Towards leibnizian possibility. Formal frame of modal theory of individual concepts
Towards leibnizian possibility. Formal frame of modal theory of individual concepts

Summary/Abstract: In the presented analyses we propose a formal complement to a certain version of the semantics of possible worlds inspired by Leibniz’s ideas and provide an adequate logic of it. As the starting point we take the approach of Benson Mates (Leibniz on possible worlds). Mates refers to Leibniz’ philosophy, but also uses tools of contemporary semantics of possible worlds and elaborates on an original conception of predication due to which possible worlds can be identified with collections of certain concepts, and not individuals. We complete a fragmentary description given by Mates in order to analyze if his conception allows for the establishment of this specific idea of a possible world. Our first step is to define a notion of the individual concept and describe possible world semantics in which possible worlds consist of individual concepts of compossible individuals (s-worlds). Our second step is to choose some version of modal free logic with the identity (S5MFLID), which is complete in our reformulation of Mates’ semantics. The connections between standard interpretation of S5MFLID and semantics inspired by Mates show that our logic does not distinguish s-worlds from i-worlds – counterparts of s-worlds that are collections of individuals.

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