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1

Thalétova matematika v zrkadle Galileovej fyziky

100%

Kvasz L.

Filosofický časopis (Philosophical Journal)

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2014

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vol. 62

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issue 5

643-659

EN

The aim of this article is to sketch a certain method of indirect reconstruction of the process by which mathematics as a deductive discipline emerged in ancient Greece. We try out this method in a reconstruction of Thales' mathematics, but the main aim for which this method has been developed is the work of Pythagoras. We consider the process of the emergence of mathematics as a process of the constitution of a new language in the framework of which one can carry out deductive proofs. Therefore we base the method of indirect reconstruction of the emergence of mathematics on the theoretical findings in the book L. Kvasz: Vedecká revolúcia ako lingvistická událosť (The Scientific Revolution as a linguistic event, Prague, Filosofia 2013).

2

Anaximandrova geometrie

88%

Kočandrle R.

Filosofický časopis (Philosophical Journal)

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2013

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vol. 61

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issue 2

163-180

EN

According to tradition Thales brought geometry to Greece from Miletus. Although discussion of the nature of Thales’ geometry has not arrived at a consensus, it seems that the theorems formulated were retrospectively applied in his concrete measurements. So far, however, we have no information about the geometry of Thales’ pupil and successor, Anaximander of Miletus. An exception is presented in the lexicon Suda which claims that Anaximander “in general showed the basics of geometry”. This lexicon at the same time states the points at which the employment of the geometry can be discerned. Most importantly, we have the question of the gnomon, with the help of which an order of measurement is realisable. Clear signs of the application of geometry are likewise shown by Anaximander’s whole conception of cosmology: the shape of the earth and its position at the centre of the universe, and the very description of the heavenly bodies. In addition one can discern geometry involved in the map of the world and the sphere. Thus, although Anaximander is not explicitly connected with geometry, extant texts demonstrate that he significantly exploited geometrical knowledge when he connected concrete observation with the geometrical organisation of the universe as a whole.

CS

Podle tradice přenesl geometrii do Řecka Thalés z Mílétu. Ačkoli v diskusích o povaze Thalétovy geometrie nepanuje konsensus, zdá se, že zformulované teorémy byly až dodatečně uplatněny na jeho konkrétní měření. Již o Thalétově „žákovi a nástupci“, Anaximandrovi z Mílétu, však nemáme žádné zprávy, které by se týkaly geometrie. Výjimku představuje lexikon Súda, který uvádí, že Anaximandros „vůbec ukázal základy geometrie“. Lexikon zároveň vyjmenovává momenty, v nichž může být užití geometrie spatřeno. V prvé řadě se jedná o gnómón, s jehož pomocí mohla být realizována řada měření. Zřejmé znaky uplatnění geometrie vykazuje též celá Anaximandrova koncepce kosmologie: tvar Země a její umístění ve středu univerza, i samotný popis nebeských těles. Podobně lze uplatnění geometrie spatřovat za mapou světa a sférou. Ačkoli tedy Anaximandros není explicitně s geometrií spojován, dochované texty ukazují, že její poznatky významně využil, když propojil konkrétní pozorování s geometrickým uspořádáním celého univerza.

3

Anaximander’s Treatise on the Earth

63%

Rossetti L.

Peitho. Examina Antiqua

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2013

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vol. 4

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issue 1

23-62

EN

The present paper argues that the teachings of Anaximander are much better knowable than they actually appear, since a number of his teachings have the privilege of being almost transparent in their predicative content as well as in their logic. As a matter of fact, one can quite easily come to understand the train of thought which lies behind Anaximander’s most momentous conjectures. Thus, a largely unexpected Anaximander comes to light despite the availability of the majority of the relevant sources since 1903. Two main areas appear to be particularly prominent: on the one hand, the complex body of various conjectures and doctrines that helps to understand the system of spatial relationships from Miletus to the stars and, on the other hand, the equally complex body of conjectures and doctrines whose primarily concern is the macro-story of the Earth from its most remote past to its predictable future. The merits of Anaximander as an earth-researcher are much greater than one could actually imagine. It is suggested here that what philosophy owes to him in particular lies in his quest for knowledge, his method, his cognitive hybris, and his intellectual discipline, rather than individual doctrines. A comparison with Thales follows in the last paragraph.

4

Normativity and Ontology of Law in Early Greek Philosophy

45%

Goździalski K.

