134 found
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  1. 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. 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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  2.  82
    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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  3.  1
    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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  4.  29
    On Expandability of Models of Peano Arithmetic. I.Roman Murawski - 1976 - Studia Logica 35 (4):409-419.
  5.  27
    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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  6. 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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  7. 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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  8.  8
    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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  9.  6
    Recursive Functions and Metamathematics.Roman Murawski - 2002 - Studia Logica 70 (2):297-299.
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  10.  2
    Logos and Máthēma: Studies in the Philosophy of Mathematics and History of Logic.Roman Murawski - 2011 - 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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  11.  20
    On Expandability of Models of Peano Arithmetic. II.Roman Murawski - 1976 - Studia Logica 35 (4):421-431.
  12.  18
    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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  13. Contribution of Polish Logicians to Decidability Theory.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:211-231.
  14. Cantor's Philosophy of Set Theory.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:15-28.
  15.  50
    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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  16. Filozofia Matematyki Antologia Tekst'ow Klasycznych.Roman Murawski - 1994
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  17. 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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  18.  21
    Truth Vs. Provability – Philosophical and Historical Remarks.Roman Murawski - 2002 - Logic and Logical Philosophy 10:93.
  19.  12
    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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  20.  12
    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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  21.  12
    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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  22.  12
    Pointwise Definable Substructures of Models of Peano Arithmetic.Roman Murawski - 1988 - Notre Dame Journal of Formal Logic 29 (3):295-308.
  23.  38
    Review: Douglas 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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  24.  73
    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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  25.  5
    Philosophie der Mathematik.Thomas Bedürftig & Roman Murawski - 2010 - De Gruyter.
    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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  26.  1
    Philosophie der Mathematik.Thomas Bedürftig & Roman Murawski - 2010 - De Gruyter.
    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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  27.  1
    Philosophie der Mathematik.Thomas Bedürftig & Roman Murawski - 2010 - De Gruyter.
    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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  28. 2. Remarks On The Structuralistic Epistemology Of Mathematics.Izabella Bondecka-Krzykowska & Roman Murawski - 2006 - Logique Et Analyse 49:85-93.
     
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  29. Structuralism and Category Theory in the Contemporary Philosophy of Mathematics.Izabela Bondecka-Krzykowska & Roman Murawski - 2008 - Logique Et Analyse 51 (204):365.
  30. REVIEWS-Historical Dictionary of Logic.H. J. Gensler & Roman Murawski - 2007 - Bulletin of Symbolic Logic 13 (3).
  31. A Note on the Variety of Satisfaction Classes Roman Murawski Instytut Matematyki UAM, Ul Matejki 48/49, PL-60-769 Poznan, Poland Received December 7, 1988/in Revised Form March 2, 1990. [REVIEW]Roman Murawski - 1991 - Archive for Mathematical Logic 30:83.
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  32. Badania logiczne prowadzone w Uniwersytecie Poznanskim w latach 1945–1955.Roman Murawski - 2006 - Investigationes Linguisticae 13:1-12.
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  33. Contribution of Polish Logicians to Predicate Calculus.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:233-243.
     
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  34. Cantor, Pascal i Eudoksos (J.-L. Garides, \"Pascal entre Eudoxe et Cantor\", Paris 1984).Roman Murawski - 1986 - Studia Filozoficzne 244 (3).
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  35. Church's Thesis and its Epistemological Status.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:123-134.
  36. Dowód w matematyce — dziś i jutro.Roman Murawski - 2013 - Filozofia Nauki 21 (2).
    The paper is a review of the book by Krzysztof Wójtowicz, O pojęciu dowodu w matematyce [ On the Concept of Proof in Mathematics ]. It presents the main theses of the book and evaluates them.
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  37.  34
    Euphony and Logos: Essays in Honour of Maria Steffen-Batóg and Tadeusz Batóg.Roman Murawski & Jerzy Pogonowski (eds.) - 1997 - Rodopi.
    Contents: Preface. SCIENTIFIC WORKS OF MARIA STEFFEN-BATÓG AND TADEUSZ BATÓG. List of Publications of Maria Steffen-Batóg. List of Publications of Tadeusz Batóg. Jerzy POGONOWSKI: On the Scientific Works of Maria Steffen-Batóg. Jerzy POGONOWSKI: On the Scientific Works of Tadeusz Batóg. W??l??odzimierz LAPIS: How Should Sounds Be Phonemicized? Pawe??l?? NOWAKOWSKI: On Applications of Algorithms for Phonetic Transcription in Linguistic Research. Jerzy POGONOWSKI: Tadeusz Batóg's Phonological Systems. MATHEMATICAL LOGIC. Wojciech BUSZKOWSKI: Incomplete Information Systems and Kleene 3-valued Logic. Maciej KANDULSKI: Categorial Grammars with (...)
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  38.  3
    Essays in the Philosophy and History of Logic and Mathematics.Roman Murawski (ed.) - 2010 - Rodopi.
    The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the (...)
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  39. E.L. Post And The Development Of Logic.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:183-193.
  40. Filozofia logiki i matematyki w Kole Krakowskim.Roman Murawski - 2014 - Filozofia Nauki 22 (2):21-36.
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  41. Filozofia Matematyki I Logiki W Lwowskiej Szkole Matematycznej.Roman Murawski - 2011 - Przeglad Filozoficzny - Nowa Seria 78.
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  42. From the History of the Concept of Number.Roman Murawski & Thomas Bedürftig - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:95-122.
     
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  43. Grassmann's Contribution to Mathematics.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:161-168.
  44. Giuseppe Peano and Symbolic Logic.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:169-182.
  45. Historical Dictionary of Logic. [REVIEW]Roman Murawski - 2007 - Bulletin of Symbolic Logic 13 (3):370-370.
  46. Hoene-Wroński - Genius or Madman?Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:149-160.
  47. Henryk Struve I Władysław Biegański – Między Tradycyjną a Nową Logiką.Roman Murawski - 2015 - Przeglad Filozoficzny - Nowa Seria 93.
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  48. JOSEPH R. SHOENFIELD, Degrees of unsolvability. [REVIEW]Roman Murawski - 1975 - Studia Logica 34:284.
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  49. John Von Neumann and Hilbert's School.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:195-209.
  50. Kilka uwag o dowodzie w matematyce.Roman Murawski - 2013 - Filozofia Nauki 21 (1).
    The aim of the paper is to study the role and features of proofs in mathematics. Formal and informal proofs are distinguished. It is stressed that the main roles played by proofs in mathematical research are verification and explanation. The problem of the methods acceptable in informal proofs, in particular of the usage of computers, is considered with regard to the proof of the Four-Color Theorem. The features of in-formal and formal proofs are compared and contrasted. It is stressed that (...)
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