Examples of possible theological influences upon the development of mathematics are indicated. The best known connection can be found in the realm of infinite sets treated by us as known or graspable, which constitutes a divine-like approach. Also the move to treat infinite processes as if they were one finished object that can be identified with its limits is routine in mathematicians, but refers to seemingly super-human power. For centuries this was seen as wrong and even today some philosophers, for (...) example Brian Rotman, talk critically about “theological mathematics”. Theological metaphors, like “God’s view”, are used even by contemporary mathematicians. While rarely appearing in official texts they are rather easily invoked in “the kitchen of mathematics”. There exist theories developing without the assumption of actual infinity the tools of classical mathematics needed for applications (For instance, Mycielski’s approach). Conclusion: mathematics could have developed in another way. Finally, several specific examples of historical situations are mentioned where, according to some authors, direct theological input into mathematics appeared: the possibility of the ritual genesis of arithmetic and geometry, the importance of the Indian religious background for the emergence of zero, the genesis of the theories of Cantor and Brouwer, the role of Name-worshipping for the research of the Moscow school of topology. Neither these examples nor the previous illustrations of theological metaphors provide a certain proof that religion or theology was directly influencing the development of mathematical ideas. They do suggest, however, common points and connections that merit further exploration. (shrink)
Temptation and Free Will. A Solution to the Problem of the Relationship Between Human Free Will and God’s Omniscience The article aims to show that none of the today discussed positions concerning the relationship between human free will and God’s omniscience—determinism, compatibilism, molinism and libertarianian revisionism—is an adequate solution and proposes a position to some extent resembling Kant’s solution to his Third Antinomy, where he made the distinction between subject as causa phenomenon and subject as causanoumenon. God possesses not only (...) an absolute knowledge concerning all processes and events in the world, but He also has a full knowledge concerning what all human subjects will decide to do. Nevertheless, His absolute knowledge in this sense is compatible with human freedom, because ‘real freedom’ is ‘located’—as a causality of freedom—in individual human natures which already exist in eternity and of which our actual inner experience gives us only a ‘sensual scheme’ (Kant). Human persons are tempted by different life experiences which they receive, i.e. they are tested by God and it cannot be excluded that some of these personal essences will turn out to be only illusory and in this sense will be condemned. For all other persons worldly experience was planned by God as a necessary element of their future eternal life. Keywords:God, omniscience, freedom, determinism, eternal life, persons. (shrink)
Contacts of the two logicians are listed, and all Gödel's written mentions of Tarski's work are quoted. Why did Gödel almost never mention Tarski's definition of truth in his notes and papers? This puzzle of Gödel's silence, proposed by Feferman, is not merely biographical or psychological but has interesting connections to Gödel's philosophical views.No satisfactory answer is given by the three “standard” explanations: no need to repeat the work already done; Tarski's achievement was obvious to Gödel; Gödel's exceptional caution. In (...) fact, , Tarski had done the work, but Gödel almost never mentioned the achievement; , the obviousness is no explanation for the omission of Tarski's work in contexts in which an application of the definition of satisfaction was useful, and even necessary; , the point was not just caution: if Gödel had felt the need to mention the program of scientific semantics he could easily have done that in his manuscripts, or in conversations.Three ideas, detectable in Gödel's approach, can help us understand Gödel's silence: the idea of truth as the intuitive provability in the most general sense; defining it set-theoretically would contribute nothing. the idea of truth as an inexhaustible idea in the sense of Kant; “truth in general” is a category that must be applicable to all kinds of sentential expressions; also, while for Gödel language was secondary, Tarski's definition is focused on language. the idea of logic as the universal language, in Hintikka's sense, as opposed to the perception of logic as a reinterpretable calculus; hence the thesis that semantics is inexpressible. Gödel always remains a Platonist who asks a natural question: what does really happen in the realm of abstract objects? (shrink)
Stanislaw Lesniewski’s interests were, for the most part, more philosophical than mathematical. Prior to taking his doctorate at Jan Kazimierz University in Lvov, Lesniewski had spent time at several continental universities, apparently becoming relatively attached to the philosophy of one of his teachers, Hans Comelius, to the chapters of John Stuart Mill’s System of Logic that dealt specifically with semantics, and, in general, to studies of general grammar and philosophy of language. In these several early interests are already to be (...) found the roots of the work that was to occupy Lesniewski’s life: a search for a definitive doctrine of what sorts of things there are in the world, or better, of what language must be like if it is adequately and efficiently to represent the world. (shrink)
The paper deals with the nature of internal experience. The views on this subject appear in I. Kant, J.G. Fichte, E. Husserl, and K. Rahner. The author seeks to prove that internal experience is an intuitive experience in which the subject presents to himself or herself in the so-called intellectual inspection (intellektuelle Anschaung). The subject has the feature of atemporality (nunc status) and is capable of transcending each content while preserving its identity. ..Speculation\" means reflection: the structure of the person (...) of God is reflected in internal experience. He is semper stans. These views are compared with the standpoint of fourteenth-century mystics (J. Eckhart, J. Tauler, H. Suzo) about the so-called ground of the soul (Seelengrund). (shrink)
Three chapters contain the results independent of each other. In the first chapter I present a set of axioms for the propositional calculus which are shorter than the ones known so far, in the second one I give a method of defining all ternary connectives, in the third one, I prove that the probability of propositional functions is preserved under reversible substitutions.
