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  1.  15
    Philosophy of Mathematics.Roman Murawski & Thomas Bedürftig (eds.) - 2018 - De Gruyter.
    The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems (...)
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  2.  35
    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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  3. 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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  4.  25
    Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Gödel's Theorems.Rod J. L. Adams & Roman Murawski - 1999 - Dordrecht, Netherland: Springer Verlag.
    Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.
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  5.  11
    The Philosophy of Mathematics and Logic in the 1920s and 1930s in Poland.Roman Murawski - 2014 - Basel: Imprint: Birkhäuser.
    The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing (...)
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  6.  12
    Mechanization of Reasoning in a Historical Perspective.Witold Marciszewski & Roman Murawski (eds.) - 1995 - Brill | Rodopi.
    This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section of (...)
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  7.  37
    On expandability of models of Peano arithmetic. I.Roman Murawski - 1976 - Studia Logica 35 (4):409-419.
  8.  18
    Proof vs Truth in Mathematics.Roman Murawski - 2020 - Studia Humana 9 (3-4):10-18.
    Two crucial concepts of the methodology and philosophy of mathematics are considered: proof and truth. We distinguish between informal proofs constructed by mathematicians in their research practice and formal proofs as defined in the foundations of mathematics (in metamathematics). Their role, features and interconnections are discussed. They are confronted with the concept of truth in mathematics. Relations between proofs and truth are analysed.
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  9. Tarski his Polish predecessors on Truth.Jan Wolenski & Roman Murawski - 2008 - In Douglas Patterson (ed.), New essays on Tarski and philosophy. Oxford University Press. pp. 21--43.
     
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  10.  30
    On expandability of models of Peano arithmetic. II.Roman Murawski - 1976 - Studia Logica 35 (4):421-431.
  11.  24
    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. Boston: De Gruyter. pp. 251-268.
  12.  64
    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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  13.  23
    The Connections Between the Lvov-Warsaw School and the University in Poznań.Roman Murawski - unknown
    Lvov-Warsaw School in Philosophy – as the very name suggests – was connected mainly with two academic centers: universities in Lvov and Warsaw. However, it had a broader impact. The members of this school were active also at other universities, in particular in Cracow, Vilnius and Poznań. The aim of the paper is to present and analyze the connections of Lvov-Warsaw School with the University in Poznań.
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  14.  21
    Mathematics and Theology in the Thought of Nicholas of Cusa.Roman Murawski - 2019 - Logica Universalis 13 (4):477-485.
    Nicholas of Cusa was first of all a theologian but he was interested also in mathematic and natural sciences. In fact philosophico-theological and mathematical ideas were intertwined by him, theological and philosophical ideas influenced his mathematical considerations, in particular when he considered philosophical problems connected with mathematics and vice versa, mathematical ideas and examples were used by him to explain some ideas from theology. In this paper we attempt to indicate this mutual influence. We shall concentrate on the following problems: (...)
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  15.  8
    Logos and máthēma: studies in the philosophy of mathematics and history of logic.Roman Murawski - 2011 - New York: Peter Lang.
    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, Goedel's theorems and computer science, philosophy of mathematics in Polish mathematical and logical (...)
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  16.  5
    Seweryna Łuszczewska-Romahnowa.Roman Murawski & Jerzy Pogonowski - 2018 - In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Cham, Switzerland: Springer- Birkhauser,. pp. 241-247.
    The paper is devoted to the description of life and scientific achievements as well as the influence of Seweryna Łuszczewska-Romahnowa.
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  17.  23
    On Chwistek’s Philosophy of Mathematics.Roman Murawski - 2011 - Russell: The Journal of Bertrand Russell Studies 31 (1):121-130.
    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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  18.  19
    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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  19.  41
    Truth vs. provability – philosophical and historical remarks.Roman Murawski - 2002 - Logic and Logical Philosophy 10:93.
  20.  38
    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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  21.  8
    Filozofia matematyki: antologia tekstów klasycznych.Roman Murawski (ed.) - 1986 - Poznań: Uniwersytet im. Adama Mickiewicza w Poznaniu.
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  22.  22
    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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  23.  21
    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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  24.  22
    Pointwise definable substructures of models of Peano arithmetic.Roman Murawski - 1988 - Notre Dame Journal of Formal Logic 29 (3):295-308.
  25.  3
    100 Years of Logical Investigations at the University of Poznań.Roman Murawski - 2024 - Studia Humana 13 (1):28-38.
    The aim of this paper is to describe the history of logical investigations at the University of Poznań. The organisational structures within the discipline as well as the outstanding logicians and their achievements are presented. Connections with the Lviv–Warsaw School are indicated.
