Metaphysics, geometry, and the problems with diagrams -- The Pythagorean theorem: Euclid I.47 and VI.31 -- Thales and geometry: Egypt, Miletus, and beyond -- Pythagoras and the famous theorems -- From the Pythagorean theorem to the construction of the cosmos out of right triangles.

Uses textual and archaeological evidence to argue that emerging Egyptian and Greek architectural technologies were crucial to the origins and development of Greek philosophy.

_Detailed study of how Anaximander’s cosmological and philosophical conceptions were affected by architectural technologies._.

Places the development of Anaximander's thought within social, political, cosmological, astronomical, and technological contexts.

The passage which occurs in Plato's Philebus 25C8-E2 examines the relation between three of four classes of Being which are introduced at 23C. Problems with the text and explication of the passage are considered. Ibis paper attempts to illuminate two central issues of the later dialogues on which the interpretation of this passage rests, the significance of πέρς or the limiting class of Being, and the overall operation of συναγωγή or collection, characterizing the method of diairesis, the foundation of the (...) later dialectic.This paper argues for the need to emend the text to read συμμισγομένων (or even συγγιγνομένων) since this is the significance required by the context; to take the referrent of έϗείνη to be πέρατος γέννα; and to understand άπείρου γέννα and πέρατος γέννα as the referrents of τούτων άμκροτέων. (shrink)

In this essay on ancient architectural technologies, I propose to challenge the largely conventional idea of the transcendent origins of philosophy, that philosophy dawned only when the mind turned inside, away from the world grasped by the body and senses. By focusing on one premier episode in the history of western thinking – the emergence of Greek philosophical thought in the cosmic architecture of Anaximander of Miletus – I am arguing that the abstract, speculative, rationalising thinking characteristic of philosophy, is (...) indeed rooted in practical activities, and emerges by means of them rather than in repudiation of them. The spirit of rational inquiry emerged from several factors but the contributing role of monumental architecture and building technologies has been vastly under-appreciated. In the process of figuring out how to build on an enormous scale that the eastern Greeks had never before tried, the architects discovered and revealed nature’s order in their thaumata, the very experience with which Aristotle claims that philosophy begins. Ancient architecture and building technologies were on display for decades with monumental temple building. In front of Anaximander and his community, a new vision of nature spawned that, surprisingly, humans could grasp and command. The building of these thaumata, these objects of wonder, offered proof of the human capacity to control nature, and opened a new vision of our human rational capacity to understand the world and our place in it. (shrink)

We can trace to archaic Greek times detailed accounts of the origins of the cosmos. Anaximander and Hesiod provide different kinds of narrative, but both assume that the cosmos as we find it now was not the way it was at the beginning, and seek to explain how things got this way. According to the conventional view provided by Aristotle in Metaphysics A, the Ionians proposed that everything is derived from a primordial substance and that, despite differences in the world (...) we now experience, all these things reduce ultimately to just one basic stuff, whether it be Thales' water, Anaximander's boundless, or Anaximenes' air . But Graham thinks Aristotle has it wrong and proposes a different story: the Ionians held that in the beginning there was a primordial substance, but it gave rise in turn to other, new substances, the original stuff perishing in the process . Graham's book sets out to challenge MM and to champion instead GST. He aims to show that GST is historically appropriate, philosophically coherent, and dialectically relevant. Ultimately, this is not just to urge a revision of Ionian beginnings but also to trace out the implications of GST in order to produce a new narrative of Presocratic philosophy, one that sees these Ionian beginnings as a clear precursor to. (shrink)

Hahn boldly corrects the misconceptions of Kant’s Copernican revolution in philosophy and explains the specific Newtonian model used by Kant to construct his own philosophy in the _Critique of Pure Reason. _ Relying on resources familiar to Kant—Newton’s _Opticks _and _Principia _and especially Christian von Wolff’s commentary on scientific method—Hahn argues that Kant viewed Copernicus as the proponent of a novel hypothesis while seeing Newton as the formulator of a rigorously deductive method. Intellectual revolutions, for Kant, are signaled by the (...) formulation of rigorous deductions. The revolution that Kant proposes to effect in the _Critique of Pure Reason _is based on Newton’s deductive method, not the hypothesis of Copernicus. Thus, the commonplace that Kant effects a Copernican revolution misrepresents Kant’s expressed views on the matter, it distorts Kant’s view of Copernicus, and it misleads us in our efforts to understand what the revolution in natural science meant to him, as the very model on which his metaphysics rests. (shrink)

Ermanno Bencivenga offers us an interpretation of what he calls "Kant's Copernican Revolution" in philosophy. He proposes to illuminate the celebrated obscurity of the Critique by suggesting that it is neither the result of the complicated theory nor of the literary imperfections of the author. Rather, it is the result of the peculiar "revolution" which Kant sought to effect. On Bencivenga's account, Kant wrote the Critique when he was in the middle of a process of fighting against "old modes of (...) expression and old canons of understanding." Thus, the obscurity is a consequence of the new and not fully worked-out language which Kant employs to convey the meaning of this conceptual revolution. (shrink)