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273Formálna epistemológia a spoločenské vedy: odpoveď Markéte PatákovejTeorie Vědy / Theory of Science 37 (3): 327-360. 2015.Cieľom článku je upozorniť na niektoré možnosti použitia metód formálnej epistemológie v oblasti sociálnych vied. Ide predovšetkým o teóriu objektácií a teóriu re-prezentácií a s nimi spojené metódy rekonštrukcie potencialít a formálnych aspektov jazyka. V článku sa ďalej snažíme zodpovedať niektoré kritické námietky Markéty Patákovej, ktoré sformulovala na adresu formálnej epistemológie vo svojom texte Predikce v Kvaszově formální epistemologii ve světle historické metody Michela Foucaulta.
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252Kuhnova Štruktúra vedeckých revolúcií medzi sociológiou a epistemológiouTeorie Vědy / Theory of Science 34 (2): 167-187. 2012.Cieľom predkladanej state je pokus o upresnenie Kuhnovej teórie vedeckých revolúcií. Navrhujem rozlíšiť pojem vedeckej revolúcie, ktorý označuje sociologický fakt zmeny postoja vedeckého spoločenstva vo vzťahu k určitej teórii a pojem epistemickej ruptúry, ktorý označuje lingvistický fakt diskontinuity jazykového rámca, v ktorom je táto teória formulovaná. Analýzou zmien jazykového rámca možno získať klasifikáciu epistemických ruptúr na štyri typy, nazvané ideácia, re-prezentácia, objektácia a r…Read more
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159On classification of scientific revolutionsJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 30 (2): 201-232. 1999.The question whether Kuhn's theory of scientific revolutions could be applied to mathematics caused many interesting problems to arise. The aim of this paper is to discuss whether there are different kinds of scientific revolution, and if so, how many. The basic idea of the paper is to discriminate between the formal and the social aspects of the development of science and to compare them. The paper has four parts. In the first introductory part we discuss some of the questions which arose durin…Read more
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152The history of algebra and the development of the form of its languagePhilosophia Mathematica 14 (3): 287-317. 2006.This paper offers an epistemological reconstruction of the historical development of algebra from al-Khwrizm, Cardano, and Descartes to Euler, Lagrange, and Galois. In the reconstruction it interprets the algebraic formulas as a symbolic language and analyzes the changes of this language in the course of history. It turns out that the most fundamental epistemological changes in the development of algebra can be interpreted as changes of the pictorial form of the symbolic language of algebra. Thu…Read more
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125History of geometry and the development of the form of its languageSynthese 116 (2). 1998.The aim of this paper is to introduce Wittgenstein’s concept of the form of a language into geometry and to show how it can be used to achieve a better understanding of the development of geometry, from Desargues, Lobachevsky and Beltrami to Cayley, Klein and Poincaré. Thus this essay can be seen as an attempt to rehabilitate the Picture Theory of Meaning, from the Tractatus. Its basic idea is to use Picture Theory to understand the pictures of geometry. I will try to show, that the historical e…Read more
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109Kant's Philosophy of Geometry--On the Road to a Final AssessmentPhilosophia Mathematica 19 (2): 139-166. 2011.The paper attempts to summarize the debate on Kant’s philosophy of geometry and to offer a restricted area of mathematical practice for which Kant’s philosophy would be a reasonable account. Geometrical theories can be characterized using Wittgenstein’s notion of pictorial form . Kant’s philosophy of geometry can be interpreted as a reconstruction of geometry based on one of these forms — the projective form . If this is correct, Kant’s philosophy is a reasonable reconstruction of such theories …Read more
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85Heidegger's Interpretation of Mathematical Science in the Light of Husserl's Concept of Mathematization in the KrisisPhilosophia Naturalis 50 (2): 337-363. 2013.There are many interpretations of the birth of modern science. Most of them are, nevertheless, confined to the analysis of certain historical episodes or technical details, while leaving the very notion of mathematization unanalyzed. In my opinion this is due to a lack of a proper philosophical framework which would show the process of mathematization as something radically new. Most historians assume that the world is just like it is depicted by science. Thus they are not aware of the radical n…Read more
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84Changes of language in the development of mathematicsPhilosophia Mathematica 8 (1): 47-83. 2000.The nature of changes in mathematics was discussed recently in Revolutions in Mathematics. The discussion was dominated by historical and sociological arguments. An obstacle to a philosophical analysis of this question lies in a discrepancy between our approach to formulas and to pictures. While formulas are understood as constituents of mathematical theories, pictures are viewed only as heuristic tools. Our idea is to consider the pictures contained in mathematical text, as expressions of a spe…Read more
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43Kuhn’s Structure of Scientific Revolutions between sociology and epistemologyStudies in History and Philosophy of Science Part A 46 78-84. 2014.The aim of the paper is to clarify Kuhn’s theory of scientific revolutions. We propose to discriminate between a scientific revolution, which is a sociological event of a change of attitude of the scientific community with respect to a particular theory, and an epistemic rupture, which is a linguistic fact consisting of a discontinuity in the linguistic framework in which this theory is formulated. We propose a classification of epistemic ruptures into four types. In the paper, each of these typ…Read more
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39Revisiting the Mathematisation Thesis: Galileo, Descartes, Newton, and the Language of NatureInternational Studies in the Philosophy of Science 30 (4): 399-406. 2016.
