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  1. Krzysztof Wójtowicz (2012). Object Realism Versus Mathematical Structuralism. Semiotica 2012 (188).
  2. Krzysztof Wójtowicz (2012). Strukturalizm a realizm obiektowy – rzeczywisty spór? Filozofia Nauki 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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  3. Krzysztof Wójtowicz (2011). Dowód matematyczny - argumentacja czy derywacja? - część I. Zagadnienia Filozoficzne W Nauce 49.
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  4. Krzysztof Wójtowicz (2011). Dowód matematyczny - argumentacja czy derywacja? - część II. Zagadnienia Filozoficzne W Nauce 49.
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  5. Krzysztof Wójtowicz (2011). On (Some) Presuppositions in Mathematics. Studia Philosophiae Christianae 4:103-116.
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  6. Krzysztof Wójtowicz (2011). Redukcje ontologiczne w matematyce. Część II: Strategie argumentacyjne na rzecz realizmu. Filozofia Nauki 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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  7. Krzysztof Wójtowicz (2011). Redukcje ontologiczne w matematyce. Część III Zagadnienie rekonstrukcji fragmentów matematyki. Filozofia Nauki 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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  8. Krzysztof Wójtowicz (2011). Status hipotezy kontinuum w świetle koncepcji Woodina. Filozofia Nauki 4 (4 (76)):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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  9. Krzysztof Wojtowicz (2011). Ontological Reductions in Mathematics. Part II: Argumentational Strategies for Realism. Filozofia Nauki 19 (2):29.
     
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  10. Krzysztof Wojtowicz (2011). Ontological Reductions in Mathematics. Part III: On Reconstruction of Some Parts of Mathematics. Filozofia Nauki 19 (3):49.
     
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  11. Krzysztof Wojtowicz (2011). The Status of the Continuum Hypothesis in the Light of Woodin's Argumentation. Filozofia Nauki 19 (4):67.
     
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  12. Krzysztof Wójtowicz (2010). Theory of Quantum Computation and Philosophy of Mathematics. Part I. 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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  13. Krzysztof Wójtowicz (2009). Matematyka - nauka o fikcjach...? Zagadnienia Filozoficzne W Nauce 45.
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  14. Krzysztof Wójtowicz (2009). Oblicza matematycznego quasi-empiryzmu. Zagadnienia Filozoficzne W Nauce 44.
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  15. Krzysztof Wójtowicz (2009). Podstawowe założenia strukturalizmu w filozofii matematyki. Zagadnienia Filozoficzne W Nauce 44.
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  16. Krzysztof Wójtowicz (2009). Teoria obliczeń kwantowych–argument w sporze o aprioryczny status matematyki? Studia Philosophiae Christianae 1:71-91.
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  17. Krzysztof Wójtowicz (2008). Redukcje ontologiczne w matematyce. Część I. 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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  18. Krzysztof Wójtowicz (2007). Dowód matematyczny z punktu widzenia formalizmu matematycznego. Część I. Roczniki Filozoficzne 55 (2):123-139.
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  19. Krzysztof Wójtowicz (2007). Dowód matematyczny z punktu widzenia formalizmu matematycznego. Część II. Roczniki Filozoficzne 55 (2):139-153.
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  20. Krzysztof Wojtowicz (2007). O filozofii matematyki Imre Lakatosa. Roczniki Filozoficzne 55 (1):229-247.
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  21. Krzysztof Wójtowicz (2006). Independence and Justification in Mathematics. 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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  22. Krzysztof Wójtowicz (2004). Filozofia matematyki Gödla na tle neopozytywistycznej koncepcji matematyki. Zagadnienia Filozoficzne W Nauce 34.
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  23. Krzysztof Wójtowicz (2004). Some Remarks on Hartry Field's Notion of “Logical Consistency”. Logic and Logical Philosophy 9:199.
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  24. Krzysztof Wójtowicz (2004). Twierdzenie Gödla i filozofia [recenzja]. Zagadnienia Filozoficzne W Nauce 34.
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  25. Krzysztof Wójtowicz (2002). Kilka uwag o problemie niezależności w matematyce. Przeglad Filozoficzny - Nowa Seria 41 (1):65-82.
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  26. Krzysztof Wójtowicz (2002). Obiekty wyższych rzędów a zobowiązania ontologiczne. Przeglad Filozoficzny - Nowa Seria 41 (1):17-33.
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  27. Krzysztof Wöjtowicz (2001). Die Reverse Mathematics und ihre philosophische Relevanz. Philosophia Naturalis 38 (1):121-144.
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  28. Krzysztof Wójtowicz (2001). Kilka uwag o twierdzeniu Gödla i intensjonalności. Filozofia Nauki 4.
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  29. Krzysztof Wójtowicz (2001). Naturalizm matematyczny Penelope Maddy: próba analizy. Filozofia Nauki 4.
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  30. Krzysztof Wójtowicz (2001). Naturalizm w filozofii matematyki. 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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  31. Krzysztof Wójtowicz (2001). O pojęciu. Przeglad Filozoficzny - Nowa Seria 37 (1):121-138.
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  32. Krzysztof Wójtowicz (2001). O tzw. programie Gödla. Zagadnienia Filozoficzne W Nauce 29.
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  33. Krzysztof Wójtowicz (2000). Analiza antyrealizmu modalnego. 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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  34. Krzysztof Wójtowicz (2000). Kilka uwag na temat zagadnienia Czas a matematyka [dyskusja]. Zagadnienia Filozoficzne W Nauce 26.
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  35. Krzysztof Wójtowicz (1998). O hipotezie Continuum. Zagadnienia Filozoficzne W Nauce 22.
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  36. Krzysztof Wójtowicz (1998). O matematyce i filozofii matematyki. Zagadnienia Filozoficzne W Nauce 23.
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  37. Krzysztof Wójtowicz (1998). Unification of Mathematical Theories. Foundations of Science 3 (2):207-229.
    In this article the problem of unification of mathematical theories is discussed. We argue, that specific problems arise here, which are quite different than the problems in the case of empirical sciences. In particular, the notion of unification depends on the philosophical standpoint. We give an analysis of the notion of unification from the point of view of formalism, Gödel's platonism and Quine's realism. In particular we show, that the concept of “having the same object of study” should be made (...)
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  38. Krzysztof Wójtowicz (1997). O losowyaniu liczby z odcinka. Zagadnienia Filozoficzne W Nauce 20.
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  39. Krzysztof Wójtowicz (1997). Problem istnienia we współczesnej filozofii matematyki. Przeglad Filozoficzny - Nowa Seria 21 (1):55-78.
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  40. Krzysztof Wójtowicz (1996). O nadużywaniu twierdzenia Gödla w sporach filozoficznych. Zagadnienia Filozoficzne W Nauce 19.
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  41. Krzysztof Wójtowicz (1996). Paradoksy skończoności. Zagadnienia Filozoficzne W Nauce 18.
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  42. Krzysztof Wójtowicz (1995). Wokół problemu realizmu teoriomnogościowego. Filozofia Nauki 4.
    The paper is devoted to the problem of the existence of mathematical objects. The ideas of Godel and the Quine-Putnam indispensability argument are discussed. A „qualitative” version of this argument, in which the results of reverse mathematics are used, is presented.
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  43. Krzysztof Wójtowicz (1994). Czy matematyka jest niezbędna w nauce? 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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