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    Wyświetlanie 1-8 z 8
    Tytuł:
    Dowód matematyczny – argumentacja czy derywacja? – część II
    Mathematical Proof – Argumentation or Derivation? – Part II
    Autorzy:
    Wójtowicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/691020.pdf
    Data publikacji:
    2011
    Wydawca:
    Copernicus Center Press
    Tematy:
    philosophy of mathematics
    mathematical proof
    formal derivation
    derivation-indicator view
    philsophy of science
    Opis:
    In the first part of the paper, Azzouni’s derivation–indicator view was presented. In the second part it is analyzed in a detailed way. It is shown, that many problems arise, which cannot be explained in a satisfactory way in Azzouni’s theory, in particular the problem of the explanatory role of proof, of its epistemic role; the relationship between first–order and second–order versions of proofs is also not clear. It is concluded, that Azzouni’s theory does not provide a satisfactory account of mathematical proof, but inspires an interesting discussion. In the article, some of the mentioned problems are discussed.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2011, 49; 81-97
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Antyrealistyczna ucieczka w sferę możliwości
    Antirealist escape to the realm of possibilities
    Autorzy:
    Wójtowicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/690612.pdf
    Data publikacji:
    2008
    Wydawca:
    Copernicus Center Press
    Tematy:
    Charles S. Chihara
    constructivism
    Geoffrey Hellman
    structuralism
    linguistic constructivism
    modal structuralism
    Opis:
    The article is devoted to a popular presentation of two important styles of thinking concerning the problem of existence of mathematical objects: Chihara's linguistic constructivism, and Hellman's modal structuralism. According to Chihara, mathematical statements should be interpreted as referring to certain linguistic construction; according to Hellman, mathematics is the science of possible structures. The motivations and main ideas are examined (without going into technical details), and the similarities and differences between these two viewpoints are highlighted.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2008, 42; 15-27
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Podstawowe założenia strukturalizmu w filozofii matematyki
    Mathematical structuralism and its basic assumptions
    Autorzy:
    Wójtowicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/690706.pdf
    Data publikacji:
    2009
    Wydawca:
    Copernicus Center Press
    Tematy:
    mathematical structuralism
    ontology of mathematics
    Stewart Shapiro
    structure
    Opis:
    The notion of a structure is one of fundamental notions in mathematics: we speak of geometrical, topological, probabilistic, differential etc. structures. This notion is also important in the philosophical discussion concerning ontology for mathematics. In the last decades, the stance of mathematical structuralism attracts more and more attention. In this article the author discusses the motivations which lie behind mathematical structuralism and briefly present Shapiro's 'ante rem' structuralism.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2009, 44; 40-60
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Oblicza matematycznego quasi-empiryzmu
    The kinds of mathematical quasi-empirism
    Autorzy:
    Wójtowicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/690708.pdf
    Data publikacji:
    2009
    Wydawca:
    Copernicus Center Press
    Tematy:
    Imre Lakatos
    mathematical realism
    quasi-empiricism
    Willard Van Orman Quine
    Opis:
    The received view concerning mathematics is the one, that mathematics is a priori, and that mathematical knowledge develops via 'intelektuelle Anschauung' rather than by analyzing empirical data. Mathematical proofs seems to be immune to empirical refutation, and in particular the development of mathematics does not in any way resemble the development of e.g. physics. On the other hand, it is quite clear, that mathematics play a fundamental role in science, and it is often considered to be rather just a useful tool, which provides a language and a conceptual system allowing to express statements concerning empirical world. Such views stress the dependence of mathematics upon physics. In the article, the author presents two quite different aspects of this problem: the ontological and the methodological aspects. According to Quine, our argumentation in favor of mathematical realism should be based on the analysis of ontological commitment of empirical theories. There is no other compelling argument for mathematical realism. According to Lakatos, mathematical knowledge develops in a way similar to empirical science: it is fallible, and the proper model to describe it is the model of proofs and refutations. In the article the author describes and contrast these two points of view.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2009, 44; 61-83
