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Logos and Máthēma

Studies in the Philosophy of Mathematics and History of Logic

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Roman Murawski

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert’s program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Gödel’s theorems and computer science, philosophy of mathematics in Polish mathematical and logical schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory.

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Part IV: Mathematical Logic in Poland

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Part IV Mathematical Logic in Poland Stanisław Piątkiewicz and the Beginnings of Mathematical Logic in Poland Co-authored by Tadeusz Batóg The paper presents information on the life and work of Stanisław Piątkiewicz (1849– ?). His Algebra w logice [Algebra in Logic] of 1888 contains an exposition of the algebra of logic and its use in representing syllogisms. This was the first original Polish publication on symbolic logic. It appeared 20 years before analogous works by Łukasiewicz and Stamm. 1. Traditional Views on the Origins of Mathematical Logic in Poland The successes of Polish logic after the First World War stimulated several authors to investigate its origins. All of them credited the beginnings of logic in Poland to Kazimierz Twardowski (1866–1938), who founded the Lvov-Warsaw school of philosophy while a professor at Lvov University, and to Jan Łukasiewicz (1878– 1956), a logician who was a professor of philosophy at Warsaw University. Thus Adjukiewicz, for example, wrote in (1934, p 401): “Łukasiewicz, well-educated not only in philosophy but also in mathematics, became a discoverer of logistic for Poland. Perhaps this resulted from the influence of Twardowski, who was the first in Poland to speak about the algebra of logic, doing so in his universi- ty lectures in [...] 1899–1900”. Likewise, Ingarden remarked in (1938, p. 28): “Twardowski was the first in Poland [...] to lecture about new attempts to reform logic”. Other authors writing on this subject have generally accepted the claims of Ajdukiewicz and Ingarden. Such was...

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