Barbara M Sattler - Böcker

Parmenides is one of the most widely studied and controversial early Greek philosophers. This edited collection examines Parmenides' modes of argument and their legacy, his poetics and intertextuality, and the relation between different parts of his poem. It also presents new research into Parmenides' poem from a range of scholarly traditions; together the essays show that we must fundamentally change our conception of the manner in which Parmenides communicated with his readers, the division of his poem, and his reasons for dividing it.Parmenides: New Perspectives challenges widespread assumptions, such as that Parmenides left his readers to grapple with the enigmatic poem unaided, that the poem is divided into three parts, and that the first part—the proem—should be interpreted as allegory. Against this it is argued that Parmenides wrote exegetical comments on his own poem, and the proem echoes representations of deities and the cosmos in previous poetry in order to subvert them and open a new world for poetic expression and intellectual inquiry. Collectively this volume showcases some of the most thought-provoking contemporary scholarship on Parmenides.Chapter 5 of this work is available under the terms of a CC BY-NC-ND 4.0 International open access licence. This part of the work is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations

This Element looks at the very beginning of the philosophy of mathematics in Western thought. It covers the first reflections on attempts to untie mathematics from its practical usage in administration, commerce, and land-surveying and discusses the first ideas to see mathematical structures as constituents underlying the physical world in the Pythagoreans. The first two sections focus on the epistemic status of mathematical knowledge in relation to philosophical knowledge and on the various ontological positions ancient Greek philosophers in early and classical times ascribe to mathematical objects - from independent and separate entities to mere abstractions and idealisations. Section 3 discusses the paradigmatic role mathematical deductions have played for philosophy, the role of mathematical diagrams, and mathematical methods of interest for philosophers. Section 4, finally, investigates a couple of individual concepts that are fundamental for both philosophy and mathematics, such as infinity.

This Element looks at the very beginning of the philosophy of mathematics in Western thought. It covers the first reflections on attempts to untie mathematics from its practical usage in administration, commerce, and land-surveying and discusses the first ideas to see mathematical structures as constituents underlying the physical world in the Pythagoreans. The first two sections focus on the epistemic status of mathematical knowledge in relation to philosophical knowledge and on the various ontological positions ancient Greek philosophers in early and classical times ascribe to mathematical objects - from independent and separate entities to mere abstractions and idealisations. Section 3 discusses the paradigmatic role mathematical deductions have played for philosophy, the role of mathematical diagrams, and mathematical methods of interest for philosophers. Section 4, finally, investigates a couple of individual concepts that are fundamental for both philosophy and mathematics, such as infinity.

This book examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.

This book examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.

This book explores a distinctive feature of ancient philosophy: the close relation between ancient ethics and the study of the natural world. Human beings are in some sense part of the natural world, and they live their lives within a larger cosmos, but their actions are governed by norms whose relation to the natural world is up for debate. The essays in this volume, written by leading specialists in ancient philosophy, discuss how these facts about our relation to the world bear both upon ancient accounts of human goodness and also upon ancient accounts of the natural world itself. The volume includes discussion not only of Plato and Aristotle, but also of earlier and later thinkers, with an essay on the Presocratics and two essays that discuss later Epicurean, Stoic, and Neoplatonist philosophers.

This book explores a distinctive feature of ancient philosophy: the close relation between ancient ethics and the study of the natural world. Human beings are in some sense part of the natural world, and they live their lives within a larger cosmos, but their actions are governed by norms whose relation to the natural world is up for debate. The essays in this volume, written by leading specialists in ancient philosophy, discuss how these facts about our relation to the world bear both upon ancient accounts of human goodness and also upon ancient accounts of the natural world itself. The volume includes discussion not only of Plato and Aristotle, but also of earlier and later thinkers, with an essay on the Presocratics and two essays that discuss later Epicurean, Stoic, and Neoplatonist philosophers.