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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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vol. 46
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issue 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.
2
Content available remote

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

100%
Czerniawski J.
Zagadnienia Naukoznawstwa
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2010
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vol. 46
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issue 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.
3
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Intuition and Hermeneutics: the Intuitive Analysis of Concepts

80%
Krol Z.
Zagadnienia Naukoznawstwa
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2006
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vol. 42
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issue 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.
4

ŠACH AKO METAFORA MATEMATIKY

80%
Kvasz L.
Filozofia (Philosophy)
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2015
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vol. 70
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issue 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
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„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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issue 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

PENELOPE MADDYOVÁ MEDZI REALIZMOM A NATURALIZMOM

80%
Kvasz L.
Filozofia (Philosophy)
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2010
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vol. 65
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issue 6
522-537
EN
Mathematics is often interpreted as an a priori discipline whose propositions are analytic. The aim of the paper is to support a philosophical position which would view mathematics as a discipline studying its own segment of objective reality and thus contributing to our knowledge of the real world. The author tries to articulate in more details such a position which has been proposed recently by Penelope Maddy.
7

PHILOSOPHY OF MATHEMATICS AND COMPUTER SCIENCE

80%
Trzesicki K.
Studies in Logic, Grammar and Rhetoric
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2010
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issue 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.
8
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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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vol. 46
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issue 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?
9

MATEMATIKA A SKUTOČNOSŤ

70%
Kvasz L.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2011
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vol. 18
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issue 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.
10

PARFIT ON MORAL DISAGREEMENT AND THE ANALOGY BETWEEN MORALITY AND MATHEMATICS

70%
Greif A.
Filozofia (Philosophy)
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2021
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vol. 76
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issue 9
688 – 703
EN
In his book On What Matters, Derek Parfit defends a version of moral non-naturalism, a view according to which there are objective normative truths, some of which are moral truths, and we have a reliable way of discovering them. These moral truths do not exist, however, as parts of the natural universe nor in Plato’s heaven. While explaining in what way these truths exist and how we discover them, Parfit makes analogies among morality on the one hand, and mathematics and logic on the other. Moral truths “exist” in a way that numbers exist, and we discover these truths in a similar way as we discover truths about numbers. By the end of the second volume, Parfit also responds to a powerful objection against his view, an objection based on the phenomenon of moral disagreement. If people widely and deeply disagree about what is the moral truth, it is doubtful whether we have a reliable way of discovering it. In his reply, he claims that in ideal conditions for thinking about moral questions, we would all have sufficiently similar moral beliefs. However, we often find ourselves in less-than-ideal conditions due to various factors that distort our ability to agree. Therefore, differences in moral opinion can be expected. In this paper, I draw a connection between these parts of Parfit’s theory and comment on them. Firstly, I argue that Parfit’s analogy with mathematics and logic and his answer to the disagreement objection are in tension because there are important epistemic differences between morality and these fields. If one would try to account for the differences, one would have to sacrifice some measure of similarity between morality and them. Secondly, I comment on Parfit’s reply to the disagreement objection itself. I believe that, although his description of ideal conditions has some potential for reaching moral agreement, it may be difficult to tell if ideal conditions prevail. This obscurity spells further trouble for Parfit’s overall theory.
11

FILOZOFIA MATEMATIKY RANÉHO ERNSTA CASSIRERA

70%
Maco R.
Filozofia (Philosophy)
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2010
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vol. 65
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issue 1
27-39
EN
The paper deals with some major themes in early Cassirer's philosophy of mathematics. It appears, that the basis of his thinking about mathematical objects and mathematical concept formation is his Neo-Kantian idealistic (transcendental) theory of concepts which he developed in opposition to what is called the 'traditional theory of concepts' going back to Aristotle. Cassirer often seeks to confirm his philosophical insights concerning mathematics by the interpretations the works of significant mathematicians. Therefore, the second part of the paper deals with Cassirer's attempt to find such a confirmation in famous Dedekind's theory of natural numbers. Cassirer's philosophical attitude to Dedekind's theory is compared with that of Russell. The author raises the sceptical question of whether Cassirer's view of mathematics - as developed in his early period - could be a sufficient or at least plausible basis for solving philosophical problems of the foundations of mathematics of that time.
12

