Page 351 - Encyclopedia of Philosophy of Language

In the Republic, Plato distinguishes between the objects a class-name applies to and the idea or concept associated with that name. This distinction has figured in philosophy ever since, be it under different names. In the logic treatises of Port-Royal, one respectively spoke of the extension and comprehension of a class- name, while Leibniz preferred the terms 'extension' and 'intension.' Other pairs of terms which are used for this purpose are Mill's 'denotation-connotation' and Frege's 'reference-sense,' but Leibniz's ter- minology is adopted here.
Frege (1892) argues that the distinction should also be made to apply to sentences, proper names, and definite descriptions and due to the work of Monta- gue, among others, all linguistic categories are attri- buted with intensions and extensions. In general terms the extension of an expression is what it refers to, while its intension is the way in which this extension is presented (see the tables in Intensionality).
1. Extensionality versus Intensionality
Whatever its intension may be, the extension of a sentence is often taken to be a truth value; i.e., either true or false (other possibilities are sometimes con- sidered as well). Extensionally, the meaning of a sen- tence consists of its truth conditions: the conditions which a situation has to satisfy in order to make the sentence true.
That extensions do not in general suffice to give a satisfactory compositional semantics, has been argued most forcefully by Frege (1892). In an extensional semantics, expressions with identical extensions can be substituted for each other within a sentence pre- serving its truth value. But plainly this is not always so, as is shown by the invalidity of the following argu- ment:
Isolde thinks that Tristan is admirable.
Tristan is the murderer of Isolde's fiance,
not .'. Isolde thinks that the murderer of her fiance is
admirable.
Even if the extension of the proper name Tristan, i.e., Tristan himself, is identical to the extension of the definite description, 'the murderer of Isolde's fiance,' the first premiss may be true and the conclusion false.
2. Matters of Priority
When formalizing these notions, one has to ask what
comes first: the intension or the extension of an expression? In the literature one finds three answers to this question. The work in the tradition of Frege, Carnap, and Montague reduces intensions to exten- sion, while property theories take the inverse route. In turn, nominalists like Quine 'unask' the question. According to them intensions should be disallowed to begin with, since such obscure abstract objects lack explanatory power.
Above, the extension and intension of an expression are distinguished as follows: the extension is what the expression refers to and its intension is the manner in which its extension is presented. Of course, these descriptions are vague, but there are different pro- posals to make these notions more precise.
The most influential theory is that of Richard Mon- tague. In his intensional type logic, Montague defines intensions in terms of extensions using the tools of possible worlds semantics. On this view, the intension of an expression is a rule that allows one to determine its extension in each context. For convenience, con- texts are taken to be possible worlds, which are per- haps best thought of as conceivable alternatives to the actual world, but richer contexts are used as well. The intensions are identified as functions from contexts to extensions in a context. For example, the intension of a common noun is a function from possible worlds to sets of individuals, whereas the proposition expressed by a sentence is a function from possible worlds to truth values, or, equivalently,a set of possible worlds. Since sets themselves are highly extensional objects— they are fully determined by their elements—this man- ner of modeling propositions immediately leads to the problem of omniscience when combined with a principle of compositionality. Within such a frame- work, attitude verbs like 'to doubt' denote relations among an individual and a proposition. It follows that if a doubts p, he cannot escape doubting all sentences that also denote p. For example, the sentence, 'Fer- mat's last theorem is true' is either equivalent with 'two plus two is four,' if the theorem holds, or with 'two plus two is three,' if it does not. Let us suppose the theorem is true, then it still does not follow from, 'Fanny doubts that Fermat's last theorem is true' that 'Fanny doubts that two plus two is four.' Similar problems arise with regard to other intensional contexts.
In Property theories one works on the assumption that intensions are primitive notions, not to be defined in terms of more basic ones. Extensions in contrast should be derived from intensions by means of the two-place relation, 'applies to,' which is also primitive.
Intension J. van der Does
Intension
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