Stanisław Brzozowski formulated the ideal of modern man in the polemic with the contemporary man, who has ceased to believe in truth and moral values and is devoid of the will to act. For Brzozowski modernity involves the discovery of truth about the human condition: about man as an autonomous subject, a creator of values, who struggles with non-human reality. This truth was formulated in Kant’s idea of autonomy and in Marx’ idea of a collective conquest of the world (...) of nature. For Brzozowski, ideal modern man is “the conscious labourer,” who labours because he wants to proudly impose a human law on the non-human world. At the same time Brzozowski used the term “modernity” to describe life of constant change in the modern world, understood as a set of results of man’s reign over nature. For the sake of human maturity, Brzozowski expected the truly modern man to perceive modern life as an unquestionable value. Undoubtedly, there is an evident tension in Brzozowski’s ideal of modern man between the affirmation of creativity in the world of change and the necessity of disciplined production, including unchangeable moral foundations of labour. There is also a major shift in this ideal, stemming from Brzozowski’s change of attitude towards religion. (shrink)
The first part of the paper_ outlines the development of causality in Greek philosophy. Some remarks are made on how some medieval philosophers approached to the problem. The paper shows also how modern philosophy understood causation. The paper inquires into the characteristics of causal relation as it is accepted in the domain of modern and recent physics. In the second part of the paper one finds some remarks concerning the programme of construing a new system CI of logic of causal (...) propositions. This system is adequate to the manner in which causality is presented in physics. The system CI is being construed to characterize the connective of relativistic conditionals ‘$\rightsquigarrow$’ by means of the methods of recent logic. This connective should be read as follows: ‘if …, then for that reason …’. The arguments of the connective ‘$\rightsquigarrow$’ may be propositional formulas describing a particular event. The new system of non-classical logic is based on the classical propositional calculus, on the one of systems of temporal logic, and on a system ZI of logic of change. The findings concerning causation, as outlined in the first part of the paper, constitute descriptive semantics of the system CI presented in the second part of the paper. This system may play a positive role in the indirect justification of theorems in philosophy in a broad sense. (shrink)
This book introduces the English-speaking reader to the thought of Stanislaw Brzozowski (1878-1911), the outstanding Polish philosopher and literary critic. Although practically unknown in the West, Brzozowski is an important but neglected forerunner of the intellectual tradition of `Western Marxism', most commonly associated with Georg Lukács and Antonio Gramsci. -/- Concentrating first on the early phase of Brzozowski's thought, Professor Walicki goes on to analyse his ideas on the working class and its relation to the intelligentsia and contemporary working-class ideologies. (...) Finally he deals with aspects of his thought which go beyond the Marxian problematic and round off the intellectual portrait of the man. -/- Brzozowski's anti-naturalistic approach resulted in a radical reinterpretation of Marxism which dealt with many of the problems of the revolt against positivism in European philosophy. Professor Walicki argues that the retrieval of the philosophical and humanist aspect of Marxism, and its separation from the Engels-inspired `scientific Marxism', was the achievement of Brzozowski and not, as frequently assumed, of Lukács, who came to similar conclusions only some ten years later. -/- By placing Brzozowski within the cross-currents of the various philosophical, sociological, literary, and political streams of Western and Eastern European thought in which Marxism was situated, Professor Walicki produces a fascinating study of an early East European challenge to orthodox Marxism. (shrink)
Historically, Ehrenfest’s theorem is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form, and we highlight its generalizations to the relativistic Dirac particle and to a particle with spin and izospin. We argue that apparent classicality of the macroscopic world can probably be explained within the framework of standard quantum mechanics.
Stanislaw Lem, Philosopher of the Future is a revealing and instructive guide to the philosophical fiction of Stanislaw Lem. Throughout the book, Swirski builds a framework of philosophical and scientific concepts within which Lem’s works should be read, in particular its most significant aspect: Lem’s unyielding concern for knowledge supported by his conviction that literature is an epistemologically valuable tool for exploring reality. Swirski offers a rich background to Lem's litrary career and unravels the depths of Lem’s philosophical fiction.