The Role of Modal Functors at the Initial Stage of Construing the Non-Fregean Logic

Abstract

Roman Suszko emphasised several times that the non-Fregean logic that he created is supposed to be a formal reconstruction of the view of the world proposed by L. Wittgenstein in his Logical-Philosophical Treatise.

In the article an attempt was made at clarifying the role played by modal functors at the initial stage of construing this logic. First it pointed to the fact that most particular axioms or theorems connected with these functors may be found in T. Feys’ system and in Lewis’ modal systems. Next, in view of what some axioms, theorems or definitions accepted by Suszko express, the author tried to establish what relations are expressed by the necessity and possibility functors. In the course of this, various difficulties were revealed that made it impossible to interpret these functors in an unambiguous way.