Acta Universitatis Lodziensis. Folia Iuridica

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2022

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vol. 100

107-125

PL

Artykuł poświęcony jest przybliżeniu problematyki powstania europejskiej nauki i filozofii, które zostały ufundowane przez antycznych Greków. W okresie nazywanym Pierwszym Oświeceniem doszło, z jednej strony do stopniowego odejścia od mitologicznych wyjaśnień rzeczywistości, z drugiej – do zbudowania nowego sposobu patrzenia na świat, zwanego badaniem przyrody. Dociekania antycznych Greków miały wymiar ontologiczny – polegały na poszukiwaniu arche świata – poszukiwali oni bowiem ostatecznej struktury rzeczywistości, a co ważne, człowiek usytuowany był w tych badaniach jako integralna ale nie najważniejsza część kosmosu, poddana jego prawom. Presokratycy nie stawiali człowieka ponad naturą, nie odróżniali bowiem ściśle praw przyrody od praw wspólnoty. Był to jeden z powodów, dla których nie powstała wówczas nauka prawa. Poza tym, Grecy nigdy nie redukowali swojego prawa do systemu, ponieważ zbyt często bogowie lub demos „wtrącali się” do praw polis. Było ono typowym przykładem „prawa bez prawoznawstwa”, ponieważ było elastyczne a także posiadało niejasno sformułowane reguły i instytucje. Istotny był tutaj również brak wyszkolonej grupy zawodowych prawników. Okres ten zakończył się wraz z pojawieniem się filozofii Sokratesa. Do jego czasów filozofia badała liczby i ruchy, a także zajmowała się zagadnieniem, skąd wszystkie rzeczy biorą swój początek i dokąd znikają; obserwowała też gwiazdy, odległości między nimi, ich obiegi oraz badała zjawiska pojawiające się na niebie. Pierwsi mędrcy uważali, że zdobywają wiedzę przez prowadzenie badań dotyczących samych zjawisk naturalnych. Sokrates odrzucił ontologię i badanie natury zapoczątkowane przez Milezyjczyków i myślicieli z obszaru Wielkiej Grecji, na rzecz poszukiwania znaczenia słów i pojęć występujących w języku ateńskiego polis. Sądził bowiem, że znalezienie znaczenia słów oznacza odsłonięcie rzeczywistości, do której inaczej dotrzeć nie można.

EN

The paper is devoted to the issues of the emergence of European science and philosophy, founded by the ancient Greeks. In the period known as the First Enlightenment, there was, on the one hand, a gradual departure from the mythological explanations of the reality, and, on the other, the construction of a new way of looking at the world, known as the study of nature. The inquiries of the ancient Greeks had an ontological dimension; they consisted in searching for the arche of the world and they were looking for the ultimate structure of reality, and, what is important, the human being was situated in these studies as an integral, but not the most important part of the Cosmos, subject to its laws. Presocratics did not put the human being above nature, because they did not strictly distinguish between the laws of nature and the laws of community. This was one of the reasons why the science of law did not arise at that time. Besides, the Greeks never reduced their right to the system, because too often gods or demos ‘interfered’ with the laws of the polis. It was a typical example of “law without jurisprudence”, because it was flexible and had vaguely formulated rules and institutions. Another significant factor here was the lack of the trained group of professional lawyers. This period ended with the advent of Socrates’ philosophy. Up to his time, philosophy had studied numbers and movements, and had dealt with the question of where all things have their origin and where they disappear; it also had observed the stars, the distances between them, their circuits, as well as had studied phenomena which appear in the sky. The early sages believed that they could gain knowledge by conducting research into natural phenomena themselves. Socrates rejected the ontology and study of nature initiated by the Milesians and other early Greek thinkers in favour of searching for the meaning of words and concepts found in the Athenian polis language. He believed that finding the meaning of words translated into revealing the reality which could not be reached otherwise.

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2 Filosofický časopis (Philosophical Journal)

1 Acta Universitatis Lodziensis. Folia Iuridica

1 Peitho. Examina Antiqua

1 2023

1 2014

2 2013

1 Goździalski K.

1 Kočandrle R.

1 Kvasz L.

1 Rossetti L.

Thalétova matematika v zrkadle Galileovej fyziky

Anaximandrova geometrie

Anaximander’s Treatise on the Earth

Normativity and Ontology of Law in Early Greek Philosophy