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 Maarten Maartensz:    Philosophical Dictionary | Filosofisch Woordenboek                      

 E - Extension


 
Extension: In semantics: The things a term is true of, in some reality or domain; the range of a predicate.

This then is contrasted with the intension of a term.

It should be noted that extensions may come to vary: Once there were many Mohicans; then there was the last of the Mohicans; and then there were no Mohicans at all.

Also, some extensions of some terms may be infinite ('natural number', 'real number'), and if Cantor is right there are - in some sense - infinities of infinitely many sizes. (See: Set theory)

Another noteworthy point is that the extension of a predicate or relation (such as 'is green' or 'loves') is not quite the same sort of thing as the extension of a name, at least intuitively.

And variables have no extension, but their constant substituends do.

Also, it should be noted that, while the extension of a term in the defined sense (whatever things the term stands for, can be used to refer to) seems fairly clear and intuitive, some of its uses in model theory, formal logic and mathematics may be less clear and intuitive, especially if they involve the assumption that extensions invariably are sets or classes (thereby inviting a lot of set theory) or the assumption that the complement of an extension (whatever things the term is not true of) is as unproblematic as the extebsion itself. This last assumption may well be false, e.g. if one speaks of infinities.

 


See also: Intension, Intuitionism, Name


Literatuur:

Carnap, Frege, Quine, Leonard, Lyons,

 Original: Aug 31, 2004                                                Last edited: 12 December 2011.   Top