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  1. Independence and Justification in Mathematics.Krzysztof Wójtowicz - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):349-373.
    In the article the problem of independence in mathematics is discussed. The status of the continuum hypothesis, large cardinal axioms and the axiom of constructablility is presented in some detail. The problem whether incompleteness is really relevant for ordinary mathematics and for empirical science is investigated. Another aim of the article is to give some arguments for the thesis that the problem of reliability and justification of new axioms is well-posed and worthy of attention. In my opinion, investigations concerning the (...)
     
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  2.  26
    O tzw. programie Gödla.Krzysztof Wójtowicz - 2001 - Zagadnienia Filozoficzne W Nauce 29.
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  3.  23
    Paradoksy skończoności.Krzysztof Wójtowicz - 1996 - Zagadnienia Filozoficzne W Nauce 18.
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  4.  22
    Throwing Spatial Light: On Topological Explanations in Gestalt Psychology.Bartłomiej Skowron & Krzysztof Wójtowicz - 2020 - Phenomenology and the Cognitive Sciences:1-22.
    It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is to (...)
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  5. Analiza antyrealizmu modalnego.Krzysztof Wójtowicz - 2000 - Filozofia Nauki 2.
    In the recent years we can observe a sort of renaissance of the philosophy of mathematics. More and more papers and books are published. A few years ago a new journal (Philosophia Mathematica) devoted exclusively to the philosophy of mathematics started appearing. In the contemporary discussions - especially in the context of the question of the applicability of mathematics to the description of the physical world - the issue of the existence and the ontological status of mathematical objects plays a (...)
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  6.  3
    A Stochastic Graphs Semantics for Conditionals.Krzysztof Wójtowicz & Anna Wójtowicz - forthcoming - Erkenntnis:1-35.
    We define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under (...)
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  7.  2
    A Stochastic Graphs Semantics for Conditionals.Krzysztof Wójtowicz & Anna Wójtowicz - forthcoming - Erkenntnis:1-35.
    We define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under (...)
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  8.  2
    A Stochastic Graphs Semantics for Conditionals.Krzysztof Wójtowicz & Anna Wójtowicz - forthcoming - Erkenntnis:1-35.
    We define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under (...)
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  9. Abstrakcyjna teoria modeli — semantyczne ujęcie logiki.Krzysztof Wójtowicz - 2015 - Filozofia Nauki 23 (2):69-82.
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  10. Czy matematyka jest niezbędna w nauce?Krzysztof Wójtowicz - 1994 - Filozofia Nauki 3.
    This article consists of the two parts: the first on presents Hartry Field's nominalistic theory of science contained in his „Science Without Numbers”. The second part points to certain difficulties, which the realization of Field's program is faced with. The problem of an exact translation of nominalistic theories to mathematical theories, the connection between the incompleteness of the nominalistic theory and the conservativeness of its mathematical extension and an example of a theorem about finite sets, which needs some strong assumptions (...)
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  11. Dowód matematyczny - argumentacja czy derywacja? - część I.Krzysztof Wójtowicz - 2011 - Zagadnienia Filozoficzne W Nauce 49.
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  12. Dowód matematyczny - argumentacja czy derywacja? - część II.Krzysztof Wójtowicz - 2011 - Zagadnienia Filozoficzne W Nauce 49.
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  13. Does Mathematical Possibility Imply Existence?Krzysztof Wójtowicz - 2019 - In Bartłomiej Skowron (ed.), Contemporary Polish Ontology. De Gruyter. pp. 161-180.
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  14.  22
    Dowód matematyczny z punktu widzenia formalizmu matematycznego. Część I.Krzysztof Wójtowicz - 2007 - Roczniki Filozoficzne 55 (2):123-139.
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  15.  17
    Dowód matematyczny z punktu widzenia formalizmu matematycznego. Część II.Krzysztof Wójtowicz - 2007 - Roczniki Filozoficzne 55 (2):139-153.
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  16. Dlaczego Nie Ma Matematycznych Możliwych Światów?Krzysztof Wójtowicz - 2008 - Przeglad Filozoficzny - Nowa Seria 66.
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  17. Die Reverse Mathematics und ihre philosophische Relevanz.Krzysztof Wöjtowicz - 2001 - Philosophia Naturalis 38 (1):121-144.
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  18.  23
    Filozofia matematyki Gödla na tle neopozytywistycznej koncepcji matematyki.Krzysztof Wójtowicz - 2004 - Zagadnienia Filozoficzne W Nauce 34.