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  26.  6
    1. Auf dem Weg zu den reellen Zahlen.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 6-27.
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  27.  10
    2. Aus der Geschichte der Philosophie und Mathematik.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 28-159.
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  28.  6
    A. Infinitesimal denken und rechnen.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 387-427.
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  29.  10
    5. Axiomatik und Logik.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 315-371.
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  30.  3
    Begriffsverzeichnis.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 458-465.
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  31.  4
    3. Über Grundfragen der Philosophie der Mathematik.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 160-269.
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  32.  8
    Einleitung.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 1-5.
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  33.  7
    Kurzbiographien.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 428-439.
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  34.  4
    Literaturverzeichnis.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 440-451.
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  35.  5
    4. Mengen und Mengenlehren.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 270-314.
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  36.  4
    Personenverzeichnis.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 452-456.
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  37.  20
    Philosophie der Mathematik.Thomas Bedürftig & Roman Murawski - 2010 - Boston: De Gruyter. Edited by Roman Murawski.
    Dieses Werk gibt eine überwiegend elementare Einführung in philosophische Probleme und Hintergründe des mathematischen Denkens und Sprechens, Lehrens und Lernens. Sie wendet sich an Lehrende und Studierende der Mathematik und der Philosophie. Ausgangspunkt und immer wieder Bezugspunkt sind die reellen Zahlen. In pointierter Weise werden mathematische und philosophische Probleme und Fragen vermerkt, die sich auf dem Weg zu ihnen stellen. Ein umfangreicher Abriss von Auffassungen aus der Geschichte der Mathematik und der Philosophie bis hin zu aktuellen Strömungen bildet den Hintergrund (...)
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  38.  9
    Philosophie der Mathematik.Thomas Bedürftig & Roman Murawski - 2010 - Boston: De Gruyter. Edited by Roman Murawski.
    Dieses Werk gibt eine überwiegend elementare Einführung in philosophische Probleme und Hintergründe des mathematischen Denkens und Sprechens, Lehrens und Lernens. Sie wendet sich an Lehrende und Studierende der Mathematik und der Philosophie. Ausgangspunkt und immer wieder Bezugspunkt sind die reellen Zahlen. In pointierter Weise werden mathematische und philosophische Probleme und Fragen vermerkt, die sich auf dem Weg zu ihnen stellen. Ein umfangreicher Abriss von Auffassungen aus der Geschichte der Mathematik und der Philosophie bis hin zu aktuellen Strömungen bildet den Hintergrund (...)
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  39.  7
    Philosophie der Mathematik.Thomas Bedürftig & Roman Murawski - 2010 - Boston: De Gruyter. Edited by Roman Murawski.
    Dieses Werk gibt eine überwiegend elementare Einführung in philosophische Probleme und Hintergründe des mathematischen Denkens und Sprechens, Lehrens und Lernens. Sie wendet sich an Lehrende und Studierende der Mathematik und der Philosophie. Ausgangspunkt und immer wieder Bezugspunkt sind die reellen Zahlen. In pointierter Weise werden mathematische und philosophische Probleme und Fragen vermerkt, die sich auf dem Weg zu ihnen stellen. Ein umfangreicher Abriss von Auffassungen aus der Geschichte der Mathematik und der Philosophie bis hin zu aktuellen Strömungen bildet den Hintergrund (...)
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  40.  6
    6. Rückblick.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 372-386.
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  41.  3
    Symbolverzeichnis.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter. pp. 457-457.
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  42.  3
    Vorwort zur 3. Auflage.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter.
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  43.  4
    Vorwort zur 2. Auflage.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter.
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  44.  4
    Vorwort zur 1. Auflage.Thomas Bedürftig & Roman Murawski - 2010 - In Thomas Bedürftig & Roman Murawski (eds.), Philosophie der Mathematik. Boston: De Gruyter.
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  45. 2. Remarks On The Structuralistic Epistemology Of Mathematics.Izabella Bondecka-Krzykowska & Roman Murawski - 2006 - Logique Et Analyse 49:85-93.
     
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  46. Structuralism and category theory in the contemporary philosophy of mathematics.Izabela Bondecka-Krzykowska & Roman Murawski - 2008 - Logique Et Analyse 51 (204):365.
  47.  6
    REVIEWS-Historical dictionary of logic.H. J. Gensler & Roman Murawski - 2007 - Bulletin of Symbolic Logic 13 (3):370-371.
  48.  15
    5. Axiomatic Approach and Logic.Roman Murawski & Thomas Bedürftig - 2018 - In Roman Murawski & Thomas Bedürftig (eds.), Philosophy of Mathematics. De Gruyter. pp. 293-346.
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  49.  17
    A correction to the paper “on expandability of models of peano arithmetic. I”.Roman Murawski - 1977 - Studia Logica 36 (3):237-237.
  50.  11
    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 -.
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