. 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.

The aim of this paper is to defend the Principle of Sufficient Reason (PSR). I analyse various versions of this principle (and their structure) and various ways of justifying it. Then I present and attempt to challenge some counterexamples allegedly refuting a universal application of the PSR. One can distinguish three versions of the PSR: for each state of affairs there is a sufficient reason for its obtaining (PSR-O); for each true proposition there is a direct or indirect justification (PSR-E); (...) for each state of affairs there exists an intellectual duty to search for a sufficient reason for obtaining of that state of affairs, and for each known true proposition - to search for its justification (PSR-M). There are standard and non-standard versions of the PSR-O. The PSR-O stand can be only valid if there are no chains of contingent reasons and outcomes with first modules, i.e. all chains are actually infinite. However, there are serious (yet debatable) arguments against the possibility of such infinity. The necessary condition of the PSR-O non-stand universal working is the existence of a necessary substance (thing): that substance would be a (free) reason of certain contingent states of affairs obtaining in its domain, and those states of affairs would then be reasons for all other contingent state of affairs and things. (The principle does not require a necessary substance to have its own reason). Limiting the chain of reasons to contingent states of affairs ended with a necessary state (if this state is a reason by necessity) would lead to the paradox of universal necessarism. An ontological \"cost\" of holding the PSR-O non-stand is a postulate of the existence of the necessary, supra-natural substance, i.e. God. However, there are serious advantages of the view which accepts that the PSR-O non-stand is generally valid: a nomological unity of the world and explanatory simplicity. (shrink)