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  19. Filozofia Matematyki J.S. Milla.Krzysztof Wójtowicz - 2006 - Przeglad Filozoficzny - Nowa Seria 60.
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  20. Filozofia Matematyki Quine’a a Kwantyfikatory Henkina I Boolosa.Krzysztof Wójtowicz - 2008 - Przeglad Filozoficzny - Nowa Seria 68.
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  21. Inspiracje empirystyczne w filozofii matematyki. Część I.Krzysztof Wójtowicz - 2015 - Filozofia Nauki 23 (3).
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  22.  28
    Kilka uwag na temat zagadnienia Czas a matematyka [dyskusja].Krzysztof Wójtowicz - 2000 - Zagadnienia Filozoficzne W Nauce 26.
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  23. Kilka uwag o twierdzeniu Gödla i intensjonalności.Krzysztof Wójtowicz - 2001 - Filozofia Nauki 4.
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  24. Kilka uwag o problemie niezależności w matematyce.Krzysztof Wójtowicz - 2002 - Przeglad Filozoficzny - Nowa Seria 41 (1):65-82.
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  25.  2
    Kategoria wyjaśniania a filozofia matematyki Gödla.Krzysztof Wójtowicz - 2018 - Studia Semiotyczne 32 (2):107-129.
    Artykuł dotyczy zagadnienia, w jakim sensie można stosować kategorię wyjaśnienia do interpretacji filozofii matematyki Kurta Gödla. Gödel – jako realista matematyczny – twierdzi bowiem, że w wypadku matematyki mamy do czynienia z niezależnymi od nas faktami. Jednym z owych faktów jest właśnie rozwiązywalność wszystkich dobrze postawionych problemów matematycznych – i ten fakt domaga się wyjaśnienia. Kluczem do zrozumienia stanowiska Gödla jest identyfikacja założeń, na których się opiera: metafizyczny realizm: istnieje uniwersum matematyczne, ma ono charakter obiektywny, niezależny od nas; optymizm epistemologiczny: (...)
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  26. Matematyka - nauka o fikcjach...?Krzysztof Wójtowicz - 2009 - Zagadnienia Filozoficzne W Nauce 45.
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  27. Naturalizm matematyczny Penelope Maddy: próba analizy.Krzysztof Wójtowicz - 2001 - Filozofia Nauki 4.
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  28. Naturalizm w filozofii matematyki.Krzysztof Wójtowicz - 2001 - Filozofia Nauki 1.
    In the contemporary philosophy of mathematics there is an ongoing discussion concerning the issue of the justification of mathematical axioms and independent sentences. The works of P. Maddy in which the author focuses on the set theory are extensive studies devoted to that problem. In one of the monographs she deals with the problem of the justification of set theory's sentences in a new way, assuming a different metaphilosophical standpoint. In the paper (which is the first part of the two-part (...)
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  29.  22
    O hipotezie Continuum.Krzysztof Wójtowicz - 1998 - Zagadnienia Filozoficzne W Nauce 22.
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  30.  34
    O losowyaniu liczby z odcinka.Krzysztof Wójtowicz - 1997 - Zagadnienia Filozoficzne W Nauce 20.
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  31.  33
    O matematyce i filozofii matematyki.Krzysztof Wójtowicz - 1998 - Zagadnienia Filozoficzne W Nauce 23.
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  32. Oblicza matematycznego quasi-empiryzmu.Krzysztof Wójtowicz - 2009 - Zagadnienia Filozoficzne W Nauce 44.
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  33.  40
    O nadużywaniu twierdzenia Gödla w sporach filozoficznych.Krzysztof Wójtowicz - 1996 - Zagadnienia Filozoficzne W Nauce 19.
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  34. O pojęciu.Krzysztof Wójtowicz - 2001 - Przeglad Filozoficzny - Nowa Seria 37 (1):121-138.
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  35.  13
    Object Realism Versus Mathematical Structuralism.Krzysztof Wójtowicz - 2012 - Semiotica 2012 (188).
  36. On (Some) Presuppositions in Mathematics.Krzysztof Wójtowicz - 2011 - Studia Philosophiae Christianae 47 (4):103-116.
  37.  4
    O uzasadnianiu w matematyce.Krzysztof Wójtowicz - 2002 - Roczniki Filozoficzne 50 (1):527-551.
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  38. Obiekty wyższych rzędów a zobowiązania ontologiczne.Krzysztof Wójtowicz - 2002 - Przeglad Filozoficzny - Nowa Seria 41 (1):17-33.
