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Intension: Difference between revisions
Mention sense and reference
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For example, "a prime number less than 10" is an intensional definition, wheres "one of {2, 3, 5, 7}" is extensional. | For example, "a prime number less than 10" is an intensional definition, wheres "one of {2, 3, 5, 7}" is extensional. | ||
By extension, in semantics, an '''intensional''' ''interpretation'' of a phrase is one that | By extension, in semantics, an '''intensional''' ''interpretation'' of a phrase is one that retains the [[wikipedia:Sense_and_reference|sense]] of the words used, whereas an '''extensional''' interpretation is one that directly gets at the referent. | ||
For example, consider the phrase ''Clark Kent is Superman''. If both phrases are given an extensional interpretation, the phrase's denotation collapses to <math>x = x</math> for the man <math>x</math> denoted by "Clark Kent" and by "Superman". Handling noun phrases this way is the easiest option, but as we can see, it fails to capture the "intensional" essence of this sentence (an equality of two ''descriptions'') and collapses it down to a tautology (an equality between <math>x</math> and itself). | For example, consider the phrase ''Clark Kent is Superman''. If both phrases are given an extensional interpretation, the phrase's denotation collapses to <math>x = x</math> for the man <math>x</math> denoted by "Clark Kent" and by "Superman". Handling noun phrases this way is the easiest option, but as we can see, it fails to capture the "intensional" essence of this sentence (an equality of two ''descriptions'') and collapses it down to a tautology (an equality between <math>x</math> and itself). | ||