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1

Poemat Parmenidesa. Fragmenty B 9-17, B 19

100%

Mrówka K.

Zagadnienia Filozoficzne w Nauce

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2012

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issue 50

118-139

PL

This is a new translation of the Fragments of Parmenides of Elea, the fifth century B.C. thinker. The text includes: a Greek poem with the fragments B 9-17, B 19, a critical apparatus which takes into consideration some new editions and a new English translation.

2

Genesis of the mystical ecstasy in the prologue of the Parmenides’ poem

100%

Mrówka K.

Filozofia Chrześcijańska

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2016

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vol. 13

54-63

PL

The preserved fragments of the Parmenides’ work is one of the oldest testimonies of the mystical experience in philosophy. Mystique meets here with metaphysics. The poem’s prologue is a transcript of the mystic passage of a young man to the goddess who symbolizes the truth of being. By knowing the goddess and her message, young man learns the nature of being. The ecstatic experience opens him on the metaphysical dimension of reality. The sources of the Parmenides’ mysticism are following: the pythagorean philosophy, orphism, shamanism and the cult of Apollo at Delphi.

3

Miedzy oczywistością a dedukcją. Platon i Euklides o równości

63%

Błaszczyk P., Mrówka K.

Zagadnienia Filozoficzne w Nauce

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2011

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issue 48

127-147

PL

We confront Plato's understanding of equality in geometry with that of Euclid. We comment on Phaedo, 74b-c, Meno, 81e-85d and Elements, Book I. We distinguish between two meanings of equality, congruence and equality of the area, and show that in Plato equality means congruence. In Euclid, starting with the first definitions until Proposition I.34, equality means congruence. In the proof of Proposition I.35 equality gains a new meaning and two figures that are not congruent, and in this sense unequal, are considered to be equal. While Plato's geometry is based on self-evident facts, Euclid's geometry rests on deduction and the axioms that are by no means self-evident. However, the shift of meaning from congruence to equality of the area can be substantiated by reference to Euclid's axioms of equality. Finally, we present an ontological interpretation of the two attitudes to equality that we find in Plato's and Euclid's writings.

4

Euclid and Aristotle about Continuity. Part I. Euclid

63%

Błaszczyk P., Mrówka K.

Filozofia Nauki

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2013

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vol. 21

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issue 4

91-115

PL

Line segment is a kind of ancient Greek μέγεθος. It is described mathematically in Euclid’s Elements and in a philosophical way in Aristotle’s Physics. In this first part of our paper we present Euclid’s twofold attitude toward a line segment: the first one developed in his theory of proportion of magnitudes (book V), the second in his plain geometry (books I-IV). Euclid’s magnitudes are of several different kinds: lines segments, triangles, convex polygons, arcs, angles. Magnitudes of the same kind can be added to one another and compared as greater–lesser. We provide a set of axioms for the line segments system (M, +, <) and show that the total order of segments < is compatible with the addition operation +. The positive part of an Archimedean field is a model of these axioms. Next, we present an interpretation of Euclid’s proposition I.10 and show that Aristotle’s famous saying “everything continuous is divisible into divisibles that are infinitely divisible” applies to a single line segment. Our study is based on Heiberg’s Euclidis Elementa.

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2 Zagadnienia Filozoficzne w Nauce

1 Filozofia Chrześcijańska

1 Filozofia Nauki

1 2016

1 2013

1 2012

1 2011

4 Mrówka K.

2 Błaszczyk P.

Poemat Parmenidesa. Fragmenty B 9-17, B 19

Genesis of the mystical ecstasy in the prologue of the Parmenides’ poem

Miedzy oczywistością a dedukcją. Platon i Euklides o równości

Euclid and Aristotle about Continuity. Part I. Euclid