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    Wyświetlanie 1-8 z 8
    Tytuł:
    The theory of ideas and Plato’s philosophy of mathematics
    Autorzy:
    Dembiński, Bogdan
    Powiązania:
    https://bibliotekanauki.pl/articles/690838.pdf
    Data publikacji:
    2019
    Wydawca:
    Copernicus Center Press
    Tematy:
    mathematical Platonism
    ontology
    Platonic Academy
    Opis:
    In this article I analyze the issue of many levels of reality that are studied by natural sciences. Particularly interesting is the level of mathematics and the question of the relationship between mathematics and the structure of the real world. The mathematical nature of the world has been considered since ancient times and is the subject of ongoing research for philosophers of science to this day. One of the viewpoints in this field is mathematical Platonism. In contemporary philosophy it is widely accepted that according to Plato mathematics is the domain of ideal beings (ideas) that are eternal and unalterable and exist independently from the subject’s beliefs and decisions. Two issues seem to be important here. The first issue concerns the question: was Plato really a proponent of present-day mathematical Platonism? The second one is of greater importance: how mathematics influences our understanding of the nature of the world on its many ontological levels? In the article I consider three issues: the Platonic theory of “two worlds”, the method of building a mathematical structure, and the ontology of mathematics.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2019, 66; 95-108
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fizyzm Rolanda Omnésa - jedność świata matematyki i fizyki. Część I: kwantowe problemy abstrakcji
    Physism of Roland Omnés - unity of the worlds of mathematics and physics; Part I - Quantum problems of abstraction
    Autorzy:
    Grygiel, Wojciech
    Powiązania:
    https://bibliotekanauki.pl/articles/690538.pdf
    Data publikacji:
    2008
    Wydawca:
    Copernicus Center Press
    Tematy:
    Roland Omnés
    philosophy of mathematics
    mathematical platonism
    physism
    Opis:
    Inasmuch as mathematical platonism can be clearly matched with the radical realism, there exists a possibility to point out an approach, promoted by a French physicist, Roland Omnés, that is equivalent to the Aristotelian position of moderate realism. This standpoint denies the existence of an independent universum of mathematical entities and claims that mathematics is encoded in the laws of physics. In analogy to logicism, where mathematics is considered to be reducible to logic, Omnés' position is called by him 'physism' to stress the reducibility of mathematics to the laws of physics. The goal of Roland Omnés is to construct a common philosophy of mathematics and physics where the realities of these two disciplines converge. The first part of the analysis aims at the description and critical evaluation of physism from the point of view of the adequacy of the consistent histories interpretation of quantum mechanics to provide physical basis of the abstraction of the mathematical structures from the physical reality.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2008, 43; 89-102
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the adequacy of qualifying Roger Penrose as a complex Pythagorean
    Autorzy:
    Grygiel, Wojciech P.
    Powiązania:
    https://bibliotekanauki.pl/articles/691078.pdf
    Data publikacji:
    2018
    Wydawca:
    Copernicus Center Press
    Tematy:
    Roger Penrose
    mathematical platonism
    realism
    pythagoreism
    complex numbers
    Opis:
    The aim of the presented article is to provide an in-depth analysis of the adequacy of designating Penrose as a complex Pythagorean in view of his much more common designation as a Platonist. Firstly, the original doctrine of the Pythagoreans will be briefly surveyed with the special emphasis on the relation between the doctrine of this school and the teachings of the late Platonic School as well as its further modifications. These modifications serve as the prototype of the contemporary claims of the mathematicity of the Universe. Secondly, two lines of Penrose’s arguments in support of his unique position on the ontology of the mathematical structures will be presented: (1) their existence independent of the physical world in the atemporal Platonic realm of pure mathematics and (2) the mathematical structures as the patterns governing the workings of the physical Universe. In the third step, a separate line of arguments will be surveyed that Penrose advances in support of the thesis that the complex numbers seem to suit these patterns with exceptional adequacy. Finally, the appropriateness of designation Penrose as a complex Pythagorean will be assessed with the special emphasis on the suddle threshold between his unique position and that of the adherents of the mathematicity of the Universe.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2018, 65
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    O platońskich ideach
