Die theoretische Logik, auch mathematische oder symbolische Logik genannt, ist eine Ausdehnung der fonnalen Methode der Mathematik auf das Gebiet der Logik. Sie wendet fUr die Logik eine ahnliche Fonnel­ sprache an, wie sie zum Ausdruck mathematischer Beziehungen schon seit langem gebrauchlich ist. In der Mathematik wurde es heute als eine Utopie gelten, wollte man beim Aufbau einer mathematischen Disziplin sich nur der gewohnlichen Sprache bedienen. Die groBen Fortschritte, die in der Mathematik seit der Antike gemacht worden sind, sind zum (...) wesentlichen Teil mit dadurch bedingt, daB es gelang, einen brauchbaren und leistungsfahigen Fonnalismus zu finden. - Was durch die Formel­ sprache in der Mathematik erreicht wird, das solI auch in der theoretischen Logik durch diese erzielt werden, namlich eine exakte, wissenschaftliche Behandlung ihres Gegenstandes. Die logischen Sachverhalte, die zwischen Urteilen, Begriffen usw. bestehen, finden ihre Darstellung durch Formeln, deren Interpretation frei ist von den Unklarheiten, die beim sprachlichen Ausdruck leicht auftreten konnen. Der Dbergang zu logischen Folgerungen, wie er durch das SchlieBen geschieht, wird in seine letzten Elemente zerlegt und erscheint als fonnale Umgestaltung der Ausgangsfonneln nach gewissen Regeln, die den Rechenregeln in der Algebra analog sind; das logische Denken findet sein Abbild in einem LogikkalkUl. Dieser Kalkiil macht die erfolgreiche Inangriffnahme von Problemen moglich, bei denen das rein inhaltliche Denken prinzipiell versagt. Zu diesen gehort z. B. (shrink)

This paper reports some attempts undertaken in Poland in the 1930s to modernize Thomism by means of modern logic. In particular, it concerns J.M. Bocheski and J. Salamucha, the leading members of the CracowCircle. They attempted to give precise logical form to the Five Ways of Thomas Aquinas. Other works concerned the concept of transcendentals, the levels of abstraction, and the concept of essence.

The paper is devoted to the presentation of Chwistek’s philosophical ideas concerning logic and mathematics. The main feature of his philosophy was nominalism, which found full expression in his philosophy of mathematics. He claimed that the object of the deductive sciences, hence in particular of mathematics, is the expression being constructed in them according to accepted rules of construction. He treated geometry, arithmetic, mathematical analysis and other mathematical theories as experimental disciplines, and obtained in this way a nominalistic interpretation of (...) them. The fate of Chwistek’s philosophical conceptions was similar to the fate of his logical conceptions. The system of rational meta-mathematics was not developed by him in detail. He worked on his own ideas without any collaboration with other logicians, mathematicians or philosophers. His investigations were not in the mainstream of the development of logic and philosophy of mathematics. (shrink)

Jan Salamucha was born on the 10th of June 1903 in Warsaw and murdered on the 11th of August 1944 in Warsaw during the Warsaw Uprising very early on in his scholarly career. He is the most original representative of the branch of the Lvov-Warsaw School known as the Cracow Circle. The Circle was a grouping of scholars who were interested in reconstructing scholasticism and Christian philosophy in general by means of mathematical logic. As Jan Lukasiewicz’s successor in the area (...) of logic and Konstanty Michalski’s student in the area of the history of medieval thought, Salamucha had an excellent preparation for this task. His main achievements include a masterful logical analysis of the proof _ex motu _for the existence of God, a modern interpretation of analogical notions and a comprehensive approach to the problem of essence. He also contributed several historical studies: he examined Aristotle’s theory of deduction, he reconstructed William Ockham’s propositional logic and established the authenticity of his treatise on _insolubilia,_ and he identified the historical sources of the antinomies in Antiquity and the Middle Ages. He did not shy away from popularizing philosophy, and in that work he was able to elucidate rather than oversimplify the complexities of philosophy. (shrink)