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1

Pythagorejská matematika vo svetle karteziánskej fyziky

100%

Kvasz L.

Filosofický časopis (Philosophical Journal)

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2017

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vol. 65

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issue 4

513-541

EN

This paper is the second part in a series of articles aimed at reconstructing the emergence of mathematics as a deductive discipline in ancient Greece in the period between Thales and Euclid. We understand the emergence of mathematics as the birth of a language which enables the undertaking of deductive proofs. While in the preceding part we focused on the beginnings of Greek mathematics in Thales, here we concentrate on Pythagorean mathematics. In the literature the significance of Pythagoras as a mathematician is called into doubt. Despite this, the main part of the paper involves a reconstruction of the cognitive style of Pythagorean mathematics and this reconstruction is the basis for a defence of its authenticity.

2

Pitagoras i kultura grecka

100%

Korczak A.

Prosopon. Europejskie Studia Społeczno-Humanistyczne

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2012

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issue 2(4)

259-265

EN

The author presents the views of Pythagoras in contrast to the views of other ancient Greek philosophers or the Pythagoreans.

3

The Figure of Socrates in Numenius of Apamea: Theology, Platonism, and Pythagoreanism (fr. 24 des Places)

88%

Volpe E.

Peitho. Examina Antiqua

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2022

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vol. 13

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issue 1

169-184

EN

Numenius is one of the most important authors who, in the Imperial Age, deal with the figure of Socrates. Socrates is important in the Platonic tradition, in particular in the sceptical tradition, when the Socratic dubitative “spirit” of the first Platonic dialogues became important to justify the “suspension of judgement.” Numenius criticises the whole Academic tradition by saying that the Academics (particularly the sceptics) betrayed the original doctrine of Plato and formulated a new image of Socrates. For Numenius, Socrates plays a central role because Plato would have inherited his doctrine. What does Socrates’s doctrine consist in? According to Numenius, Socrates theorised a “doctrine of three Gods” (which can be likely found in the second Platonic epistle) which is strictly bound up with the main aspect of Plato’s thought. In fact, in Numenius’s view, Plato belongs to a genealogy which can be linked to Pythagoras himself. From this perspective, Numenius says that Socrates’s original thought is a theology which also belongs to the Pythagorean tradition and which Plato further developed. For Numenius, Socrates is not the philosopher of doubt, but a theologian who first theorised the existence of three levels of reality (Gods), which is also the kernel of Numenius’s metaphysical system. For this reason, Numenius puts Socrates within a theological genealogy that begins with Pythagoras and continues with Socrates and Plato, and that the Academics and the Socratics failed to understand.

4

On Symbolic Allegoresis of the First Pythagoreans

75%

Domaradzki M.

Peitho. Examina Antiqua

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2013

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vol. 4

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issue 1

93-104

EN

The present paper argues that the early Pythagoreans contributed significantly to the development of ancient hermeneutics. The article builds on the assumption that even if the thinkers did not deal with allegoresis directly, the very manner of articulating their thought was, nevertheless, quite conducive to the growth of allegorical interpretation. Thus, at least indirectly, Pythagoreanism must have played an important role in the development of allegoresis. The paper identifies two crucial aspects of Pythagorean influence on the allegorical tradition. Firstly, the Pythagoreans made a very specific use of the poetry of Homer and Hesiod as well as of the traditional mythology in general. Secondly, the teachings of Pythagoras were expressed in terms of various ambiguous symbols that required special exegesis. Both these factors must have contributed considerably to the development of allegoresis: the idiosyncratic use of conventional mythology, on the one hand, and the enigmatic nature of the Pythagorean symbols, on the other, must have provoked extensive search for the latent (i.e., “allegorical”) meaning of the “messages” in question.

5

Arist. Rhet. 2.23.1398b and the cult of Pythagoras

63%

Mojsik T.

Classica Cracoviensia

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2015

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issue 18

293-310

EN

In the present article I would like to focus on three things: the usefulness of Alcidamas’s fragment (cited in Arist. Rhet. 2.23.1398b) for the procedure of establishing when the cult of poets/intellectuals began, the suitability of the terminology in scholarly papers which refer to the problem, and the validity of the information about Pythagoras. In conclusion it is proposed that there are no existing testimonies supporting the (weak) hypothesis that the phrase καὶ Ἰταλιῶται Πυθαγόραν featuring in manuscripts of Rhetoric is authentic. Few late testimonies are either too vague or they indicate only Crotone and Metapontum, and not Greeks from the Italian peninsula in general. Such a perspective is not typical (to say the least) and at most reveals that the mention of respecting Pythagoras by those Greeks is not to be trusted fully. In the form as we know it, the phrase does not harmonize neither with the times of Alcidamas nor with the passage quoted by Aristotle.

6

Antyczna tradycja o Pitagorasie z Samos jako twórcy fizjonomiki

51%

Domazet R.

Studia Antiquitatis et Medii Aevi Incohantis

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2023

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vol. 8

27-41

EN

This paper collects and analyzes ancient sources that refer to Pythagoras of Samos as the founder of physiognomy. Interest in physiognomy, which deals with the relationship between the body and the spirit, has become more popular over the last few years; however, many aspects of research into the topic are still obscure and worthy of further study. Physiognomy was assumed by ancient authors to be the method by which candidates were selected to enter the Pythagorean community, used by the Greek philosopher and his followers. Information about Pythagoras, who – by simply looking at somebody – could recognize their character appears, in the works of Aulus Gellius, Hippolytus, Porphyry, Iamblichos, Proclos and Olympiodorus. Apart from discussing testimonia about Pythagoras and his physiognomic examinations, the text explores the role of physiognomy during the selection process for the Pythagorean community in order to provide a better understanding of elite traditions within society. The paper also supplies further insight with regards to the methodology behind physiognomical surveys, which were popular during antiquity.

7

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 Peitho. Examina Antiqua

1 Acta Universitatis Lodziensis. Folia Iuridica

1 Classica Cracoviensia

1 Filosofický časopis (Philosophical Journal)

1 Prosopon. Europejskie Studia Społeczno-Humanistyczne

1 Studia Antiquitatis et Medii Aevi Incohantis

1 Domaradzki M.

1 Domazet R.

1 Goździalski K.

1 Korczak A.

1 Kvasz L.

1 Mojsik T.

1 Volpe E.

2 2023

1 2022

1 2017

1 2015

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