    On Plato’s Doctrine of Ideas
    Autorzy:
    Dembiński, Bogdan
    Powiązania:
    https://bibliotekanauki.pl/articles/691207.pdf
    Data publikacji:
    2016
    Wydawca:
    Copernicus Center Press
    Tematy:
    philosophy of mathematics
    mathematical platonism
    history of philosophy
    Plato
    platonism
    Platonic idealism
    Opis:
    This paper is an attempt to clarify the ontological status of Platonic ideas. My considerations are based on the example of mathematical ideas and their relation to the subjects of mathematics and phenomena, since such modes of existence are distinguished in the philosophy of Plato.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2016, 60; 83-98
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    O niektórych aspektach platońskiej filozofii matematyki
    On some aspects of mathematical platonism
    Autorzy:
    Dembiński, Bogdan
    Powiązania:
    https://bibliotekanauki.pl/articles/690766.pdf
    Data publikacji:
    2015
    Wydawca:
    Copernicus Center Press
    Tematy:
    philosophy of mathematics
    mathematical platonism
    history of philosophy
    Plato
    Opis:
    Modern philosophers of mathematics in their discussions tend to refer to mathematical Platonism. Usually they believe that they talk about philosophical thought of Plato himself and understanding of mathematics that was introduced by the ancient philosopher. Unfortunately, contemporary mathematical Platonism has very little in common with original Platonism. In this paper I would like to clarify this issue and present Plato’s philosophy of mathematics.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2015, 58; 45-61
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Platonizm w strukturalistycznej refleksji nad czasoprzestrzenią. Próba aplikacji myśli filozoficznej Józefa Życińskiego.
    Platonism in Structuralit Inquiries in the Philosophy of Spacetime. An Attempt of Applying Józef Życińskis Philosophical Thought
    Autorzy:
    Luty, Damian
    Powiązania:
    https://bibliotekanauki.pl/articles/1621978.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Szczeciński. Wydawnictwo Naukowe Uniwersytetu Szczecińskiego
    Tematy:
    platonism
    spacetime
    mathematical structures
    Opis:
    The main aim of this paper is to provide an interpretative application of Józef Życiński’s philosophical work. I claim that one can find in Życiński’s thought criteria for evaluating certain positions which use platonistic concepts in order to solve specific problems in the context of philosophy of physics, especially philosophy of spacetime. After reconstructing Życiński’s philosophy, I use the derived criteria to evaluate positions of Howard Stein’s and Max Tegmark’s. I conclude that, according to criteria taken from Życiński’s philosophy, the former’s views are more plausible, and so create a better starting point in developing a platonistic structuralist position.
    Źródło:
    Analiza i Egzystencja; 2017, 39; 73-96
    1734-9923
    2300-7621
    Pojawia się w:
    Analiza i Egzystencja
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Creating new concepts in mathematics: freedom and limitations. The case of Category Theory
    Autorzy:
    Semadeni, Zbigniew
    Powiązania:
    https://bibliotekanauki.pl/articles/1047591.pdf
    Data publikacji:
    2020-12-28
    Wydawca:
    Copernicus Center Press
    Tematy:
    categories
    functors
    Eilenberg-Mac Lane Program
    mathematical cognitive transgressions
    phylogeny
    platonism
    Opis:
    In the paper we discuss the problem of limitations of freedom in mathematics and search for criteria which would differentiate the new concepts stemming from the historical ones from the new concepts that have opened unexpected ways of thinking and reasoning. We also investigate the emergence of category theory (CT) and its origins. In particular we explore the origins of the term functor and present the strong evidence that Eilenberg and Carnap could have learned the term from Kotarbiński and Tarski.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2020, 69; 33-65
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dowód matematyczny z punktu widzenia formalizmu matematycznego. Część II
    Mathematical Proof from the Formalistic Viewpoint. Part II
    Autorzy:
    Wójtowicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2013331.pdf
    Data publikacji:
    2007
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    program Hilberta
    platonizm Fregego
    intuicja matematyczna
    Hilbert’s program
    Frege’s Platonism
    mathematical intuition
    Opis:
    In the second part I discuss Frege’s and Hilbert views on the nature of mathematical proof, in particular their discussion concerning the problem of implicit definitions. I also discuss Hilbert’s program and conclude with some remarks concerning the problem of the “decline of intuition” in the formalistic conception of mathematical proof.
    Źródło:
    Roczniki Filozoficzne; 2007, 55, 2; 139-153
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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