115 found
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  1.  41
    Undefinability of Truth. The Problem of Priority:Tarski Vs Gödel.Roman Murawski - 1998 - 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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  2.  11
    On Expandability of Models of Peano Arithmetic. I.Roman Murawski - 1976 - Studia Logica 35 (4):409-419.
  3.  8
    On Expandability of Models of Peano Arithmetic. II.Roman Murawski - 1976 - Studia Logica 35 (4):421-431.
  4. On Chwistek’s Philosophy of Mathematics.Roman Murawski - 2011 - Russell: The Journal of Bertrand Russell Studies 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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  5.  36
    Główne koncepcje i kierunki filozofii matematyki XX wieku.Roman Murawski - 2003 - Zagadnienia Filozoficzne W Nauce 33.
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  6.  15
    Between Theology and Mathematics. Nicholas of Cusa’s Philosophy of Mathematics.Roman Murawski - 2016 - Studies in Logic, Grammar and Rhetoric 44 (1):97-110.
  7.  15
    Some Properties of the Family of Expansions to Models of A2−/Δ11 + Σ11-AC.Roman Murawski - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (17):265-272.
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  8.  16
    Some Remarks on the Structure of Expansions.Roman Murawski - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (34-35):537-546.
  9.  14
    Iterations of Satisfaction Classes and Models of Peano Arithmetic.Roman Murawski - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):59-84.
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  10.  15
    Some More Remarks on Expandability of Initial Segments.Roman Murawski - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (25-30):445-450.
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  11.  15
    Trace Expansions of Initial Segments.Roman Murawski - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (30):471-476.
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  12.  9
    On Expandability of Models of Peano Arithmetic. III.Roman Murawski - 1977 - 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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  13.  4
    Truth Vs. Provability – Philosophical and Historical Remarks.Roman Murawski - 2002 - Logic and Logical Philosophy 10:93.
  14.  48
    Gödel's Incompleteness Theorems and Computer Science.Roman Murawski - 1997 - 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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  15.  9
    Reviews. [REVIEW]Marian Przełęcki, Roman Murawski & Witold Marciszewski - 1975 - Studia Logica 34 (3):275-291.
  16.  11
    Books Received. [REVIEW]Jan Woleński, Roman Murawski & Adam Grobler - 1995 - Studia Logica 54 (1):129-137.
  17.  11
    Kant o matematyce [recenzja].Roman Murawski - 2004 - Zagadnienia Filozoficzne W Nauce 34.
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  18.  20
    Review of D. Patterson, Alfred Tarski: Philosophy of Language and Logic[REVIEW]Roman Murawski - 2013 - Journal for the History of Analytical Philosophy 1 (9).
    Review of Douglas Patterson. Alfred Tarski: Philosophy of Language and Logic.
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  19.  32
    Philosophy of Mathematics in the Warsaw Mathematical School.Roman Murawski - 2010 - 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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  20.  4
    Some Historical, Philosophical and Methodological Remarks on Proof in Mathematics.Roman Murawski - 2016 - In Peter Schuster & Dieter Probst (eds.), Concepts of Proof in Mathematics, Philosophy, and Computer Science. De Gruyter. pp. 251-268.
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  21.  15
    Mathematical Objects and Mathematical Knowledge.Roman Murawski - 1996 - Grazer Philosophische Studien 52:257-259.
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  22.  12
    Jan Woleński, Essays on Logic and its Applications in Philosophy.Roman Murawski - 2012 - Polish Journal of Philosophy 6 (1):106-108.
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  23.  10
    Cracow Circle and Its Philosophy of Logic and Mathematics.Roman Murawski - 2015 - 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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  24. Philosophy of Mathematics in the 20th Century: Main Trends and Doctrines.Roman Murawski - 2006 - 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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  25.  11
    Benedykt Bornstein’s Philosophy of Logic and Mathematics.Roman Murawski - 2014 - 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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  26.  8
    Undefinability Vs. Definability of Satisfaction and Truth.Roman Murawski - 1999 - 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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  27.  15
    Philosophy of Mathematics.Roman Murawski - 2009 - Polish Journal of Philosophy 3 (1):145-147.