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38How Can Abstract Objects of Mathematics Be Known?†Philosophia Mathematica 27 (3): 316-334. 2019.The aim of the paper is to answer some arguments raised against mathematical structuralism developed by Michael Resnik. These arguments stress the abstractness of mathematical objects, especially their causal inertness, and conclude that mathematical objects, the structures posited by Resnik included, are inaccessible to human cognition. In the paper I introduce a distinction between abstract and ideal objects and argue that mathematical objects are primarily ideal. I reconstruct some aspects of…Read more
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36A Ludic Book on Ludic Proof * Reviel Netz. Ludic Proof, Greek Mathematics and Alexandrian Aesthetic. Cambridge: Cambridge University Press, 2009. ISBN 978-0-521-89894-2. Pp. xvi + 255 (review)Philosophia Mathematica 19 (1): 91-95. 2011.The latest book of Reviel Netz presents a highly erudite analysis of the style of Hellenistic mathematics. Besides the Introduction and Conclusion the book is composed of four chapters. Before turning to more general remarks I would like first to outline the contents of the book.The Introduction starts with the presentation of Archimedes’ Spiral lines. In a condensed form, the author outlines his approach and calls attention to the stylistic peculiarities of that work. Most of the themes discuss…Read more
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33A Problem for Popper's FallibilismIn Zuzana Parusniková & R. S. Cohen (eds.), Rethinking Popper, Springer. pp. 71--81. 2009.
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30Epistemologické otázky modernej fyzikyOrganon F: Medzinárodný Časopis Pre Analytickú Filozofiu 1 (1): 40-61. 2005.The aim of the paper is to describe the main epistemological ruptures in the history of modern physics. Our approach is based on the reconstruction of the formal language of physical theories. We examine how particular aspects of the formal language, such as its analytical, expressive, or explanatory power, as well as its analytical and expressive boundaries, have changed in the course of the historical development of physics. In the closing part of the paper we discuss the results of our hi…Read more
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27Matematika a skutočnosťOrganon F: Medzinárodný Časopis Pre Analytickú Filozofiu 18 (3): 302-330. 2011.The aim of the present paper is to offer a new analysis of the multifarious relations 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 . 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, b…Read more
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26Appraising Lakatos: Mathematics, Methodology and the Man (edited book)Kluwer Academic Publishers. 2002.The volume also publishes for the first time a part of his Debrecen Ph.D. thesis and it is concluded by a bibliography of his Hungarian writings.
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24Tarski and Wittgenstein on Semantics of Geometrical FiguresVienna Circle Institute Yearbook 6 179-191. 1999.The aim of this paper is to compare two approaches to semantics, namely the standard Tarskian theory and Wittgenstein’s picture theory of meaning. I will compare them with respect to an unusual subject matter, namely to geometrical pictures. The choice of geometry rather than arithmetic or set theory as the basis, on which this comparison will be made has two reasons. One reason is related to Wittgenstein’s picture theory of meaning. This theory was developed more or less as a metaphor, comparin…Read more
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23Cognitive Unity of Thales’ MathematicsFoundations of Science 25 (3): 737-753. 2020.The aim of the paper is to argue for the cognitive unity of the mathematical results ascribed by ancient authors to Thales. These results are late ascriptions and so it is difficult to say anything certain about them on philological grounds. I will seek characteristic features of the cognitive unity of the mathematical results ascribed to Thales by comparing them with Galilean physics. This might seem at a first sight a rather unusual move. Nevertheless, I suggest viewing the process of turning …Read more
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22Diskusie-æ olemik›Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 9 (2): 205-211. 2002.
