In any of several fields of study that treat the use of signs—for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language—an intension is any property or quality connoted by a word, phrase, or another symbol. In the case of a word, the word's definition often implies an intension. For instance, the intensions of the word plant include properties such as "being composed of cellulose (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 or idea 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 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, 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. 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 sibling with two X-chromosomes."
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 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 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 whose body was capable of producing egg cells"; "had a sister" → "had a parent who had a female child".
See also
- Description logic
- Connotation
- Extension (predicate logic)
- Extensionality
- Intensional definition
- Intensional logic
- Montague grammar
- Temperature paradox
Notes
- Antony Flew (1979). Dictionary of Philosophy. p. 117.
- Putnam, Hilary (1973). "Meaning and Reference". The Journal of Philosophy. 70 (19): 699–711. doi:10.2307/2025079. JSTOR 2025079.
- Simon Blackburn, Oxford Dictionary of Philosophy, 132-33
- Carnap, Rudolf (April 1955). "Meaning and synonymy in natural languages". Philosophical Studies. 6 (3): 33–47. doi:10.1007/BF02330951. ISSN 0031-8116. S2CID 170508331.
References
- Ferdinand de Saussure, Course in General Linguistics. Open Court Classics, July 1986. ISBN 0-8126-9023-0
- S. E. Palmer, Vision Science: From Photons to Phenomenology, 1999. MIT Press, ISBN 0-2621-6183-4
External links
- Chalmers, David, "On Sense and Intension".
- Rapaport, William J., "Intensionality v. Intentionality".
In any of several fields of study that treat the use of signs for example in linguistics logic mathematics semantics semiotics and philosophy of language an intension is any property or quality connoted by a word phrase or another symbol In the case of a word the word s definition often implies an intension For instance the intensions of the word plant include properties such as being composed of cellulose not always true alive and organism among others A comprehension is the collection of all such intensions OverviewThe 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 or idea 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 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 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 formsA 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 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 sibling with two X chromosomes 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 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 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 whose body was capable of producing egg cells had a sister had a parent who had a female child See alsoDescription logic Connotation Extension predicate logic Extensionality Intensional definition Intensional logic Montague grammar Temperature paradoxSense and reference Set builder notationNotesAntony Flew 1979 Dictionary of Philosophy p 117 Putnam Hilary 1973 Meaning and Reference The Journal of Philosophy 70 19 699 711 doi 10 2307 2025079 JSTOR 2025079 Simon Blackburn Oxford Dictionary of Philosophy 132 33 Carnap Rudolf April 1955 Meaning and synonymy in natural languages Philosophical Studies 6 3 33 47 doi 10 1007 BF02330951 ISSN 0031 8116 S2CID 170508331 ReferencesFerdinand de Saussure Course in General Linguistics Open Court Classics July 1986 ISBN 0 8126 9023 0 S E Palmer Vision Science From Photons to Phenomenology 1999 MIT Press ISBN 0 2621 6183 4External linksChalmers David On Sense and Intension Rapaport William J Intensionality v Intentionality
