Ancient Pythagoreanism Research Articles

Entre Sonido y Sentido. Acusmática y Blackboxing.

This personal research understands the concept of acousmatic as a contemporary praxis in sound art. This ancient Pythagorean practice, -utilized to a strange sound, - shares the essence of nowadays virtuality. As devices’ screens for example share features and processes with the old Pythagorean curtain. Although acousmatic practice avoids any visual representation, and hides the internal functioning of communication, behaving like a black box. External stimuli directly affect it, triggering sound-image feelings and emotions that are (un)known to us. Rather than investigating the response triggered by these inputs, the research aims to analyse the internal resonances of these black boxes. The more complex machines become, the simpler our relations to them are. The devices and formats used in sound-intermedia practice act as “black boxes”, but this apparent “blackboxing” caused by the use of the technological in the codes of the sensible performs as a catalyst for the apprehension of sound and its esthesic exploration.

What is Pythagorean in the Pseudo-Pythagorean Literature?

AbstractThis paper discusses continuity between ancient Pythagoreanism and the pseudo-Pythagorean writings, which began to appear after the end of the Pythagorean school ca. 350 BC. Relying on a combination of temporal, formal and substantial criteria, I dividePseudopythagoricainto three categories: 1) early Hellenistic writings (late fourth – late second centuries BC) ascribed to Pythagoras and his family members; 2) philosophical treatises written mostly, yet not exclusively, in pseudo-Doric from the turn of the first century BC under the names of real or fictional Pythagoreans; 3) writings attributed to Pythagoras and his relatives that continued to appear in the late Hellenistic and Imperial periods. I will argue that all three categories of pseudepigrapha contain astonishingly little that is authentically Pythagorean.

Sinfonia e confessione. Forme letterarie e pitagorismo in José Vasconcelos e María Zambrano

The Vasconcelos and Zambrano attempt to reconcile life and reason, Wisdom and Philosophy, is particularly affected by the influence of the aesthetic and ‘musical’ component of Pythagoreanism. This, that would cross the history of philosophy as an heterodox current, intends to reassert itself, as much in Vasconcelos aesthetic thought as in Zambrano’s Poetic Reason, against the constraints of rationalism, its formal rigidity and its dogmatism. With this objective, their reflection about the complex articulation and declination of the history of philosophy in literary genres, as places of its intimate drama, flows in the analysis of two specific and, in some respects, similar forms of literature: the symphony (Vasconcelos) and the confession (Zambrano). The latter is nothing new in the literary scene but, recognized as true of Western thinking method, is proposed as a conditio sine qua non of its authentic rebirth. Symphony and confession, which in their analogical and musical process would realize the ancient Pythagorean inspiration, insist on the need to invalidate that world devoid of subject, to reveal the immobilism and the absolutism of the concept and to rethink the tragedy, as a genre and in its historical manifestations, to forestall its ending. They share, therefore, the same purpose: the fulfillment of an ‘ethical Hystory’.

Bernulf Kanitscheider.Natur und Zahl: Die Mathematisierbarkeit der Welt[Nature and Number: The Mathematizability of the World]. Berlin: Springer Verlag, 2013. ISBN: 978-3-642-37707-5 (hbk); 978-3-642-37708-2 (e-book). Pp. vii + 385

The title of Bernulf Kanitscheider's Natur und Zahl has an even better ring in English: Nature and Number. The book is a wide-ranging discussion of the mathematical nature of the physical world. It takes the form of a sort of perambulation through history, beginning with the ancient Pythagorean philosophers, with stops along the way to note analogies or parallels in contemporary science, especially cosmology and astrophysics, Kanitscheider's area of specialization, in order to illustrate the viewpoints under discussion. Unfortunately, this procedure results in a rambling and unsystematic exploration of the issues and eventually breaks down in the later chapters, where Kanitscheider tends to desert the historical approach in favor of a more thematic discussion. The book presents itself as an exploration of the reason for the astonishing applicability (Anwendbarkeit) of mathematics in physics, a question neglected, according to Kanitscheider, in Germanic philosophy in contrast to anglophone philosophy (pp. 12–13). In fact, however, Kanitscheider treats this issue only tangentially in the book. The actual question with which he struggles is the compatibility of mathematics with naturalism. Kanitscheider is a committed naturalist, and he is acutely aware of the problems for his metaphysical worldview posed by mathematical truth (which he wants to affirm) and the underlying ontology of mathematical platonism (which he wants to avoid). Thus, the book's center of gravity is its longest chapter ‘Naturalism in the world of mathematics’.1

UNA METAFISICA PITAGORICA NEL FILERO?

