111 found
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  1.  7
    Roman Murawski (1976). On Expandability of Models of Peano Arithmetic. I. Studia Logica 35 (4):409 - 419.
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  2.  28
    Roman Murawski (1998). Undefinability of Truth. The Problem of Priority:Tarski Vs Gödel. History and Philosophy of Logic 19 (3):153-160.
    The paper is devoted to the discussion of some philosophical and historical problems connected with the theorem on the undefinability of the notion of truth. In particular the problem of the priority of proving this theorem will be considered. It is claimed that Tarski obtained this theorem independently though he made clear his indebtedness to Gödel?s methods. On the other hand, Gödel was aware of the formal undefinability of truth in 1931, but he did not publish this result. Reasons for (...)
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  3. Roman Murawski (2011). On Chwistek’s Philosophy of Mathematics. Russell 31 (1).
    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 (...)
     
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  4.  17
    Roman Murawski (2003). Główne koncepcje i kierunki filozofii matematyki XX wieku. Zagadnienia Filozoficzne W Nauce 33.
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  5.  6
    Jan Woleński, Roman Murawski & Adam Grobler (1995). Books Received. [REVIEW] Studia Logica 54 (1):129-137.
  6.  7
    Roman Murawski (2015). Cracow Circle and Its Philosophy of Logic and Mathematics. Axiomathes 25 (3):359-376.
    The paper is devoted to the presentation and analysis of the philosophical views concerning logic and mathematics of the leading members of Cracow Circle, i.e., of Jan Salamucha, Jan Franciszek Drewnowski and Józef Maria Bocheński. Their views on the problem of possible applicability of logical tools in metaphysical and theological researches is also discussed.
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  7.  19
    Roman Murawski (2013). Review of D. Patterson, Alfred Tarski: Philosophy of Language and Logic. [REVIEW] Journal for the History of Analytical Philosophy 1 (9).
    Review of Douglas Patterson. Alfred Tarski: Philosophy of Language and Logic.
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  8.  41
    Roman Murawski (1997). Gödel's Incompleteness Theorems and Computer Science. Foundations of Science 2 (1):123-135.
    In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.
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  9.  7
    Roman Murawski (1976). On Expandability of Models of Peano Arithmetic. II. Studia Logica 35 (4):421 - 431.
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  10.  3
    Marian Przełęcki, Roman Murawski & Witold Marciszewski (1975). Reviews. [REVIEW] Studia Logica 34 (3):275-291.
  11.  4
    Roman Murawski (2004). Kant o matematyce [recenzja]. Zagadnienia Filozoficzne W Nauce 34.
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  12.  9
    Roman Murawski (2014). Benedykt Bornstein’s Philosophy of Logic and Mathematics. Axiomathes 24 (4):549-558.
    The aim of this paper is to present and discuss main philosophical ideas concerning logic and mathematics of a significant but forgotten Polish philosopher Benedykt Bornstein. He received his doctoral degree with Kazimierz Twardowski but is not included into the Lvov–Warsaw School of Philosophy founded by the latter. His philosophical views were unique and quite different from the views of main representatives of Lvov–Warsaw School. We shall discuss Bornstein’s considerations on the philosophy of geometry, on the infinity, on the foundations (...)
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  13.  12
    Roman Murawski (2011). Mathematical Objects and Mathematical Knowledge. Grazer Philosophische Studien 52:257-259.
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  14.  8
    Roman Murawski (1977). On Expandability of Models of Peano Arithmetic. III. Studia Logica 36 (3):181 - 188.
    Already after sending the first two parts of this paper ([5], [6]) to the editor, two new results on the subject have appeared — namely the results of G. Wilmers and Z. Ratajczyk. So for the sake of completeness let us review them here.
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  15.  26
    Roman Murawski (2010). Philosophy of Mathematics in the Warsaw Mathematical School. Axiomathes 20 (2-3):279-293.