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  39. Problem istnienia we współczesnej filozofii matematyki.Krzysztof Wójtowicz - 1997 - Przeglad Filozoficzny - Nowa Seria 21 (1):55-78.
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  40. Podstawowe założenia strukturalizmu w filozofii matematyki.Krzysztof Wójtowicz - 2009 - Zagadnienia Filozoficzne W Nauce 44.
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  41. Redukcje ontologiczne w matematyce. Część II: Strategie argumentacyjne na rzecz realizmu.Krzysztof Wójtowicz - 2011 - Filozofia Nauki 19 (2).
    This is the second part of the study concerning the problem of ontological reductions in mathematics. In this part, some major strategies of argumentation in favor of mathematical realism are presented. The versions to be considered are: Gödel’s realism, Quine’s quasi-empiricism and Balaguer’s Full-Blooded Platonism. Some introductory remarks considering the problem of ontological reductions in the context of these three stances are also presented.
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  42. Redukcje ontologiczne w matematyce. Część III Zagadnienie rekonstrukcji fragmentów matematyki.Krzysztof Wójtowicz - 2011 - Filozofia Nauki 19 (3).
    This is the third part of the study concerning the problem of ontological reductions in mathematics. In this part, the problem of reconstruction of (parts of) mathematics in theories weaker than full ZFC is discussed. The tools from reverse mathematics are used, and the results are discussed from the point of view of various versions of realism (Gödel’s realism, Quine’s quasi-empiricism and Balaguer’s Full-Blooded Platonism). Some problems concerning the possibility of discussing these problem outside the conceptual system of set theory (...)
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  43. Redukcje ontologiczne w matematyce. Część I.Krzysztof Wójtowicz - 2008 - Filozofia Nauki 3.
    The article is the first part of a series of papers devoted to the problem of ontological reductions in mathematics – in particular, of choosing the basic category of mathematical entities. The received view is that such a category is provided by set theory, which serves as the ontological framework for the whole of mathematics (as all mathematical entities can be represented as sets). However, from the point of view of "naive mathematical realism" we should rather think of the mathematical (...)
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  44. Strukturalizm a realizm obiektowy – rzeczywisty spór?Krzysztof Wójtowicz - 2012 - Filozofia Nauki 20 (2).
    In the article, I discuss the differences between mathematical structuralism and object realism. I argue that they are partly only a matter of formulation and that some basic theses of both standpoints can be translated into the opponent’s language.
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  45.  9
    Status hipotezy kontinuum w świetle koncepcji Woodina.Krzysztof Wójtowicz - 2011 - Filozofia Nauki 19 (4):67-82.
    In the article, Woodin’s program (for setting up axioms, which decide the continuum hypothesis) is presented, and some philosophical aspects of it are discussed. In particular, the general problem of justifying axioms of set theory is discussed in the context of the relation between set theory and mainstream mathematics.
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  46.  23
    Some Remarks on Hartry Field's Notion of “Logical Consistency”.Krzysztof Wójtowicz - 2001 - Logic and Logical Philosophy 9:199.
  47.  35
    Twierdzenie Gödla i filozofia [recenzja].Krzysztof Wójtowicz - 2004 - Zagadnienia Filozoficzne W Nauce 34.
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  48. The Notion of Explanation in Gödel’s Philosophy of Mathematics.Krzysztof Wójtowicz - 2019 - Studia Semiotyczne—English Supplement 30:85-106.
    The article deals with the question of in which sense the notion of explanation can be applied to Kurt Gödel’s philosophy of mathematics. Gödel, as a mathematical realist, claims that in mathematics we are dealing with facts that have an objective character. One of these facts is the solvability of all well-formulated mathematical problems—and this fact requires a clarification. The assumptions on which Gödel’s position is based are: metaphysical realism: there is a mathematical universe, it is objective and independent of (...)
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  49. Teoria obliczeń kwantowych–argument w sporze o aprioryczny status matematyki?Krzysztof Wójtowicz - 2009 - Studia Philosophiae Christianae 45 (1):71-91.
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  50.  24
    Theory of Quantum Computation and Philosophy of Mathematics. Part I.Krzysztof Wójtowicz - 2009 - Logic and Logical Philosophy 18 (3-4):313-332.
    The aim of this paper is to present some basic notions of the theory of quantum computing and to compare them with the basic notions of the classical theory of computation. I am convinced, that the results of quantum computation theory (QCT) are not only interesting in themselves, but also should be taken into account in discussions concerning the nature of mathematical knowledge. The philosophical discussion will however be postponed to another paper. QCT seems not to be well-known among philosophers (...)
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