Jan Wolenski

.  This papers examines formal properties of logical squares and their generalizations in the form of hexagons and octagons. Then, several applications of these constructions in philosophical analysis are elaborated. They concern contingency (accidentality), possibility, permission, axiological concepts (bonum and malum), the generalized Hume thesis (deontic and epistemic modalities), determinism, truth and consistency (in various senses. It is shown that relations between notions used in various branches of philosophy fall into the same formal scheme.

Abstract.The authors concentrate on the analysis of the concept of permission. After a general account of differing concepts of permission both with regard to different legal theories and to different legal ideologies, they argue in favour of a “radical” imperativism which leaves no place for permissive norms. Thus, in contrast with the logic of normative language (LNL) purported by Alchourrón and Bulygin, the authors figure out a system of deontic logic ‐ supplemented by devices of the possible world semantics ‐ according to which a normative system (N) is conceived as a set of logical consequences of a certain finite set of basic obligations and no room is left either for the concept of weak permission or for the concept of strong permission. Finally the authors raise some criticisms concerning the view maintained by Alchourron and Bulygin on strong permission.*