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Rozumienie dowodu matematycznego a zagadnienie wyjaśnienia w matematyce
    The Notion of Mathematical Proof and the Problem of Explanation in Mathematics
    Autorzy:
    Wójtowicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/690770.pdf
    Data publikacji:
    2015
    Wydawca:
    Copernicus Center Press
    Tematy:
    philosophy of mathematics
    mathematical proof
    explanation in mathematics
    explanatory proofs
    mathematical intuition
    Opis:
    In the article, I present two possible points of view concerning mathematical proofs: (a) the formal view (according to which the formalized versions of mathematical proofs reveal their “essence”); (b) the semantic view (according to which mathematical proofs are sequences of intellectual acts, and a form of intuitive “grasp” is crucial). The problem of formalizability of mathematical proofs is discussed, as well as the problem of explanation in mathematics – in particular the problem of explanatory versus non-explanatory character of mathematical proofs. I argue, that this problem can be analyzed in a fruitful way only from the semantic point of view.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2015, 58; 89-114
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dowód matematyczny – argumentacja czy derywacja? – część I
    Mathematical Proof – Argumentation or Derivation? – Part I
    Autorzy:
    Wójtowicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/691022.pdf
    Data publikacji:
    2011
    Wydawca:
    Copernicus Center Press
    Tematy:
    philosophy of mathematics
    mathematical proof
    formal derivation
    derivation-indicator view
    philsophy of science
    Opis:
    The article is devoted to the problem of status of mathematical proofs, in particular it tries to capture the relationship between the real, „semantic” notion of mathematical proof, and its formal (algorithmic) counterpart. In the first part, Azzouni’s derivation–indicator view is presented in a detailed way. According to the DI view, there is a formal derivation underlying every real proof.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2011, 49; 63-80
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Matematyka - nauka o fikcjach?
    Mathematics - science about fictions...?
    Autorzy:
    Wójtowicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/691150.pdf
    Data publikacji:
    2009
    Wydawca:
    Copernicus Center Press
    Tematy:
    fictionalism
    field
    mathematical realism
    Quine's indispensability argument
    philosophy of mathematics
    Opis:
    According to mathematical realism, mathematics describes an abstract realm of mathematical entities, and mathematical theorems are true in the classical sense of this term. In particular, mathematical realism is claimed to be the best theoretical explanation of the applicability of mathematics in science. According to Quine's indispensability argument, applicability is the best argument available in favor of mathematical realism. However, Quine's point of view has been questioned several times by the adherents of antirealism. According to Field, it is possible to show, that - in principle - mathematics is dispensable, and that so called synthetic versions of empirical theories are available. In his 'Science Without Numbers' Field follows the 'geometric strategy' - his aim is to reconstruct standard mathematical techniques in a suitable language, acceptable from the point of view of the nominalist. In the first part of the article, the author briefly presents Field's strategy. The second part is devoted to Balaguer's fictionalism, according to which mathematics is indispensable in science, but nevertheless can be considered to be a merely useful fiction.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2009, 45; 3-26
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Kilka uwag o (meta)filozofii matematyki
    A few remarks on the (meta)philosophy of mathematics
    Autorzy:
    Wójtowicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/691184.pdf
    Data publikacji:
    2007
    Wydawca:
    Copernicus Center Press
    Tematy:
    philosophy of mathematics
    Opis:
    The present essay deals with the problem of how to choose the correct method of doing philosophy of mathematics taking into account the importance of technical mathematical results for philosophical analysis. After a short historical introduction presenting the formation of the present mathematical paradigm, it is pointed out that the current mathematical praxis has, in principle, no connection with philosophical investigations. Two radically different approaches to philosophy of mathematics are outlined. Basing on selected examples it is argued that the correct method of doing philosophy of mathematics should take into account both technical results obtained by mathematicians (which often throw a new light on old philosophical questions) and the autonomy of philosophical method.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2007, 40; 12-29
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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