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Logos and Máthēma

Studies in the Philosophy of Mathematics and History of Logic


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 III: Philosophy of Mathematics in Poland


Part III Philosophy of Mathematics in Poland The Philosophy of Hoene-Wroński 15th August 1803, the catholic Feast of the Assumption played a significant roˆle in the scientific biography of Hoene-Wroński (1776–1853). On that day, during a ball on the occasion of birthday of the First Consul, Wroński experienced an illumination. In remembrance of this he assumed a new name – Maria. Two problems stood in the center of Wroński’s interests: – the creation of a new philosophy – achrematic philosophy1 which overco- ming the world of things will reach the Absolute and the creation principles in order to deduce from them a logically consistent theory of the whole reality, – a profound reconstruction of the system of science, a beginning of which should be a reform of mathematics (the latter should consists of deducing all domains of mathematics from a unique general principle, namely from “the absolute law of algorithm”). We are interested here mainly in the first problem. 1. Predecessors and Contemporaries Philosophical system of Hoene-Wroński developed at the turn of the 18th and 19th centuries is usually counted as a messianistic philosophy. This philosophy was established under the influence of German thinkers such as Kant , Fichte, Schelling and Hegel. But it has various specific features making it different than German thought. It was rather spiritualistic than idealistic, it maintained the existence of a personalistic God, was convinced of the eternity of soul, of the absolute superiority of spiritual powers over the corporal ones. Hoene-Wroński...

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