The present essay will cross, inside the matter of the sources of the platonic thought, the suggestion of Damascius of Damascus, with the intention to draw clear understanding, unless in this particular point, of the relationship between the ancient pythagoreanism and the platonic philosophy. In this, the study of the matter of the dialectics of the limiters/unlimited one is central. The page 16c of the Philebus is the crucial point of this discussion: here Socrates introduces the theme of the unity/multiplicity as a very beautiful hodos, a run that comes from a very distant point of departure: it’s a “gift of the gods” and a discovery of the ancient ones. The comparative study of these footsteps of the Philebus and the fragments of Philolaus, especially В 2, 3, 6 and 7 bring us to conclude that the presence in the pages of the Philebus of the theory of the limiter/unlimited be taken as a pre-platonic “discovery” of the more ancient pythagorean philosophy.

Incommensurability, Music and Continuum: A Cognitive Approach

"How did the Greeks discover incommensurability?" This is one of the most puzzling 'scripts' of the history of mathematics. The 'movie' usually shows a Pythagorean (Hippasus or Archytas for example) drawing a square with its diagonals (or a pentagon with its golden sections on sides and diagonals) (von Fritz 1944), or drawing dots in a square (Knorr 1975), or even making some computations (successive subtractions, ccvGixpocipeaic) (Fowler 1987), and exclaiming: "But this is impossible! If I am not wrong, this means that geometrical, continuous magnitudes cannot be reduced to numbers, discrete entities! Pythagoras was wrong!". Then a meeting of the sect takes place and all Pythagoreans swear to keep the secret of the 'scandal'. A Grundlagenkrisis for the ancient Pythagoreanism follows, for whose solution a brand new axiomatization will be necessary, which will lead to Eudoxus and Euclid. This movie deserves great attention because its scenes are the background of our modern perception of the mathematical continuum, and, at the same time, these scenes are forced by this perception. To question the movie means also to discuss the most basic and undisputed premises of our current philosophical view of mathematics. It is the aim of this paper to try to shed some light on the connection between the historical interpretation of the discovery of incommensurability and our idea of continuum: this is what I mean by a 'cognitive' approach. To this aim I am going to outline an alternative historical interpretation of the involved discovery, centered on music instead of geometry, which in turn suggests an alternative view of the continuum considered as something far from being 'natural' and 'empirical'. My aim is to address the music-theoretical origin of the discovery of incommensurability, together with the question why this origin was subsequently forgotten, while at the same time the theory of incommensurability was translated into a geometric form. I claim that there were two main reasons for both the oblivion and the translation: first, the negative character of this discovery vs. the positive character of the geometric version (side-diagonal of the square, or of the pentagon); second, the connected breakdown of the ancient musical-arithmetical idea of 'linear numerical magnitude'. This alternative perspective looks at mathematics as deeply involved in the whole culture, its discoveries being always perceived by the protagonists through the glasses of the general cognitive aspects of a civilization, so that I can say that nothing relevant in mathematics can be actually and distinctly discovered 'empirically' or 'by

Ancient Philosophy, Mystery, and Magic: Empedocles and Pythagorean Tradition.

