Metafizyka ruchu w Geometrii Kartezjusza

In Book II of The Geometry, Descartes distinguishes some special lines, which he calls geometrical curves. From the mathematical perspective, these curves are identified with polynomials of two variables. In this way, curves, which were understood as continuous quantities in Greek mathematics, turned into objects composed of points in The Geome- try. In this article we present assumptions which led Descartes to this radical change of the concept of curve

Podwójna negacja w B 2 poematu Parmenidesa

In our article we focus on an analysis of the structure of double negation in the poem of Parmenides,paying attention to the fragment B 2. The starting point for the analysis is the classificationof varieties of negation contained in Diogenes Laertius (VII.69-70): negation, denial,privation and double negation. We provide an example of double negation as given by Diogenes: “Not (is not a day) ↔ it is a day”. In terms of the poetic expression the law of double negationserves to strengthen the goddess’ speech. However, in the context of Parmenides’ ontology, thelaw of double negation serves as an affirmation of “is”. Our goal is to give a detailed analysis ofthe structure of double negation. In the next step we introduce Euclid’s proofs by comparison.We show that all four forms of negation indicated by Diogenes occur in the Elements and thereis a richer set of the linguistic forms used as an expression of negation, including that of doublenegation. Finally, we show that Parmenides applies consciously the law of double negation,and the poem is the first philosophical text confirming the use of this law. In short, doublenegation can be summarized as follows: for the Stoics, in Diogenes Laertius (VII.69-70): “not(is not a day) ↔ is a day”; for Euclid: “not (is not-equal) ↔ is equal” (Elements, I.6). “is notlike that (.... is not around ...) ↔ is around” (Elements VI.26); and in Parmenides: “is ↔ not(is not to be)” (B 2, v. 3)

Poem of Parmenides

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

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

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

Poemat Parmenidesa. Fragmenty B 9-17, B 19

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

Radosława Nowakowskiego świat nieopisany

The article contains an attempt of philological and philosophical analysis of Radosław Nowakowski’s works – a writer and a musician associated with the Ossian music group. Due to the vast achievements of this author, we limit our discussion to the Treatise on Pageography or a question of liberature, one of the most representative works of Nowakowski, which has been written in the years 2002–2008. This text has the features of a literary work and is a summary of the philosophical and aesthetic views of the author. The philological aspect is discussed in relationship with liberature and the concept of “non-description of the world” and the philosophical aspect is focused on the identity and the ontological difference. The first part of the article contains a brief biography of Nowakowski and a recapitulation of his artistic achievements. In the second part it is discussed the writer’s work in relationship with liberature. The last part is a reflection on the phenomenon of “non-description of the world” and on the overcoming of the ontological dualism of matter and spirit. The article is supplemented by the complete bibliography of the Radosław Nowakowski’s works created up to the year 2014

Between obviousness and deduction. Plato and Euclid on equality

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

Radosław Nowakowski’s Inexpressible World

Artykuł zawiera próbę filologiczno-filozoficznej analizy twórczości liberackiej Radosława Nowakowskiego – pisarza i muzyka związanego z grupą Osjan. Z uwagi na obszerny dorobek tego twórcy, piszący ograniczą się do omówienia reprezentatywnego dzieła Nowakowskiego, jakim jest napisany w latach 2002–2008 Traktat kartkograficzny czyli rzecz o liberaturze. Tekst ten ma bowiem cechy utworu literackiego, dzieła liberackiego, a przede wszystkim stanowi wykładnię poglądów filozoficznych i estetycznych autora. W aspekcie filologicznym został omówiony związek twórczości Nowakowskiego z liberaturą oraz stworzone przezeń pojęcie nieopisania świata, w aspekcie filozoficznym autorzy skoncentrowali się natomiast na kwestii tożsamości i różnicy ontologicznej. W pierwszej części artykułu zawarto krótką biografię Nowakowskiego oraz rekapitulację jego dotychczasowego dorobku artystycznego. W części drugiej poruszono związki twórczości tego artysty z liberaturą. W części ostatniej omówiono natomiast zjawisko nieopisania świata oraz przekroczenia ontologicznego dualizmu materii i ducha. Artykuł uzupełniono bibliografią dzieł liberackich Radosława Nowakowskiego powstałych do roku 2014.The article contains an attempt of philological and philosophical analysis of Radosław Nowakowski’s works – a writer and a musician associated with the Ossian music group. Due to the vast achievements of this author, we limit our discussion to the Treatise on Pageography or a question of liberature, one of the most representative works of Nowakowski, which has been written in the years 2002–2008. This text has the features of a literary work and is a summary of the philosophical and aesthetic views of the author. The philological aspect is discussed in relationship with liberature and the concept of “non-description of the world” and the philosophical aspect is focused on the identity and the ontological difference. The first part of the article contains a brief biography of Nowakowski and a recapitulation of his artistic achievements. In the second part it is discussed the writer’s work in relationship with liberature. The last part is a reflection on the phenomenon of “non-description of the world” and on the overcoming of the ontological dualism of matter and spirit. The article is supplemented by the complete bibliography of the Radosław Nowakowski’s works created up to the year 2014

Euclid and Aristotle about Continuity. Part I. Euclid

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