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Model prožívaného času podle Petra Vopěnky

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Havel I.
Filosofický časopis (Philosophical Journal)
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2016
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vol. 64
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issue 4
539-560
EN
In the Ninth Meditation, entitled „O změnách jevů v čase“ (“On Changes in Pheno­mena in Time”), in the book Meditace o základech vědy (Meditations on the Foundations of Science; Praha, Práh 2001), Petr Vopěnka presents a certain non-traditional conception of experienced time, founded on his new infinite mathematics. The point of departure for his model is the idea of an “atomistic rhythm”, which is a linearly structured discrete sequence of beats. It is assumed that this rhythm is so fine that it runs far (or deeply) beyond our ability to distinguish individual beats from each other, so that it appears to us to be a continual temporal line. In this paper, Vopěnka’s model is interpreted in detail, but in the absence of mathematical formalism, and a view is presented as to how we might, on the basis of this model, formalise intuitive concepts such as past, future, present and the momentary “Now”. The interpretation is accompanied by a detailed analysis of Vopěnka’s approach and a sketching of the prospects for alternatives to it.
2
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Vopěnkova alternatívna teória množín alebo ťažký údel génia mimo hlavného prúdu

75%
Zlatoš P.
Filosofický časopis (Philosophical Journal)
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2016
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vol. 64
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issue 4
513-537
EN
In connection with Lem’s three degrees classification of genies, I will offer a personal view of Vopěnka’s alternative set theory and of its relation to Cantor’s set theory and Robinson’s nonstandard analysis. I will sketch some reasons which, in my opinion, restrict the potential of the Alternative Set Theory in particular, as well as of phenomenologically-founded mathematics in general. Finally, I will try to grasp the philosophical message of Vopěnka’s phenomenological exposition of mathematical infinity which may permanently influence some branches of mathematics, beyond the scope of its foundations
3
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Vopěnkova Alternativní teorie množin v matematickém kánonu 20. století

75%
Haniková Z.
Filosofický časopis (Philosophical Journal)
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2022
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vol. 70
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issue 3
485-504
EN
Vopěnka’s Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem’s construction of a nonstandard model of arithmetic, and its inception has been explicitly mentioned as an attempt to axiomatize Robinson’s nonstandard analysis. Vopěnka preferred working in an axiomatic theory to investigating its individual models; he also viewed other areas of nonclassical mathematics through this prism. This article is a contribution to the mapping of the mathematical neighbourhood of the Alternative Set Theory, and at the same time, it submits a challenge to analyze in more detail the genesis and structure of the philosophical links that eventually influenced the Alternative Set Theory.
CS
Vopěnkovu Alternativní teorii množin lze vnímat jak jako evoluci, tak stejně dobře jako revoluci: vychází z jeho předchozí zkušenosti s nestandardními univerzy, inspirované Skolemovou konstrukcí nestandardního modelu aritmetiky, a je ve svých počátcích explicitně zmiňována jako pokus axiomatizovat Robinsonovu nestandardní analýzu. Vopěnka upřednostňoval práci v axiomatické teorii před zkoumáním jejích jednotlivých modelů; tímto prizmatem nahlížel i některé další partie neklasické matematiky. Text je příspěvkem k mapování matematického okolí Alternativní teorie množin, zároveň otevírá otázku po podrobnější genezi a struktuře filosofických souvislostí, které Alternativní teorii množin postupně ovlivnily.
4
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Nekonečno a kontinuum v pojetí Petra Vopěnky

63%
Trlifajová K.
Filosofický časopis (Philosophical Journal)
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2016
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vol. 64
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issue 4
561-574
EN
One of the key themes of Petr Vopěnka was his understanding of mathematical infinity. He put forward many objections to Cantor’s established set theory. He worked out a new, alternative, theory in which he surprisingly interpreted infinity as a means of mathematising indeterminacy. He interpreted the continuum in a similar way. He drew on phenomenology, on Husserl’s motto “Return to things themselves”, and he employed a range of phenomenological concepts. At the same time, however, he did not give up the claim to mathematical precision in his theory. This claim brings with it certain pitfalls which centre on mathematical idealisation and its relation to the natural real world.
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