Сөздер мен символдардың мағыналық қасиеттері

Property or quality connoted by a word, phrase, or another symbol
referential context

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.

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.

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.

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.

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.

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".