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  1. Dwa oblicza matematyki.Jarosław Mrozek - 2004 - Przeglad Filozoficzny - Nowa Seria 51 (3):65-71.
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  2. Matematyka i świat.Jarosław Mrozek - 1997 - Filozofia Nauki 4.
    The author presents Einstein's viewpoint on the issue of the relation between mathematics and the world. Mathematics, as Einstein seems to suggest, cannot model the structure of the world in an absolutely adequate way since, if mathematical theorems are certain, they don't apply to the reality. However from the fact that something cannot be done in an adequate way, it doesn't follow that it can't be done at all. Mathematics can and should be applied to desrcibe the reality, but in (...)
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  3. Matematyka - narzędzie czy opis? Instrumentalistyczna i realistyczna interpretacja zastosowań matematyki.Jarosław Mrozek - 1996 - Filozofia Nauki 2.
    In the paper there are presented two proposals of the interpretations of the applications of mathematics in the natural sciences - realistic and instrumentalistic. The realistic conception, in accordance with the successes of science, maintains that there exists some kind of correspondence between the mathematical structures and the internal structure of the world. It is expressed in the thesis of the mathematicality of nature. The instrumentalistic approach separates the cognitive content of the scientific theory from the mathematical means of expression (...)
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  4. Poznawcze funkcje matematyki.Jarosław Mrozek - 2001 - Filozofia Nauki 4.
    The paper is an attempt to present the cognitive functions of mathematics in relation to empirical sciences. Firstly - mathematics is a 'generator' of mathematical categories used in natural sciences. In this sense mathematics is a science about the tools of cognition which it creates or perfects. Secondly - mathematics plays the role of 'prism' through which we view the world because some phenomena e.g. from the micro- and macro-world can only be seen through the prism of mathematical structures and (...)
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  5. Powstanie i perspektywy dowodu matematycznego.Jarosław Mrozek - 2000 - Filozofia Nauki 1.
    This paper is an attempt to review the historically existing types of demonstration of mathematical theorems. The author shows how the notion of mathematical proof has changed through the time from the moment when mathematicians realised (thanks to the philosophical method) the necessity to justify their theses until a precise notion of proof has appeared in the framework of the formal method. Next, the author considers the possibility of modifying the notion of mathematical proof under the influence of the development (...)
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  6. Problem matematyczności przyrody.Jarosław Mrozek - 2004 - Filozofia Nauki 2.
    The aim of this paper is a presentation, specification and criticism of the thesis proclaiming the mathematicality of nature. The author distinguishes between the structural and the functional aspects of this thesis. With such an interpretation this thesis has a strong methaphysical interpretation. However such thesis is linked with some problems, concerning the issue of its verification. Therefore the author proposes to consider a neutral thesis proclaiming that nature is amathematical. Then we avoid strong assumptions concerning the structure of the (...)
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