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Wyświetlanie 1-15 z 45
Tytuł:
Bernard Bolzano: pierwsze (historycznie) matematyczne ujęcie pojęcia kontinuum
Bernhard Bolzano: the first (historically) mathematical approach to the concept of continuum
Autorzy:
Dadaczyński, Jerzy
Powiązania:
https://bibliotekanauki.pl/articles/690870.pdf
Data publikacji:
2018
Wydawca:
Copernicus Center Press
Tematy:
mathematics
philosophy of mathematics
history of mathematics
continuum
Bernard Bolzano
Opis:
Book review: Lukas Benedikt Kraus, Der Begriff des Kontinuums bei Bernard Bolzano, Beiträge zur Bolzano-Forschung, vol. 25, Academia Verlag, Sankt Augustin 2014, pp. 112.
Recenzja książki: Lukas Benedikt Kraus, Der Begriff des Kontinuums bei Bernard Bolzano, Beiträge zur Bolzano-Forschung, vol. 25, Academia Verlag, Sankt Augustin 2014, ss. 112.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2018, 64; 195-199
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Giuseppe Veronesego podstawy matematyki
Giuseppe Veronese’s foundations of mathematics
Autorzy:
Dadaczyński, Jerzy
Powiązania:
https://bibliotekanauki.pl/articles/690818.pdf
Data publikacji:
2013
Wydawca:
Copernicus Center Press
Tematy:
foundations of mathematics
epistemology of mathematics
ontology of mathematics
mathematical subject
Giuseppe Veronese
Opis:
The aim of this paper is to analyze Veronese’s philosophical principles of mathematics. He tried to begin the construction of mathematics (geometry) with the concept of the Thinking Subject and the phenomenon of thinking, which is discussed in detail. It is very likely that this idea had an impact on Hilbert’s concept of the Mathematical Subject. Some similarities between Veronese’s view and the intuitionistic thinkers are also shown.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2013, 53; 53-92
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Znaczenie edukacji matematycznej w humanistyce
Mathematics in humanities
Autorzy:
Szostek, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/690726.pdf
Data publikacji:
2009
Wydawca:
Copernicus Center Press
Tematy:
education
humanities
mathematics
Opis:
The topic of the article is the role of the mathematical education in the humanistic education (history, history of literature and art etc.). The author underlines the meaning understanding as the fundamental notion of the humanities. The lack of the understanding perspective leads the humanistic education to the superficial knowledge of facts and dates, always incomplete and not very useful for the grasping of the specific world of the human thinking and motivation. Mathematics, as the only pure formal subject in the Polish school educational program (there is no classes in logic in these schools), can provide the student at least with the three important abilities. Namely, mathematics education improves the imagination of the school-boys and girls (starting with the simple summing up and multiplication operations), deduction (as opposite to funding our convictions only on the opinions) and integrity of the knowledge (it is impossible to comprehend the more advanced mathematics theses with no knowledge of the other, more fundamental parts of it; much the same it is impossible e. g. to comprehend the essence of the historical processes without knowledge of the all important elements of them). However, what is needed in the school program in mathematics is some information about the more advanced mathematical theories and its applications to the other kinds of science (mathematics in cosmology, fractal theory, topology), These theories cannot be presented completely on this stage of education, yet can improve the imagination of the young men and help them to recognize the meaning of the mathematics for the understanding of the whole world, its structure and dynamism.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2009, 44; 13-24
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
Tytuł:
Metoda matematyki według B. Bolzano
Bernard Bolzanos conception of the mathematical method
Autorzy:
Dadaczyński, Jerzy
Powiązania:
https://bibliotekanauki.pl/articles/690898.pdf
Data publikacji:
2006
Wydawca:
Copernicus Center Press
Tematy:
axiomatic method
Bernard Bolzano
methodology of mathematics
philosophy of mathematics
Opis:
