THE LOGICS OF ANALYTIC EQUIVALENCE
Marek Nowak · 2008
A notion of so-called analytic equivalence is considered, in the form of Suszko's connective of propositional identity. Two axiomatic strengthenings of the Sen- tential Calculus with Identity of Suszko involving that connective are presented. Both realize the following principle due to Wojcicki: two sentences whose logical forms in sentential language are logically equivalent and have the same sentential variables, express the same proposition. The paper is devoted to some axiomatic strengthenings of the SCI logic of Suszko. These logics can be viewed as possible formalizations (in the framework of Suszko) of some important notion of the identity of proposi- tions expressed by sentences (or situations described by sentences). This notion was introduced by Wojcicki in (13) (however mentioned earlier in (11, 12) and later independently considered by Vanderveken, cf. for exam- ple (8, 9) and Bi lat (3, 4)) by means of the principle: two sentences whose logical forms in sentential language are logically equivalent and have the same sentential variables, describe the same situation (that is, according to our understanding, express the same proposition). Wojcicki's principle (hereafter called WP ) on the one hand, is a particularization of the princi- ple considered by Barwise and Perry (1): two sentences whose logical forms are logically equivalent and have the same extralogical constants, desribe the same situation, on the other hand, is a weakening of some criterion of identity of propositions known in Polish literature as Wittgenstein's prin- ciple (cf. (10)): two sentences whose logical forms are logically equivalent express the same proposition. Nowadays Wittgenstein's principle is rather rejected as leading, in a presence of some other principles, by so-called