. 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.

. Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition (...) is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. (shrink)

Thomas Hobbes took a new look at the ways in which society should function, and he ended up formulating the concept of political science. His crowning achievement, Leviathan, remains among the greatest works in the history of ideas. Written during a moment in English history when the political and social structures as well as methods of science were in flux and open to interpretation, Leviathan played an essential role in the development of the modern world. This edition of Hobbes' landmark (...) work is based on the original text. It incorporates the author's own corrections and retains the period spelling and punctuation, offering both flavorful authenticity and the utmost clarity of expression. (shrink)

The concept of right (jus) as a moral power is traced in Leibniz's earliest to latest philosophical work.