Page 354 - Encyclopedia of Philosophy of Language

Formal Semantics
A Fregean theory of meaning has a tripartite charac- ter: it combines a theory of the extensions of expressions with one of their intension and their force. Sentence (1), for instance, has a truth value as its extension—it is either true or false—while its intension is the thought it expresses.
William will buy this Breitner. (1)
The force of a sentence determines its function. In particular, (1) can be used to assert that the thought it expresses is true, but one could also use the cor- responding interrogative to query whether that thought is true; similarly for promises, commands, and the like.
In logical semantics it is often assumed that the intension of an expression is the core of its meaning,
so that most proposals in this area are intensional. In particular, work in the tradition of Richard Montague is based on this presumption. The force of an expression, in contrast, is the locus of much research in speech act theory.
Prior to discussing intensional phenomena in more detail, Table 1 gives the intension of some important classes of expressions:
the context f"(x) is opaque if the corresponding sub- stitution principle fails. This is in contradistinction to the so-called 'transparent' or 'extensional contexts' for which these substitution principles do hold. For example, the context 'x compiled a thesaurus' is trans- parent, as the following valid reasoning indicates:
Roget compiled a thesaurus.
Roget is Romilly's grandfather.
.'. Romilly's grandfather compiled a thesaurus.
It is far from true that all expressions are extensional. Herearesomeconstructionswhichgiverisetoopaque contexts, together with examples which show that they violate the principle of extensionality:
Quotation. Sentence (4) does not follow from (2) and (3):
1
The gladiator spoke the words 'Ave Caesar. (2)
Caesar is Gaius Julius. (3)
The gladiator spoke the words 'Ave Gaius Julius.' (4)
Indirect speech. Sentence (7) does not follow from (5) and (6):
Harry said that John kissed Mary. (5)
John is the smartest boy in the class. (6)
Harry said that the smartest boy in the class
kissed Mary. (7)
Propositional attitudes, i.e., relations denoted by verbs like 'to discover,' 'to believe,' 'to suspect,' and 'to know.' Sentence (10) does not follow from (8) and (9):
The detective knows that the thief entered
through the skylight. (8)
Biggies is the thief. (9)
The detective knows that Biggies entered
through the skylight. (10)
Intensions, i.e., relations denoted by verbs such as 'to look for,' 'to wish for,' and the like. Sentence (13) does not follow from (11) and (12):
John is looking for the supreme commander of the Armed Forces of the United States of America. (11)
The President of the United States of America is the supreme commander of the United States
Armed Forces. (12)
John is looking for the President of the United States
of America. (13)
Temporal designation. Sentence (16) does not follow from (14) and (15):
Table 1.
Expression
proper names, definite descriptions
sentences common nouns,
intransitive verbs transitive verbs
determiners conjunctions
Intension individuals
propositions first-order properties
two-place relation between individuals and properties of sets of individuals
two-place relations between properties
two-place functions from propositions to propositions
A more formal account of the references associated with these categories is given below.
1. Opaque Contexts
Intensional constructions are constructions which violate a principle of extensionality:
If t=f, then [t/x]t"(x) = [t'/x]t"(x)
(Here, the notion of substituting a term t for a free variable x in a term t' is employed; notation: [//*]/')• Following Quine, these intensional constructions are said to create 'opaque' or 'intensional contexts.' So
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Intensionality J. van der Does