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21Matematika a skúsenosťOrganon F: Medzinárodný Časopis Pre Analytickú Filozofiu 16 (2): 146-182. 2009.Mathematics is traditionally considered being an apriori discipline consisting of purely analytic propositions. The aim of the present paper is to offer arguments against this entrenched view and to draw attention to the experiential dimension of mathematical knowledge. Following Husserl’s interpretation of physical knowledge as knowledge constituted by the use of instruments, I am trying to interpret mathematical knowledge also as acknowledge based on instrumental experience. This interpretatio…Read more
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20„Niekoľko poznámok k vzťahu prírodných a spoločenských vied.“Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 10 (2): 157-172. 2003.The aim of the paper is to present a theoretical framework which would make it possible to embed the conflict between the natural and human sciences into a broader historical context. With the help of categories such as paradigmatic disciplines, mixed discipline of the paradigm, metaphorical realm of the paradigm, and elusive realm of the paradigm we describe the dynamics of changes in the classification of scientific disciplines which accompany a scientific revolution. Our approach is thus an a…Read more
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19How Can a Falsified Theory Remain Corroborated?In Friedrich Stadler (ed.), Vienna Circle Institute Yearbook, Springer. pp. 263. 2004.Coming from a mathematical background, I was always puzzled by Popper’s view, according to which, after the falsification of a scientific theory its degree of corroboration becomes zero. Most of the scientific theories taught in the physics departments have already been falsified, and what is the point of teaching theories, whose degree of corroboration is zero? The first important observation to make is that not all cases of falsification are the same. In some cases, as for instance in the case…Read more
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18Je aristoteles reálnou alternatívou?Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 15 (2): 206-210. 2008.
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17Prolegomena k formálnej epistemológiiOrganon F: Medzinárodný Časopis Pre Analytickú Filozofiu 6 (1999): 223-239. 1999.The aim of this paper is a philosophical generalisation of the results, which we obtained through the analysis of the development of synthetic geometry. I our papers Náčrt analytickej teórie subjektu and Topológia versus teória množín we proposed a method of analysis of the development of geometry based on Wittgensteinś Picture theory of meaning from the Tractatus. It turned out, that the concept of the form of language can be effectively used to characterise the changes, which occured in the co…Read more
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17K niektor› M aspektom vzniku analytickej filozofieOrganon F: Medzinárodný Časopis Pre Analytickú Filozofiu 11 (1): 32-41. 2004.Cieľom článku je osvetliť niektoré historické okolnosti vzniku analytickej filozofie. Prvou z nich je zrod novovekej fyziky, ktorý viedol k rozšíreniu nového, empirického prístupu ku skutočnosti. Snažíme sa ukázať úlohu, ktorú v procese vzniku novovekej fyziky zohrala scholastická filozofia spolu s kartezianizmom. Ďalšia časť state objasňuje niektoré aspekty subjektivizmu, ktorý zohral významnú úlohu v novovekej filozofii. V jadre subjektivizmu leží podľa nášho názoru dezinterpretácia Descartove…Read more
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15Na obranu osamelých bežcovOrganon F: Medzinárodný Časopis Pre Analytickú Filozofiu 11 (2,198-201): 198-201. 2004.
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15Stupne nekonzistentnostiOrganon F: Medzinárodný Časopis Pre Analytickú Filozofiu 19 95-115. 2012.
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13The propositional content of the Popper-Lakatos riftIn G. Kampis, L.: Kvasz & M. Stöltzner (eds.), Appraising Lakatos: Mathematics, Methodology and the Man, Kluwer Academic Publishers. pp. 1--3. 2002.
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12K vyjasneniu jedn é ho nedorozumeniaOrganon F: Medzinárodný Časopis Pre Analytickú Filozofiu 12 (4): 438-446. 2005.