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In
linguistics Linguistics is the scientific study of language A language is a structured system of communication Communication (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo ...

linguistics
,
logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statements and ar ...

logic
,
philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such questio ...

philosophy
, and other fields, 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, r ...
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 disciplin ...
connoted
connoted
by a
word In linguistics Linguistics is the scientific study of language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sign language) and writing. Most lang ...

word
,
phrase In syntax In linguistics Linguistics is the scientific study of language, meaning that it is a comprehensive, systematic, objective, and precise study of language. Linguistics encompasses the analysis of every aspect of language, as ...

phrase
, 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 In linguistics, a word of a spoken language can be defined as the smallest sequence of phonemes that can be uttered in isolation with semantic, objective or pragmatics, practical ...

definition
often implies an intension. For instance, the intensions of the word ''
plant Plants are predominantly photosynthetic Photosynthesis is a process used by plants and other organisms to Energy transformation, convert light energy into chemical energy that, through cellular respiration, can later be released to fuel ...

plant
'' include properties such as "being composed of
cellulose Cellulose is an organic compound In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior ...

cellulose
", "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 Ferdinand de Saussure (; ; 26 November 1857 – 22 February 1913) was a Swiss Swiss may refer to: * the adjectival form of Switzerland , french: Suisse(sse), it, svizzero/svizzera or , rm, Svizzer/Svizra , government_type = Fed ...

Ferdinand de Saussure
(1857–1913) contrasts three concepts: # the ''signifier'' – the "sound image" or the string of
letters Letter, letters, or literature may refer to: Characters typeface * Letter (alphabet) A letter is a segmental symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, Object (philosophy ...
on a page that one recognizes as the form of a
sign A sign is an object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Entity, something that is tangible and within the grasp of the senses ** Object (abstract), an object which does not exist at ...
# the ''signified'' – the meaning, the
concept Concepts are defined as abstract ideas A mental representation (or cognitive representation), in philosophy of mind Philosophy of mind is a branch of philosophy that studies the ontology and nature of the mind and its relationship with the bo ...

concept
or
idea In common usage and in philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosoph ...

idea
that a sign expresses or evokes # the ''referent'' – the actual
thing Thing or The Thing may refer to: Philosophy * An object (philosophy), object, being, or entity * Thing-in-itself (or ''noumenon''), the reality that underlies perceptions, a term coined by Immanuel Kant * Thing theory, a branch of critical the ...
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
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 writer of children's fiction, notably ''Alice's Adventures in Wonderland'' and its sequel ''Through the Looking-Glass'' ...

Lewis Carroll
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 Dualism most commonly refers to: * Mind–body dualism, a philosophical view which holds that mental phenomena are, at least in certain respects, not physical phenomena, or that the mind and the body are distinct and separable from one another ** P ...
versus
monism Monism attributes oneness or singleness (Greek: μόνος) to a concept e.g., 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., i ...
, 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 Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, la ...
. 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 wrote it. #It is possible that Aristotle did not tutor Alexander the Great. #Aristotle was pleased that he had a sister. To see that these are intensional, make the following substitutions: (1) "Mark Twain" → "The author of 'Corn-pone Opinions'"; (2) "Aristotle" → "the tutor of Alexander the Great"; (3) can be seen to be intensional given "had a sister" → "had a female sibling." 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 formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal sys ...
or for other special purposes and small fragments of natural languages.


Examples

#Mark Twain wrote ''Huckleberry Finn''. #Aristotle had a sister. 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 Predicate or predication may refer to: Computer science *Syntactic predicate (in parser technology) guidelines the parser process Linguistics *Predicate (grammar), a grammatical component of a sentence Philosophy and logic * Predication (philo ...
any other predicate belonging to Mark Twain and only to Mark Twain, without changing the logical value. For (2), likewise, consider the following substitutions: "Aristotle" → "The tutor of Alexander the Great"; "Aristotle" → "The author of the 'Prior Analytics'"; "had a sister" → "had a sibling with two X-chromosomes"; "had a sister" → "had a parent who had a female child".


See also

*
Description logic Description logics (DL) are a family of formal knowledge representation Knowledge representation and reasoning (KR², KR&R) is the field of artificial intelligence Artificial intelligence (AI) is intelligence demonstrated by machines, unlike ...
*
Connotation A connotation is a commonly understood cultural Culture () is an umbrella term which encompasses the social behavior Social behavior is behavior among two or more organisms within the same species, and encompasses any behavior in which o ...
*
Extension (predicate logic) The extension of a predicate Predicate or predication may refer to: Computer science *Syntactic predicate (in parser technology) guidelines the parser process Linguistics *Predicate (grammar), a grammatical component of a sentence Philosophy a ...
*
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 with ...
*
Intensional definition In logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label ...
*
Intensional logic Intensional logic is an approach to predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and ...
*
Montague grammar__notoc__ Montague grammar is an approach to natural language semantics Semantics (from grc, wikt:σημαντικός, σημαντικός ''sēmantikós'', "significant") is the study of meaning, reference, or truth. The term can be used to ...
* Temperature paradox *
Set-builder notation In set theory illustrating the intersection (set theory), intersection of two set (mathematics), sets. Set theory is a branch of mathematical logic that studies Set (mathematics), sets, which informally are collections of objects. Although any ...


Notes


References

*
Ferdinand de Saussure Ferdinand de Saussure (; ; 26 November 1857 – 22 February 1913) was a Swiss Swiss may refer to: * the adjectival form of Switzerland , french: Suisse(sse), it, svizzero/svizzera or , rm, Svizzer/Svizra , government_type = Fed ...

Ferdinand de Saussure
, ''
Course in General Linguistics ''Course in General Linguistics'' (french: Cours de linguistique générale) is a book compiled by Charles Bally and Albert Sechehaye from notes on lectures given by Ferdinand de Saussure at the University of Geneva between 1906 and 1911. It was ...
''. Open Court Classics, July 1986. * S. E. Palmer, ''Vision Science: From Photons to Phenomenology'', 1999. MIT Press,


External links

*
Chalmers, David
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)