    The aim of this paper is to present and discuss the philosophical views concerning mathematics of the founders of the so called Warsaw Mathematical School, i.e., Wacław Sierpiński, Zygmunt Janiszewski and Stefan Mazurkiewicz. Their interest in the philosophy of mathematics and their philosophical papers will be considered. We shall try to answer the question whether their philosophical views influenced their proper mathematical investigations. Their views towards set theory and its rôle in mathematics will be emphasized.
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  16.  7
    Roman Murawski (2012). Jan Woleński, Essays on Logic and its Applications in Philosophy. Polish Journal of Philosophy 6 (1):106-108.
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  17.  22
    Roman Murawski (2006). Philosophy of Mathematics in the 20th Century: Main Trends and Doctrines. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):331-347.
    The aim of the paper is to present the main trends and tendencies in the philosophy of mathematics in the 20th century. To make the analysis more clear we distinguish three periods in the development of the philosophy of mathematics in this century: (1) the first thirty years when three classical doctrines: logicism, intuitionism and formalism were formulated, (2) the period from 1931 till the end of the fifties - period of stagnation, and (3) from the beginning of the sixties (...)
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  18.  3
    Roman Murawski (1990). A Note on the Variety of Satisfaction Classes. Archive for Mathematical Logic 30 (2):83-89.
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  19.  5
    Roman Murawski (1977). A Correction to the Paper “on Expandability of Models of Peano Arithmetic. I”. Studia Logica 36 (3):237-237.
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  20.  5
    Roman Murawski (1980). Some Remarks on the Structure of Expansions. Mathematical Logic Quarterly 26 (34‐35):537-546.
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  21.  5
    Roman Murawski (1988). The Development of Symbolism in Logic and Its Philosophical Background. Proceedings of the Aristotelian Society 89:65 - 78.
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  22. Roman Murawski (1976). On Expandability of Models of Peano Arithmetic. I. Studia Logica 35 (4):409-419.
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  23.  11
    Roman Murawski (2009). Philosophy of Mathematics. Polish Journal of Philosophy 3 (1):145-147.
  24.  5
    Roman Murawski (2007). Troubles with (the Concept of) Truth in Mathematics. Logic and Logical Philosophy 15 (4):285-303.
    In the paper the problem of definability and undefinability of the concept of satisfaction and truth is considered. Connections between satisfaction and truth on the one hand and consistency of certain systems of omega-logic and transfinite induction on the other are indicated.
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  25.  2
    Roman Murawski (2013). Kilka Słów o Dowodzie W Matematyce. Filozofia Nauki 21 (1 (81)):7-22.
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  26.  2
    Roman Murawski (1998). The Contribution of Polish Logicians to Recursion Theory. In Katarzyna Kijania-Placek & Jan Woleński (eds.), The Lvov-Warsaw School and Contemporary Philosophy. Kluwer Academic Publishers 265--282.
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  27.  2
    Roman Murawski (1990). Appendix to the Paper “Definable Sets and Expansions of Models of Peano Arithmetic”. Archive for Mathematical Logic 30 (2):91-92.
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  28.  3
    Roman Murawski (1992). Iterations of Satisfaction Classes and Models of Peano Arithmetic. Mathematical Logic Quarterly 38 (1):59-84.
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  29.  4
    Roman Murawski (2004). Philosophical Reflection on Mathematics in Poland in the Interwar Period. Annals of Pure and Applied Logic 127 (1-3):325-337.
    In the paper the views and tendencies in the philosophical reflection on mathematics in Poland between the wars are analyzed. Views of most outstanding representatives of Lvov–Warsaw Philosophical School and of Polish Mathematical School are presented. Their influence on logical and mathematical researches is considered.
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  30.  3
    Roman Murawski (1997). Satisfaction Classes-a Survey. Poznan Studies in the Philosophy of the Sciences and the Humanities 57:259-282.
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  31. Roman Murawski (1976). On Expandability of Models of Peano Arithmetic. II. Studia Logica 35 (4):421-431.
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  32.  3
    Roman Murawski (2004). Truth Vs. Provability – Philosophical and Historical Remarks. Logic and Logical Philosophy 10:93.
