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1

MATHEMATICS AND EXPERIENCE (Matematika a skusenost)

100%
Kvasz L.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2009
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vol. 16
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issue 2
146-182
EN
By definition mathematics is traditionally considered to be a 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, the author is trying to interpret mathematical knowledge also as acknowledge based on instrumental experience. This interpretation opens a new view on the role of the logistical program, both in philosophy of mathematics and in philosophy of science.
2

PHILOSOPHY OF MATHEMATICS AND COMPUTER SCIENCE

100%
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.
3

LOGICISM AND PARADOX I.

100%
Kolman V.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2005
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vol. 12
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issue 1
1-20
EN
This is the first part of the essay devoted to the story of logicism, in particular to its Fregean version. Reviewing the classical period of Fregean studies, we first point out some critical moments of Frege's argumentation in the 'Grundlagen', in order to be able later to differentiate between its salvageable and defective features. We work on the presumption that there are no easy, categorical answers to questions like 'Is logicism dead?': Wittgenstein's critique of the foundational program as well as the remarkable neo-Fregean discoveries of Boolos and Wright have to be confronted with the effects which the logicistic idea actually had on logico­matematical practice. But that is another story, a sequel to this essay, the purpose of which is systematic rather than critical.
4

Říká logicismus něco, co se říkat nemá?

88%
Kolman V.
Teorie vědy (Theory of Science)
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2010
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vol. 32
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issue 1
37-57
EN
The objective of this paper is to analyze the broader significance of Frege's logicist project against the background of Wittgenstein's philosophy from both Tractatus and Philosophical Investigations. The article draws on two basic observations, namely (1) that Frege's project aims at saying something that was only implicit in everyday arithmetical practice, as the so-called recursion theorem demonstrates, and (2) that the explicitness involved in logicism does not concern the arithmetical operations themselves, but rather the way they are defined. It thus represents the attempt to make explicit not the (arithmetical) rules alone, but rather the rules governing their following, i.e. rules of second-order type. I elaborate on these remarks with short references to Brandom's refinement of Frege's expressivist and Wittgenstein's pragmatist project.
5

INTUITION AND THE END OF ALL –ISMS

75%
Kolman V.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2018
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vol. 25
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issue 3
392 – 409
EN
In his paper, some of the most influential –isms in the philosophy of mathematics are discussed with respect to their attitude to intuition. By the end of the all -isms, at first, their tendency to arrive eventually at just the opposite of their previously proclaimed principle is meant. The positive significance to the given tag line is connected with as a simple observation (due to both William James and Wittgenstein) that most of the -isms are justifiable if treated as practical attitudes rather than theoretical systems. Accordingly, intuition’s role will be twofold: first, as a reference point with respect to which the given -isms were portrayed as turning into their very opposites; and, second, as the focal point to which all of them might be seen as contributing to intuition’s pragmatic reading. Along these lines, the path of intuition might be transformed from an epistemological Calvary — or the path of despair, to use Hegel’s words from the beginning of his Phenomenology in which one particular theory is replaced by another which is itself later replaced, etc. — into the path of progress in which some traditional dilemmas such as that between mathematical realism and nominalism are solved.
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