THE SEKED: ON ANCIENT EGYPTIAN MATHEMATICS AND ASTRONOMY

70%
Magdolen D.
Asian and African Studies
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2004
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vol. 13
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issue 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.
13

MORITZ SCHLICK, VIEDENSKÝ SCIENTIZMUS A NOVÁ FILOZOFIA

61%
Mihina F.
Filozofia (Philosophy)
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2016
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vol. 71
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issue 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.
14

V.I. VERNADSKY: METHEMATICS IN THE DOMAIN OF SCIENCE (V.I.Vernadsky: Matematika v prostranstve nauki)

61%
Mochalov I. I., Onopriyenko V. I.
Nauka ta naukoznavstvo (Science and Science of Science)
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2010
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issue 4
60-69
EN
V. I. Vernadsky left a unique legacy in the fields of philosophy and methodology of science. The logical structure of science, elaborated by him, is based on the principle of the objective truthfulness of scientific knowledge and its various manifestations in various parts of science, which are unequal in terms of truthfulness (authenticity). The first part is the one being quite authentic and constituting the frame of science, e.g. the core manifestation and content of scientific knowledge, whereas the second part 'clothes' the frame of science and constructs upon its. The notion of the frame of science, introduced by Vernadsky to signify the core structure of the scientific knowledge, seems to be a very accurate reflection of the knowledge system of logics, mathematics and scientific apparatus. Considering Vernadsky's theses on the issue, a series of arguments can be given in favor of treating mathematics, logics and scientific apparatus as the fundament of scientific knowledge. Yet, V. I. Vernadsky treats mathematics as a central component in the notion 'frame of science', introduced by him, as a genetic turn in its creation. Mathematics integrates 'frame of science' through logics, and this determines the exclusive role of mathematics in the science. The Vernadsky's treatment of mathematics is shown in great detail with reference to original works of him.
15

ATTITUDE TOWARDS MATHEMATICS AMONG CHINESE AND HUNGARIAN SECONDARY SCHOOL STUDENTS (Kinai es magyar szakkozepiskolas diakok matematika iranti attitudje)

61%
Sebestyen N.
Magyar Pszichologiai Szemle (Hungarian Psychological Review)
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2009
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vol. 64
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issue 1
155-177
EN
In recent decades, intercultural psychologists and educators have paid increasing attention to the East Asian cultures, mostly focusing on knowing and understanding their education successes and revealing the cultural and social factors that cause these results. Despite of much research on Chinese–American comparison, just a few investigations compare China to another, non-american country, especially to Hungary. One of the authoress' purposes was to attempt to fill this gap and broaden the literature in this subject. The goal of this study was to explore mathematical beliefs and behaviors among 128 Chinese and 106 Hungarian Grade 10-11 vocational secondary school students. Their mathematical attitude was investigated with a questionnaire - developed by Schoenfeld (1989) - containing 70 closed questions in 6 sections: attributions of success and failure; perception of mathematics and school practice; student's views of school mathematics, English and social studies; the views of the nature of geometry; motivation; and personal and scholastic performance and motivational data. The findings show important cultural differences in the field of effort (more important for the Chinese students), motivation (negative motivation, like fear of serious consequences of low achievement in mathematics is more significant among the Hungarian students) and family support (in the Chinese sample it was considered more important that both parents are interested in the performance of their child). These results can help to organize Hungarian math teaching and education in a more effective way, furthermore to support the Chinese students in Hungary.
16

INTUÍCIA V MATEMATIKE

61%
Maco R.
Filozofia (Philosophy)
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2016
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vol. 71
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issue 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.
17

KANTOVSKÉ MOTÍVY PROSTORU V GAUSSOVE DIFERENCIÁLNÍ GEOMETRII

61%
Benediktová Větrovcová M.
Filozofia (Philosophy)
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2012
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vol. 67
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issue 6
476 – 484
EN
The aim of this contribution is to show the Kantian concept of space as a hidden presupposition of Gauss’ geometrical treatises. First, the introduction of mathematization, origins of mathematics and geometry is depicted on the philosophical background of Husserl’s phenomenology as one possible interpretation of space. Further, Kant’s ideas on mathematics and space are summarized. The motivations of Gauss’ differential geometry exemplify the revolution in mathematics in 19th century. In conclusion Kantian motives of space in Gauss’ differential geometry as the intrinsic geometry of a curved surface are shown.
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