This anthology looks at the early sages of Western philosophy and science who paved the way for Plato and Aristotle and their successors. Democritus's atomic theory of matter, Zeno's dazzling "proofs" that motion is impossible, Pythagorean insights into mathematics, Heraclitus's haunting and enigmatic epigrams-all form part of a revolution in human thought that relied on reasoning, forged the first scientific vocabulary, and laid the foundations of Western philosophy. Jonathan Barnes has painstakingly brought together the surviving Presocratic fragments in their original (...) contexts, utilizing the latest research and a major new papyrus of Empedocles. Translated and edited by Jonathan Barnes. (shrink)

This paper focuses on Anaximander's pinax, the first map according to Western tradition. Its aim is to demonstrate that it is only after the realization of the pinax that it was possible to distinguish between Being and beings in a Heideggerian sense, that is to pose the question of the ontological difference. Consequently, all the history of Western thought is nothing but the history of the raising of cartographical representation, and of reason here embodied, from the dark rigidity of death (...) to the rarefied splendours of Pure Reason. (shrink)

The latest computerized reconstruction of the “Antikythera mechanism” reveals a striking similarity to the model of the universe of Anaximander of Miletus.

Because of a widespread criticism of the Enlightenment sense of reason for its unilateral privileging of unity and its solipsistic conception of the thinking subject, many turn to postmodern difference as a remedy. But an alternative can also be found in a renewed appropriation of the tradition. This essay is an attempt at such an appropriation, through a philosophical analysis of Heraclitus' conception of logos. A new interpretation of Heraclitus is offered, which affirms the equiprimordiality of unity and difference. This (...) view is shown to have implications first of all for the mode of reasoning: thought, in its most genuine sense, cannot be accomplished in isolation but is an essentially joint act. Further, the view has implications for the content or object of thought: the 'seat' of intelligibility is not the abstract idea which the mind assimilates to itself but rather the concrete whole, the complex 'one-many' structure in the world, in which minds constitutively participate. An attempt is made, at the end of the essay, to show how the convergence of form and content, and the concrete sense of rationality it implies, comes to dramatic expression in Heraclitus' style. (shrink)

: Some of the great physicists' belief in the existence of a connection between the aesthetical features of a theory (such as beauty and simplicity) and its truth is still one of the most intriguing issues in the aesthetics of science. In this paper I explore the philosophical credibility of a version of this thesis, focusing on the connection between the mathematical beauty and simplicity of a theory and its truth. I discuss a heuristic interpretation of this thesis, attempting to (...) clarify where the appeal of this Pythagorean view comes from and what are the arguments favoring its acceptance or rejection. Along the way, I sketch the historical context in which this heuristic interpretation gained credibility (the quantum crisis in physics in the 1920s), as well as the more general implications of this thesis for physicists' metaphysical outlook. (shrink)

This book investigates the link Kant discerned between our experience of beauty and our experience of the moral law. By examining Kant's relation to Greek philosophy, to Plato and Pythagoras, as found in Kant's own writings, the author sheds new light on one the most intriguing and mysterious doctrines of Kant's third Critique.

In this work I propose an analogy between Pythagoras's theorem and the logical-formal structure of Werner Heisenberg's "relations of uncertainty." The reasons that they have pushed to me to place this analogy have been determined from the following ascertainment: Often, when in exact sciences a problem of measurement precision arises, it has been resolved with the resource of the elevation to the square. To me it seems also that the aporie deriving from the uncertainty principle can find one solution with (...) the resource to this stratagem. In fact, if the first classic example of the argument is the solution of the incommensurability between catheti and the hypotenuse of the triangle rectangle, one of the last cases is that which is represented from Heisenberg's principle of uncertainty. (shrink)

The long haired Pythagoras is an unlikely figure after to whom to name a complex specific to common lawyers. Ironically, however, the mythical figure of Pythagoras "and his school" was one of the most often declared sources of the distinctiveness of common law. His followers, the Druids, were the first lawyers in Anglia - specifically, the dark island - and the strange sacrificial and mystagogic practices of the Druid law givers founded the early rites of the tradition of unwritten law. (...) Using the humanistic technique of history and reminiscence, this article traces the idiosyncracies of the pythagorean philosophy: the refusal to put law in writing, the use of hieroglyphs, the dependence upon oracular judgment, the belief in multiple lives, askesis and akousmata, and places them at the root of what is most emblematically common law. (shrink)

Archytas of Tarentum was a central figure in fourth-century Greek life and thought and the last great philosopher in the early Pythagorean tradition. He solved a famous mathematical puzzle, saved Plato from the tyrant of Syracuse, led a powerful Greek city state, and was the subject of three books by Aristotle. This first extensive study of Archytas' work in any language presents a radically new interpretation of his significance for fourth-century Greek thought and his relationship to Plato, as well as (...) a full commentary on all the fragments and testimonia. (shrink)

Recent developments in astrophysical cosmology have revived support for the design argument among a growing clique of astrophysicists. I show that the scientific/mathematical evidence cited in support of intelligent design of the universe is infected with a mathematical sharp practice: the concepts of two numbers being of the same order of magnitude, and of being within an order of each other, have been stretched from their proper meanings so as to doctor the numbers evidentially. This practice started with A. S. (...) Eddington and P. A. M. Dirac in the 1920s and 1930s, but it is still very much alive today. 1 Introduction 2 The birth of a sharp practice 3 High tide for the anthropic principle 4 How not to do things with numbers 5 The recalcitrant sloppiness of crud 6 How excited can excited carbon-12 be? 7 Is a pile of doubts a doubtful pile? 8 Conclusion. (shrink)