Intensions

[Andreas Nolda]

Dear subscribers,

Integrational Semantics makes abundant use of intensions: properties 
and intensional relations are assumed in the intension of potential 
concepts (word meanings), sentence meanings are conceived as 
intensional relations between potential utterances and potential 
speakers, etc.

The nature of these intensions, however, has been left unspecified:

   We shall leave it undecided how exactly relations-in-intension and
   properties are to be construed, whether in the way proposed by
   Richard Montague or in some other way.   (Lieb 1980: 126)

Montague conceives intensions as functions from possible worlds to 
extensional entities. Thus, two intensions are identical if their 
values are identical for every possible world.

According to another explication of "intension", which is due to 
Carnap, intensions are identical if they are logically equivalent. 
According to common assumptions, logically true statements hold in 
every possible world (and logically false statements hold in no 
possible world). Thus, the conceptions of Montague and Carnap 
amount to the same identity conditions for intensions.

Now, as far as I can see, constructing intensions along these lines 
leads to problems in Integrational Semantics. Consider the following 
two properties:

(1)  the property of not being identical with oneself

(2)  the property of being circular as well as non-circular

Let us assume that in no possible world there is anything which has 
(1) or (2). Thus, (1) and (2) have the same value for every possible 
world: that is, the empty set.

Equivalently, we may assume, that "for every x, x has (1) if and only 
if x has (2)" is a logically true statement.

In other words, according to Montague's and Carnap's conceptions, (1) 
and (2) are identical: they are the 'contradictory property' or 'null 
property'.

As a consequence, given that (1) and (2) make up the intension of two 
possible concepts (say, .non-identical with oneself. and .circular 
and non-circular.), both concepts are identical, too. Despite the 
somewhat artifical nature of the examples, this consequence is quite 
unwelcome.

Similar problems arise when assuming intensions of some kind 
(intensional relations or states-of-affairs) as the content of 
propositional attitudes like 'believe' or 'communicate'.

The reason for these problems is obvious: they result -- as far as 
natural language is concerned -- from a counter-intuitive conception 
of intensions. For, according to the ordinary-language use of 
"property", (1) and (2) clearly are different properties.

Therefore I'd claim that Montague's (or Carnap's) conception of 
intensions is too weak for Integrational Semantics. What we need are 
'hyper-intensions' or something of the kind.

Andreas Nolda

Reference

Lieb, Hans-Heinrich (1980). Syntactic meanings. In _Speech Act Theory 
and Pragmatics_, ed. by John R. Searle, Ferenc Kiefer, and Manfred 
Bierwisch, Synthese Language Library 10, Dordrecht: Reidel, 121-153.
-- 
Andreas Nolda      http://www2.hu-berlin.de/linguistik/institut/nolda/

Humboldt-Universität zu Berlin
Philosophische Fakultät II
Institut für deutsche Sprache und Linguistik