Wyniki wyszukiwania - Biblioteka Nauki

1

INTUITION AND THE GROUNDS OF MATHEMATICS (Naocznosc a podstawy matematyki)

100%

Czerniawski J.

Zagadnienia Naukoznawstwa

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2010

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tom 46

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nr 1(183)

93-100

EN

The paper deals with the issue of the nature of mathematical objects. The author discusses them in the perspective of intuition (as derived from Kant). The main issue consists in the presentation of these objects to human mind.

2

HOW TO COUNT THE UNCOUNTABLE? THE ARCHIMEDES' OF SYRACUSE METHOD(Jak policzyc niepoliczalne? Metoda Archimedesa z Syrakuz)

100%

Roszkowski M.

Zagadnienia Naukoznawstwa

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2010

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tom 46

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nr 2

321-330

EN

The paper discusses Archimedes' of Syracuse ideas concerning the problem of quantities too great for a given numeral system to be expressed. The analysis of solvings proposed by the mathematician of Syracuse is accompanied by remarks on problems with Greek writing systems before Archimedes' works.

3

PHILOSOPHY OF MATHEMATICS AND COMPUTER SCIENCE

80%

Trzesicki K.

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2010

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nr 22(35)

47-80

EN

It is well known fact that the foundation of modern computer science were laid by logicians. Logic is at the heart of computing. The development of contemporary logic and the problems of the foundations of mathematics were in close mutual interaction. We may ask why the concepts and theories developed out of philosophical motives before computers were even invented, prove so useful in the practice of computing. Three main programmes together with the constructivist approach are discussed and the impact on computer science is considered.

4

ŠACH AKO METAFORA MATEMATIKY

80%

Kvasz L.

Filozofia (Philosophy)

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2015

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tom 70

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nr 3

175 - 187

EN

The proponents of analytical philosophy often draw a comparison between mathematics and chess. Their metaphor is to suggest that both the result of mathematical calculation and the content of the mathematical statement are determined by the rules of “mathematical game” of some kind and independent of status quo. The steps made in a given calculation or proof arguments are game moves – and similarly to a position in chess the position in a “mathematical game” has no factual content. The aim of the article is to question the metaphor at issue and show the multiple characteristics of mathematical symbols that make them principally different from chessmen. The arguments introduced are to show that contrary to chess mathematics enables us to understand the world, discern its structure and grasp its coherence. The metaphor in question thus can be labelled as systematically misleading.

5

„Płeć matematyki”. Zróżnicowania osiągnięć ze względu na płeć wśród uzdolnionych uczniów

80%

Zawistowska A.

Studia Socjologiczne

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2013

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nr 3(210)

75–95

EN

Research on performance in mathematics shows that an average achievement of men and women is only slightly different. A much bigger difference exists among students at high achievement levels; in this group, there are more boys than girls. This paper addresses the question how mathematical subdisciplines and types of tests shape gender proportion at higher percentiles of achievement distribution. An analysis of a wide range of data including the results of PISA, exams taken at the end of lower secondary school and high school as well as so-called “mathematical Olympics” brings out three conclusions: (1) there is a gender gap in all subscales of PISA scales, (2) the largest differences exist in scales related to spatial abilities, (3) gender gap widens together with an increase in the level of difficulty as well as with the transition to higher educational levels.

6

Intuition and Hermeneutics: the Intuitive Analysis of Concepts

80%

Krol Z.

Zagadnienia Naukoznawstwa

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2006

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tom 42

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nr 2(168)

251-271

EN

This paper presents certain aspect of intuitive reasoning in mathematics called the 'intuitive analysis of concepts' along some schemes of that kind of intuitive analysis. The method of the intuitive analysis of concept of polyhedra based on the historical findings as presented by Lakatos in 'Proofs and Refutations' is described. Some important consequences for phenomenology as well as philosophy and history of mathematics follow. Mathematical knowledge seems to be created within the 'hermeneutical horizon' distinct for ancient and modern mathematics.

7

MATEMATIKA A SKUTOČNOSŤ

70%

Kvasz L.

Organon F. medzinárodný časopis pre analytickú filozofiu

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2011

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tom 18

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nr 3

302 – 330

EN

The aim of the present paper is to offer a new analysis of the multifarious relation between mathematics and reality. We believe that the relation of mathematics to reality is, just like in the case of the natural sciences, mediated by instruments (such as algebraic symbolism, or ruler and compass). Therefore the kind of realism we aim to develop for mathematics can be called instrumental realism. It is a kind of realism, because it is based on the thesis, that mathematics describes certain patterns of reality. And it is instrumental realism, because it pays attention to the role of instruments by means of which mathematics identifies these patterns.

8

THE SEKED: ON ANCIENT EGYPTIAN MATHEMATICS AND ASTRONOMY

70%

Magdolen D.

Asian and African Studies

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2004

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tom 13

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nr 2

134 -140

EN

In this article the ancient Egyptian terms expressing the slope of a pyramid and voyage of the sun god across the sky are discussed in context of ancient Egyptian mathematics, astronomy and religious iconography.

9

FRACTALS: CONSTRUCTION OR EMERGENCE? PART II. FRACTALS' EMERGENCE IN QUASI-EMPIRICAL APPROACH (Fraktale: konstrukcja czy emergencja? Cz.II. Emergencja fraktalna w podejsciu quasi-empirycznym)

70%

Pietrak J. , Szydlowski M. , Tambor P.

Zagadnienia Naukoznawstwa

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2010

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tom 46

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nr 2

271-302

EN

The aim of the second part of this philosophical diptych is an attempt at discussing the place of the meta-subject reflection concerning fractal structures in classical issues of the philosophy of mathematics. The authors show that fractal structures lead toward essential broadening of that issues beyond traditional frames of the questions about the nature of mathematical objects (ontology of mathematics) or the status of mathematical knowledge (epistemology of mathematics). Particularly, they are interested in two problems: (1) Does process of generating fractal structures prove that co-called new mathematics has quasi-empirical character and in what meaning of that? and (2) Can the philosophical idea of emergence be applied to characterise the features of that structures?

10

INTUÍCIA V MATEMATIKE

60%

Maco R.

Filozofia (Philosophy)

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2016

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tom 71

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nr 9

746 – 758

EN

In mathematics we witness a certain tension between intuitive and non-intuitive elements or between intuitive and rigorous approach. Some philosophizing mathematicians remind us of the intuitive as a necessary background of all productive mathematical work, while others prefer to steer clear of anything „merely intuitive“ since they view it as something leading us to mistakes and paradoxes. The aim of this paper is to point out the variety of the intuitive in mathematical praxis and appeal for its more adequate appreciation both in the didactics and philosophy of mathematics. As a sort of a preliminary semantical map we make use of Reuben Hersh’s list of the distinctive usage of term „intuitive“ in contemporary mathematical discourse.

11

MORITZ SCHLICK, VIEDENSKÝ SCIENTIZMUS A NOVÁ FILOZOFIA

60%

Mihina F.

Filozofia (Philosophy)

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2016

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tom 71

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nr 8

680 – 695

EN

Moritz Schlick, the founder and leader of the Vienna Circle, occupies a position of importance in the history of modern philosophy. Our article is dedicated to memory of the thinker, who tragically died after a plot on him inside the Vienna University in June 1936. Schlick’s enduring contribution to the world philosophy is the fount of logical positivism. He was well prepared to give a new impetus to the philosophical questing of the future of philosophy. This paper offers a description of the foundations of Schlick’s philosophy.