Empedocles played a crucial role in the development of western culture; yet little is known or understood about this man, who lived in Sicily in the fifth-century BC. This is mainly becuase his teaching has been reconstructed by modern shcolars first and formost on the basis of Aristotle's hostile reports - producing a picture which is disconnected and lacking in depth. Using material never exploited before, Peter Kingsley presents the first full-scale study of Empedocles to situate his fragmentary writings in their original context of philosophy as a way of life, mystery religion and magic, and of the struggle to realize one's own divinity. This study also explores fresh evidence which proves Empedocles was not an isolated figure and reveals new links between his work and ancient Pythagoreanism. The process of establishing these links now makes it possible to demonstrate, in detail, the Pythagorean origin of Plato's myths. Kingsley re-examines problems regarding the connections between ancient magic, science, and religion. More specifically, he traces for the first time a line of transmission from Empedocles and the early Pythagoreans down to southern Egypt, and from there into the world of Islam. 'highly polemical new book...The thesis is argued with immense learning.' Times Higher Education Supplement

The Authenticity of Archytas fr. 1

In a long note in his epoch-making book on ancient Pythagoreanism Walter Burkert raised some grave doubts about the authenticity of Archytas Fr. 1 which have recently been challenged in an article by A. C. Bowen. In this paper I have two goals. First, I will evaluate Burkert's doubts and the success of some of Bowen's arguments against them. Second, I will present a further consideration that both clarifies the text of the fragment and also removes the most serious problem raised by Burkert. The upshot of both these points is to increase the likelihood that the fragment is authentic.I reproduce the text of just the first part of the fragment as given in DK followed by the text as it appears in the two primary sources, Nicomachus and Porphyry.

The Consonant Eleventh and the Expansion of the Musical Tetractys: A Study of Ancient Pythagoreanism

The interval of the eleventh, that is, the octave plus fourth, stands at the crease between rationalism and empiricism in ancient musical treatises. For convenience, I refer to the interval as the eleventh, and to its neighbor as the twelfth, although most ancient and medieval treatises refer to these intervals, respectively, as the diapason plus diatessaron and diapason plus diapente. By extracting the eleventh, I perform a biopsy on ancient Pythagoreanism and thus hope to elucidate the Pythagorean world view as well as to indicate some avenues along which ancient Pythagoreanism may have traveled to the Middle Ages.' By tracing the Pythagorean treatment of the eleventh, I show the role of number in early musical theory to be both causal and descriptive. The causal nature of number would seem to be more primitive and therefore older than the descriptive role played by number in Pythagorean harmonics. Modern musical theory tends to use numbers as a general, abstract system or metaphor for sound. Thus, our modern disposition invites us to see a development from a time when numbers determined the consonance or dissonance of an interval to a time when numbers simply described an interval, that is, provided a quantitative metaphor without evaluating the interval according to its consonant or dissonant character. The history of mathematics reflects this development

Book Review: Pythagoras, Lore and Science in Ancient Pythagoreanism

Book Review: Pythagoras, Lore and Science in Ancient Pythagoreanism

Spinoza and Jeffers on man in nature

Western society has been diverted from the goal of spiritual freedom and autonomy as expressed in the ancient Pythagorean ‘theory of the cosmos’. Indeed, following Heidegger's analysis, it can be seen that modern Western society has arrived at the opposite pole of anthropocentric ‘absolute subjectivism’ in which the entire non‐human world is seen as a material resource to be consumed in the satisfaction of our egoistic passive desires. It is further argued that Spinozism is actually a modern version of the ‘theory of the cosmos’ which, when supplemented by a vision of man's identity with the ecological world, would provide us with the only adequate portrayal of the God/Nature/Man relationship.

Walter Burkert: Lore and Science in Ancient Pythagoreanism. Translated by E.L. Minar. Pp. iv + 535. Cambridge, Mass.: Harvard University Press (London: Oxford University Press), 1972. Cloth, £12·50.

Walter Burkert: Lore and Science in Ancient Pythagoreanism. Translated by E.L. Minar. Pp. iv + 535. Cambridge, Mass.: Harvard University Press (London: Oxford University Press), 1972. Cloth, £12·50. - Volume 26 Issue 1

Lore and Science in Ancient Pythagoreanism

Lore and Science in Ancient Pythagoreanism

Lore and Science in Ancient Pythagoreanism. Walter Burkert , Edwin L. Minar, Jr.

<i>Lore and Science in Ancient Pythagoreanism</i>. Walter Burkert , Edwin L. Minar, Jr.