The matter under discussion is the methodology of mathematics presented by Bernard Bolzano (1782-1848) in his early pamphlet 'Beitraege zu einer begruendeteren Darstellung der Mathematik' (Prague 1810). Bolzano built, with success, the classical axiomatic-deductive method of nonspacial and atemporal concepts (Begriffe). He abandoned the traditional custom of formulating primitive concepts of deductive theories. Bolzano opposed the traditional conviction that the axioms of mathematical theories should be clear and distinct sentences. He divided the domain of nonspacial and atemporal sentences into the subdomains of objectively provable and objectively nonprovable sentences. In his view, the axioms of mathematical (deductive) theories are only the objectively nonprovable sentences, and each of the objective nonprovable sentences is an axiom of a certain deductive theory. He postulated, at the time when only the (Euclidean) geometry was axiomatized, the axiomatization of all mathematical theories.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2006, 38; 76-113
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
U zródeł współczesnego nominalizmu w filozofii matematyki
Sources of contemporary nominalism in the philososphy of mathematics
Autorzy:
Frąckowiak–Ciesielska, Anna
Powiązania:
https://bibliotekanauki.pl/articles/691148.pdf
Data publikacji:
2006
Wydawca:
Copernicus Center Press
Tematy:
nominalism
philosophy of mathematics
Opis:
Nominalism is one of the most important positions in the contemporary philosophy of mathematics. The goal of this article is to point out various factors that have effected the rapid development of nominalism. In particular, the figures of the Polish precursors of nominalism are presented, that is, Lesniewski, Kotarbinski and Tarski. Consequently, the article of Quine and Goodman entitled 'Steps Toward a Constructive Nominalism' is discussed. The article became the ideological declaration of nominalism and initiated reconstructionist tendencies within it. The presentation is concluded with the attempt of the modal interpretation of mathematics according to Putnam. This interpretation inspired the nominalists to enrich the existing logical apparatus with new methods and tools that are more efficient in the implementation of the strategy indicated by Quine and Godman.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2006, 39; 92-114
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Matematyka i kosmologia
Mathematics and Cosmology
Autorzy:
Heller, Michał
Powiązania:
https://bibliotekanauki.pl/articles/691306.pdf
Data publikacji:
2012
Wydawca:
Copernicus Center Press
Tematy:
mathematics
cosmology
noncommutative geometry
Opis:
The mathematical and cosmological works of a group associated with the Copernicus Center for Interdisciplinary Studies in Cracow are summarized. The group consists mainly of M. Heller, L. Pysiak, W. Sasin, Z. Odrzygóźdź and J. Gruszczak. The first paper by members of the group was published in 1988, and research has been continued to the present day. The main mathematical tool used in the first part of the group’s activity was the theory of differential spaces and, in the second, methods of noncommutative geometry. Among the main topics investigated have been classical singularities in relativistic cosmology and the unification of general relativity with quantum mechanics.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2012, 50; 63-74
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mathematics as a love of wisdom: Saunders Mac Lane as philosopher
Autorzy:
McLarty, Colin
Powiązania:
https://bibliotekanauki.pl/articles/1047615.pdf
Data publikacji:
2020-12-28
Wydawca:
Copernicus Center Press
Tematy:
naturalism
philosophy
mathematics
Aristotle
Opis:
This note describes Saunders Mac Lane as a philosopher, and indeed as a paragon naturalist philosopher. He approaches philosophy as a mathematician. But, more than that, he learned philosophy from David Hilbert’s lectures on it, and by discussing it with Hermann Weyl, as much as he did by studying it with the mathematically informed Göttingen Philosophy professor Moritz Geiger.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2020, 69; 17-32
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:
Maxime Bôchers concept of complementary philosophy of mathematics
Autorzy:
Dadaczyński, Jerzy
Piechowicz, Robert
Powiązania:
https://bibliotekanauki.pl/articles/691235.pdf
Data publikacji:
2020
Wydawca:
Copernicus Center Press
Tematy:
philosophy
mathematics
Maxim Bôcher
metamathematics
Opis:
The main purpose of the present paper is to demonstrate that as early as 1904 pre-eminent American mathematician Maxime Bôcher was an adherent to the presently relevant argument of reasonableness, or even necessity of parallel development of two philosophical methods of reflection on mathematics, so that its essence could be more fully comprehended. The goal of the research gives rise to the question: what two types of philosophical deliberation on mathematics were proposed by Bôcher?
