This is a companion article to the translation of ‘Zasada sprzeczności a logika symboliczna’, the appendix on symbolic logic of Jan Łukasiewicz's 1910 book O zasadzie sprzeczności u Arytotelesa (On the Principle of Contradiction in Aristotle). While the appendix closely follows Couturat's 1905 book L'algebra de la logique (The Algebra of Logic), footnotes show that Łukasiewicz was aware of the work of Peirce, Huntington and Russell (before Principia Mathematica). This appendix was influential in the development of the Polish school of (...) logic, directly inspiring Stanisław Leśniewski and Leon Chwistek and more widely by serving as a text of the new symbolic logic. This appendix was an important source of the dominant algebraic logic in Poland, but also indicates that Łukasiewicz appreciated Russell's axiomatic approach to logic. (shrink)

The triangle in general or the man as such are general objects. These are objects that possess the properties common to all the individual objects in their range. Stanisław Leśniewski and Tadeusz Kotarbiński, two Polish philosophers and logicians belonging to the Lvov-Warsaw School, produced several proofs aiming to show that such objects are impossible because the principles that govern them lead to a contradiction. In this paper I first clarify the structure of their proofs. Then I suggest a way to (...) elude their conclusion. In order to do that I use two Meinongian distinctions: the distinction between complete and incomplete objects, on the one hand, and the distinction between nuclear and extranuclear properties, on the other hand. I claim first that general objects are incomplete objects, i.e. they do not satisfy the ontological principle of the excluded middle, and second that the principle that governs the relations between the properties of general objects and the properties of the individual objects in their range should be restricted to nuclear properties. (shrink)

With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...