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Pythagorejská matematika vo svetle karteziánskej fyziky

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Kvasz L.
Filosofický časopis (Philosophical Journal)
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2017
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vol. 65
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issue 4
513-541
EN
This paper is the second part in a series of articles aimed at reconstructing the emergence of mathematics as a deductive discipline in ancient Greece in the period between Thales and Euclid. We understand the emergence of mathematics as the birth of a language which enables the undertaking of deductive proofs. While in the preceding part we focused on the beginnings of Greek mathematics in Thales, here we concentrate on Pythagorean mathematics. In the literature the significance of Pythagoras as a mathematician is called into doubt. Despite this, the main part of the paper involves a reconstruction of the cognitive style of Pythagorean mathematics and this reconstruction is the basis for a defence of its authenticity.
2
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O idealizácii v exaktných vedách

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Kvasz L.
Filosofický časopis (Philosophical Journal)
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2012
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vol. 60
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issue 4
483-503
EN
The philosophical analysis of the process of idealisation has developed in two independent directions. In the framework of analytical philosophy of science, idealisation is understood as a simplification or deformation of the description of a certain appearance or natural law. In the framework of the phenomenological tradition idealisation is understood as the quantification of a certain phenomenon of the life-world. The aim of this paper is to give an exposition of these two conceptions of idealisation and to attempt to clarify their mutual relation. In conclusion I sketch a third conception of idealisation which has not received attention in the literature.
SK
Filozofická analýza procesu idealizácie je rozvíjaná v dvoch nezávislých smeroch. V rámci analytickej filozofie vedy je idealizácia chápaná ako zjednodušenie či deformácia opisu určitého javu či prírodného zákona. V rámci fenomenologickej tradície je idealizácia chápaná ako kvantifikácia určitého fenoménu žitého sveta. Cieľom predkladanej state je obe tieto pojatia idealizácie stručne predstaviť a pokúsiť sa objasniť ich vzájomný vzťah. V závere state je načrtnuté tretie pojatie idealizácie, ktorému zatiaľ v literatúre nebola venovaná pozornosť.
3

ŠACH AKO METAFORA MATEMATIKY

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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.
4

MATEMATIKA A SKUTOČNOSŤ

100%
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.
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