truth-valued functionis the set of tuples of values that, used as arguments, satisfy the predicate. Such a set of tuples is a relation. Examples For example, the statement "''d2'' follows the weekday ''d1''" can ...
*
Extensionality In logic, extensionality, or extensional equality, refers to principles that judge objects to be equality (mathematics), equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned wi ...
* Intensional definition * Intensional logic *
Montague grammar Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on mathematical logic, especially higher-order predicate logic and lambda calculus, and makes use of th ...
* Temperature paradox * Sense and reference * Set-builder notation


Notes


References

* Ferdinand de Saussure, '' Course in General Linguistics''. Open Court Classics, July 1986. * S. E. Palmer, ''Vision Science: From Photons to Phenomenology'', 1999. MIT Press,


External links

* Chalmers, David
"On Sense and Intension"
* Rapaport, William J.
''s''ionality v. Inten''t''ionality"">"Inten''s''ionality v. Inten''t''ionality"
{{Formal semantics Concepts in logic Semantics Definition Formal semantics (natural language) Concepts in the philosophy of language