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.
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.
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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.
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.
Ve druhé části studie Analýza psychických struktur u vybraných spirituálních a náboženských koncepcích se zabývám prezentací vybraných pojetí duše u starých Řeků. Text je rozčleněn na analýzu nejstarších literárních pramenů, v nichž se můžeme setkat s termínem duše a příbuz-nými pojmy, jež se vztahují nejen k duševnímu a spirituálnímu životu člověka, ale i k jeho interakci s fyzickým tělem. K tomuto účelu se čtenář bude moci seznámit nejen s přístupem Homéra, ale také s příslušnou řeckou mytologií a starořeckými mystérii. Klasickou řeckou filosofii ve vztahu k duši prezentují v tomto článku Pýthagoras, Platón, Aristoteles a stoicismus. Helénské a posthelénské období v podobě neoplatonismu si na závěr přiblížíme prostřednictvím analýzy pojetí duše a ducha u Plotína a Jamblicha. Výsledkem studie je odhalení pestrého vývoje tohoto esenciálního pojmu, který se stal nepostradatelným instrumentem pro další směřování myšlení vztaženému k tomu, co jednak ve skutečnosti zakládá podstatu lidství a co se současně paradoxně v podobě odborné psychologie vzniklé ve druhé polovině 19. století vyprázdnilo bohužel v téměř bezobsažný pojem.
EN
In the second part of the study Analysis of psychic structures in selected spiritual and religious concepts, I am concerned with the presentation of selected concepts of the soul in the ancient Greeks. The text is divided into an analysis of the earliest literary sources in which we can encounter the term soul and related concepts relating not only to the mental and spiritual life of man, but also to his interaction with the physical body. To this end, the reader will be able to become familiar not only with Homer's approach but also with the relevant Greek mythology and the ancient Greek mysteries. Classical Greek philosophy in relation to the soul is presented in this article by Pythagoras, Plato, Aristotle and Stoicism. Finally, the Hellenistic and post Hellenistic periods in the form of Neoplatonism will be approached through an analysis of the concepts of soul and spirit in Plotinus and Iamblichus. The result of the study is the revelation of the varied development of this essential concept, which became an indispensable instrument for the further direction of thought relating to that which, on the one hand, actually constitutes the essence of humanity and, at the same time, which, paradoxically, in the form of the professional psychology that emerged in the second half of the nineteenth century, unfortunately emptied itself into an almost contentless concept.
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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