Toward a new theory of content. (English) Zbl 0842.03022

Bealer, George

Casati, Roberto (ed.) et al., Philosophy and the cognitive sciences. Proceedings of the 16th international Wittgenstein symposium, 15-22 August 1993, Kirchberg am Wechsel, Austria. Vienna: Hölder-Pichler-Tempsky. Schriftenreihe der Wittgenstein-Gesellschaft. 21, 179-192 (1994).

Taking Donnellan’s and Kripke’s refutation of Frege’s distinction between sense and reference concerning proper names as granted, an algebraic approach is proposed towards a solution of the “that”-clause puzzle: “how can \(\ulcorner \text{that } A(a)\urcorner\) and \(\ulcorner \text{that }A(b)\urcorner\) refer to different propositions when the names \(\ulcorner a\urcorner\) and \(\ulcorner b\urcorner\) are co-referential” (p. 179).
The algebraic approach is preferred because it is not reductionistic (contrary to its alternatives, the possible-worlds theory, the propositional-function theory and the propositional-complex theory). In order to obtain an intensional model for the predicate calculus, the Boolean algebra \(\langle D, K, \text{disj, conj, neg, exist, }\tau, F, T\rangle\) is proposed, with \(D\) as the union of denumerably many disjoint subdomains \(D_{-1}\) (particulars), \(D_0\) (propositions), \(D_1\) (properties), \(D_2\) (binary relations-in-intension), \(D_n\) (\(n\)-ary relations-in-intension). \(K\) stands for the set of possible extensionalization functions; disj, conj, neg, exist behave similar to the respective logical particles; \(\tau\) gives a set of further operations; \(F\) and \(T\) are similar to the truth values.
This structure is applied to the leading theories of definite descriptions by Frege, Russell, Evans and Prior, discussing Frege’s theory in some detail. It is used for sketching a theory of propositions, based on non-Platonic modes of presentation and applied especially to proper names. The article closes with applications of this theory to several naming puzzles including the one mentioned in the beginning.
For the entire collection see [Zbl 0849.00032].

Reviewer: V.Peckhaus (Erlangen)

MSC:

03B65	Logic of natural languages
03A05	Philosophical and critical aspects of logic and foundations
06E25	Boolean algebras with additional operations (diagonalizable algebras, etc.)
68T50	Natural language processing

Keywords:

“that”-clause puzzle; Boolean algebra; theories of definite descriptions; propositions; proper names; naming puzzles