  28.  8
    A Correction to the Paper “on Expandability of Models of Peano Arithmetic. I”.Roman Murawski - 1977 - Studia Logica 36 (3):237-237.
  29.  7
    Some Remarks on the Structure of Expansions.Roman Murawski - 1980 - Mathematical Logic Quarterly 26 (34‐35):537-546.
  30.  6
    Iterations of Satisfaction Classes and Models of Peano Arithmetic.Roman Murawski - 1992 - Mathematical Logic Quarterly 38 (1):59-84.
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  31.  7
    Troubles with (the Concept of) Truth in Mathematics.Roman Murawski - 2006 - 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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  32.  6
    The Development of Symbolism in Logic and Its Philosophical Background.Roman Murawski - 1988 - Proceedings of the Aristotelian Society 89 (1):65 - 78.
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  33.  4
    The Contribution of Zygmunt Ratajczyk to the Foundations of Arithmetic.Roman Murawski - 1995 - 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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  34.  4
    Satisfaction Classes-a Survey.Roman Murawski - 1997 - Poznan Studies in the Philosophy of the Sciences and the Humanities 57:259-282.
  35.  3
    A Note on the Variety of Satisfaction Classes.Roman Murawski - 1990 - Archive for Mathematical Logic 30 (2):83-89.
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  36.  3
    Kilka Słów o Dowodzie W Matematyce.Roman Murawski - 2013 - Filozofia Nauki 21 (1 (81)):7-22.
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  37.  3
    Appendix to the Paper “Definable Sets and Expansions of Models of Peano Arithmetic”.Roman Murawski - 1990 - Archive for Mathematical Logic 30 (2):91-92.
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  38.  4
    Philosophical Reflection on Mathematics in Poland in the Interwar Period.Roman Murawski - 2004 - 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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  39.  3
    Some More Remarks on Expandability of Initial Segments.Roman Murawski - 1986 - Mathematical Logic Quarterly 32 (25‐30):445-450.
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  40.  4
    Review of M. D. Resnik (Ed.), Mathematical Objects and Mathematical Knowledge[REVIEW]Roman Murawski - 1996 - Grazer Philosophische Studien 52:257-259.
  41.  2
    Definable Sets and Expansions of Models of Peano Arithmetic.Roman Murawski - 1988 - 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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  42.  2
    Some Properties of the Family of Expansions to Models of A 2−/Δ 11 + Σ 11‐AC.Roman Murawski - 1991 - Mathematical Logic Quarterly 37 (17):265-272.
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  43.  2
    The Contribution of Polish Logicians to Recursion Theory.Roman Murawski - 1998 - In Katarzyna Kijania-Placek & Jan Woleński (eds.), The Lvov-Warsaw School and Contemporary Philosophy. Kluwer Academic Publishers. pp. 265--282.
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  44.  2
    Pointwise Definable Substructures of Models of Peano Arithmetic.Roman Murawski - 1988 - Notre Dame Journal of Formal Logic 29 (3):295-308.
  45.  1
    A Correction to the Ppaer "On Expandability of Models of Peano Arithmetic. I" Studia Logica 35 (1976), Pp. 409-419.Roman Murawski - 1977 - Studia Logica 36 (3):237 -.
  46.  1
    Trace Expansions of Initial Segments.Roman Murawski - 1984 - Mathematical Logic Quarterly 30 (30):471-476.
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  47.  1
    Generalizations and Strengthenings of Gödel's Incompleteness Theorem.Roman Murawski - 1987 - In Jan T. J. Srzednicki (ed.), Initiatives in Logic. M. Nijhoff. pp. 84--100.
  48.  1
    Hilbert's Program: Incompleteness Theorems Vs. Partial Realizations.Roman Murawski - 1994 - In Jan Wolenski (ed.), Philosophical Logic in Poland. Kluwer Academic Publishers. pp. 103--127.
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  49.  1
    Mathematical Knowledge.Roman Murawski - 2004 - In M. Sintonen, J. Wolenski & I. Niiniluoto (eds.), Handbook of Epistemology. Kluwer Academic Publishers. pp. 571--606.
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  50. 1. Auf dem Weg zu den reellen Zahlen.Thomas Bedürftig & Roman Murawski - 2015 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. De Gruyter. pp. 6-27.
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