Intensional

A large class of intensional statements, but by no means all, can be spotted from the fact that they contain intensional operators.

An intensional statement is a statement that is an instance of an intensional statement-form.

Classes of intensional definitions main A genus–differentia definition is a type of intensional definition that takes a large category (the genus) and narrows it down to a smaller category by a distinguishing characteristic (i.e. the differentia).

A non-intensional statement is also known as an extensional statement, since substitution of co-extensive expressions into it always preserves logical value.

Broadview Press, 1996. p. 49 Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which proceed by listing the objects that a term describes).

English, in common with every other natural language, is an intensional language.

He notes that this first "intensional definition" is simply "to drink", but that this is only a metaphor "much as English 'I see' often means the same as 'I understand'".

It will be noted that the intensional statements above feature expressions like "knows", "possible", and "pleased".

Significance Intensional languages cannot be given an adequate semantics in terms of the extensions of expressions in them, since the extensions themselves do not suffice to determine a logical value.

Such terms, it may be argued, are always intensional since they connote the property 'meaningless term' but this paradox does not constitute a counterexample to the claim that without intension a word has no meaning.

The notation with braces may also be used in an intensional specification of a set.

This generality comes at a steep price either typechecking is undecidable ( extensional type theory ), or extensional reasoning is more difficult ( intensional type theory ).