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  33.  2
    Roman Murawski (1986). Some More Remarks on Expandability of Initial Segments. Mathematical Logic Quarterly 32 (25‐30):445-450.
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  34.  2
    Roman Murawski (1988). Pointwise Definable Substructures of Models of Peano Arithmetic. Notre Dame Journal of Formal Logic 29 (3):295-308.
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  35.  1
    Roman Murawski (1988). Definable Sets and Expansions of Models of Peano Arithmetic. Archive for Mathematical Logic 27 (1):21-33.
    We consider expansions of models of Peano arithmetic to models ofA 2 s -¦Δ 1 1 +Σ 1 1 −AC which consist of families of sets definable by nonstandard formulas.
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  36.  1
    Roman Murawski (1987). Generalizations and Strengthenings of Gödel's Incompleteness Theorem. In Jan T. J. Srzednicki (ed.), Initiatives in Logic. M. Nijhoff 84--100.
  37.  1
    Roman Murawski (1994). Hilbert's Program: Incompleteness Theorems Vs. Partial Realizations. In Jan Wolenski (ed.), Philosophical Logic in Poland. Kluwer 103--127.
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  38.  1
    Roman Murawski (2004). Mathematical Knowledge. In M. Sintonen, J. Wolenski & I. Niiniluoto (eds.), Handbook of Epistemology. Kluwer 571--606.
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  39.  1
    Roman Murawski (1991). Some Properties of the Family of Expansions to Models of A 2−/Δ 11 + Σ 11‐AC. Mathematical Logic Quarterly 37 (17):265-272.
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  40.  1
    Roman Murawski (1999). Undefinability Vs. Definability of Satisfaction and Truth. Vienna Circle Institute Yearbook 6:203-215.
    Among the main theorems obtained in mathematical logic in this century are the so called limitation theorems, i.e., the Löwenheim-Skolem theorem on the cardinality of models of first-order theories, Gödel’s incompleteness theorems and Tarski’s theorem on the undefinability of truth. Problems connected with the latter are the subject of this paper. In Section 1 we shall consider Tarski’s theorem. In particular the original formulation of it as well as some specifications will be provided. Next various meanings of the notion of (...)
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  41.  1
    Roman Murawski (1995). The Contribution of Zygmunt Ratajczyk to the Foundations of Arithmetic. Notre Dame Journal of Formal Logic 36 (4):502-504.
    Zygmunt Ratajczyk was a deep and subtle mathematician who, with mastery, used sophisticated and technically complex methods, in particular combinatorial and proof-theoretic ones. Walking always along his own paths and being immune from actual trends and fashions he hesitated to publish his results, looking endlessly for their improvement.
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  42.  3
    Roman Murawski (1996). Review of M. D. Resnik (Ed.), Mathematical Objects and Mathematical Knowledge. [REVIEW] Grazer Philosophische Studien 52:257-259.
  43. Thomas Bedürftig & Roman Murawski (2015). 1. Auf dem Weg zu den reellen Zahlen. In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. De Gruyter 6-27.
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  44. Thomas Bedürftig & Roman Murawski (2015). 2. Aus der Geschichte der Philosophie und Mathematik. In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. De Gruyter 28-159.
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  45. Thomas Bedürftig & Roman Murawski (2015). A. Infinitesimal denken und rechnen. In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. De Gruyter 387-427.
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  46. Thomas Bedürftig & Roman Murawski (2015). 5. Axiomatik und Logik. In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. De Gruyter 315-371.
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  47. Thomas Bedürftig & Roman Murawski (2015). Begriffsverzeichnis. In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. De Gruyter 458-465.
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  48. Thomas Bedürftig & Roman Murawski (2015). 3. Über Grundfragen der Philosophie der Mathematik. In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. De Gruyter 160-269.
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  49. Thomas Bedürftig & Roman Murawski (2015). Einleitung. In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. De Gruyter 1-5.
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  50. Thomas Bedürftig & Roman Murawski (2015). Kurzbiographien. In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. De Gruyter 428-439.
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