Źródło:
Zagadnienia Filozoficzne w Nauce; 2020, 68; 9-36
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Category Theory in the hands of physicists, mathematicians, and philosophers
Autorzy:
Stopa, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/1047610.pdf
Data publikacji:
2020-12-29
Wydawca:
Copernicus Center Press
Tematy:
category theory
physics
mathematics
philosophy
Źródło:
Zagadnienia Filozoficzne w Nauce; 2020, 69; 283-293
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
What are the limits of mathematical explanation? Interview with Charles McCarty by Piotr Urbańczyk
Autorzy:
McCarty, David Charles
Urbańczyk, Piotr
Powiązania:
https://bibliotekanauki.pl/articles/691211.pdf
Data publikacji:
2016
Wydawca:
Copernicus Center Press
Tematy:
mathematics
logic
mathematical explanation
limits of explanation
mathematical proof
proof-core
intuitionism
constructivsim
Gödel’s Incompleteness Theorems
intuitionistics mathematics
classical mathematics
Axiom of Choice
Opis:
An interview with Charles McCarty by Piotr Urbańczyk concerning  mathematical explanation.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2016, 60; 119-137
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Gottlob Frege o liczbie. Przyczynek do określenia roli, jaką dla filozofów pełni historia matematyki
Gottlob Frege on numbers. An attempt to determine the role of the history of mathematics in the work of philosophers
Autorzy:
Besler, Gabriela
Powiązania:
https://bibliotekanauki.pl/articles/691010.pdf
Data publikacji:
2013
Wydawca:
Copernicus Center Press
Tematy:
history of mathematics
number
Gottlob Frege
Opis:
In this paper I will focus on Frege’s six crucial claims on numbers. I begin with indicating the reasons for his interest in this topic and conclude with a reflection on the role of the history of mathematics in the practice of philosophy. Frege believed that the study on numbers is a common task for both philosophers and mathematicians. In this article, priority is given to the philosophical aspect.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2013, 53; 133-164
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kilka uwag o Tezie Churcha i Aksjomacie Hilberta
Some remarks concerning Church's Thesis and Hilbert's Axiom
Autorzy:
Olszewski, Adam
Powiązania:
https://bibliotekanauki.pl/articles/690900.pdf
Data publikacji:
2006
Wydawca:
Copernicus Center Press
Tematy:
Church's Thesis
Hilbert's Axiom
philosophy of mathematics
Opis:
Some facts concerning Church's Thesis are first reminded, then Hilbert's Axiom of Thought is formulated. Hilbert proposed this axiom in 1905. He believed that it belongs to a domain of knowledge that is prior with respect to mathematics. An attempt is made to apply this axiom to some considerations concerning Church's Thesis
Źródło:
Zagadnienia Filozoficzne w Nauce; 2006, 38; 114-126
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
P. Bernaysa koncepcja poznania matematycznego
Bernays conception of mathematical cognizance
Autorzy:
Kaczmarek, Jerzy
Powiązania:
https://bibliotekanauki.pl/articles/690592.pdf
Data publikacji:
2008
Wydawca:
Copernicus Center Press
Tematy:
Paul Bernays
epistemology of mathematics
open philosophy
Opis:
Bernays' philosophical thought evolved from L.Nelson's and J.F.Frics' epistemological outlook to Gonseth's open epistemology (from the Kantian doctrine to open phenomenology). The paper is divided into two parts. The first part deals with philosophical inspirations and the evolution of Bernays' metascientific outlook. The second part considers his epistemological views from the period of inspiration by Gonseth's open philosophy. It is the final, mature stage of Bernays' evolution that is important for mathematical epistemology.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2008, 42; 28-51
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 45

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