Barbara Michaela Sattler

This paper has two main goals: first, it reconstructs Aristotle’s account of measurement in the _Metaphysics_ and shows how it connects to modern notions of measurement. Second, it demonstrates that Aristotle’s notion of measurement works only for simple measures, and leads him into a dilemma once it comes to measuring complex phenomena, such as motion, where two or more different aspects, such as time _and_ space, have to be taken into account. This is shown with the help of Aristotle’s reaction to one of the problems that Zeno’s dichotomy paradox raises: Aristotle implicitly employs a complex measure of motion when solving this problem, while he explicitly characterizes the measure of motion as a simple measure in the _Physics_.

In this chapter it is argued that Parmenides’ poem can be understood as the beginning of indirect proof in philosophy and it is shown how these proofs work in his poem. This is also meant as the first step of an investigation into whether there may have been some influence of Eleatic logic and methodology on the mathematicians and their frequent use of reductio ad absurdum proofs. The author shows that in Parmenides, indirect proofs are the basis for (a) the overall argumentative strategy of his poem, as well as (b) the individual deductions characterizing what-is in fragment 8. While counterfactuals are already found in Xenophanes, the author demonstrates that it is only in Parmenides that indirect proofs are used as a main argumentative strategy.

This chapter aims to show that the earliest discussion about continuity in Western thought is a debate within metaphysics and natural philosophy about homogeneity and divisibility. All parties to this dispute – the main proponents are Parmenides, Zeno, and Aristotle – agree that magnitudes which are continuous (_suneches_) are homogenous and without any gaps. They disagree, however, on which inferences to draw from this for the possibility of divisibility – whether it implies indivisibility, as Parmenides and Zeno assumed, or divisibility, as Aristotle claimed, building on a mathematical understanding of extended magnitudes. Furthermore, while a modern understanding of continuity may seem to be essentially anti-Aristotelian, Aristotle is shown to prepare many of the crucial features of a modern account of continuity in this debate.

This chapter explores Plato’s and Aristotle’s thoughts on omnipresence. Neither Plato nor Aristotle provides a unified theory of divine omnipresence. In each we see tension between opposing tendencies. Plato posits in the Timaeus a world-soul aware of particular things and events throughout the cosmos, although it is unclear whether this implies that the world-soul is omnipresent. But if it is, Plato may face conflict with his doctrine that human souls are the individual loci of responsibility. Similarly, Aristotle’s metaphysics of organic substances seems to preclude any strong notion of an omnipresent being, since it is based on the idea that each organic substance is governed by its own essence-providing soul. Even so, the everlasting species of such substances owe the sempiternity of their life conditions to the eternal actuality of the divine prime mover. While this ultimate principle is particularly associated with the outermost celestial sphere, its effects are certainly omnipresent.

This book 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 Pythag-oreans. 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 idealizations. Section 3 dis-cusses 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.

In this paper I investigate central temporal and spatial notions in the second part of Plato’s Parmenides and argue that also these notions, and not only the metaphysical ones usually discussed in the literature, can be understood as a response to positions and problems put on the table by Parmenides and Zeno. Of the spatial notions examined in the dialogue, I look at the problems raised for possessing location and shape, while with respect to temporal notions, I focus on the discussion of ‘being in time’ and exaiphnês (the latter notion will be shown to be also an important influence for Aristotle’s Physics). In displaying a paradoxical character and taking up crucial notions from Parmenides, the second part of the Parmenides seems to display some resemblance to Zeno’s paradoxes. I will show, however, that in contrast to Zeno, the second part of Plato’s Parmenides also demonstrates Parmenides’ One to be problematic on its own terms. Furthermore, the dialogue presents not only important problems that these spatial and temporal notions seem to lead us into, but also establishes some positive features necessary to think of time and space. In this way, Plato’s Parmenides can be seen as contributing to the development of temporal and spatial conceptualisations in ancient Greek thought.

What did the early Greek philosophers think about animals and their lives? How did they view plants? And, ultimately, what type of relationship did they envisage between all sorts of living beings? On these topics there is evidence of a prolonged investigation by several Presocratics. However, scholarship has paid little attention to these issues and to the surprisingly "modern" development they received in Presocratics' doctrines. This book fills this lacuna through a detailed (and largely unprecedented) analysis of the extant evidence. The volume includes also the first extensive collection of the ancient sources pertaining to living beings and life in early Greek philosophy, organized chronologically and thematically.

In this paper I show that one of the most fruitful ways of employing paradoxes has been as a philosophical method that forces us to reconsider basic assumptions. After a brief discussion of recent understandings of the notion of paradoxes, I show that Zeno of Elea was the inventor of paradoxes in this sense, against the background of Heraclitus’ and Parmenides’ way of argumentation: in contrast to Heraclitus, Zeno’s paradoxes do not ask us to embrace a paradoxical reality; and in contrast to Parmenides, Zeno shows common assumptions to be internally problematic, not just in light of Eleatic positions.

While Aristotle provides the crucial testimonies for the paradoxes of motion, topos, and the falling millet seed, surprisingly he shows almost no interest in the paradoxes of plurality. For Plato, by contrast, the plurality paradoxes seem to be the central paradoxes of Zeno and Simplicius is our primary source for those. This paper investigates why the plurality paradoxes are not examined by Aristotle and argues that a close look at the context in which Aristotle discusses Zeno holds the answer to this question.

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 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.

Whatever our metaphysics of time, today we usually work with the assumption that we have one unified temporal framework, which allows for situating all events, processes, and happenings in the sense that we can put them all in a temporal relation to each other; they are all either before, after, or simultaneous with each other. In this paper, I show that for the early Greeks, by contrast, the very idea of such a unified notion of time would be foreign; instead, they assume different temporal (and not necessarily comparable) struc-tures belonging to different events. And I show what effect this lack has on the quality of temporal experiences – it means that different temporal experiences are thus seen as expe-riences of genuinely different kinds.

In this paper, I want to show that continuity is of crucial philosophical significance in Parmenides, who is the first thinker in the West to use the notion of continuity in a philosophically interesting and systematic way, and what being continuous (suneches) means for him. I look in some detail at the three passages in fragment 8 of Parmenides’ poem that are central for Parmenides’ notion of being suneches and discuss whether being suneches refers to something being temporally uninterrupted, spatially connected, or ontologically holding together. An analysis of these three passages shows that suneches for Parmenides implies complete homogeneity and indivisibility. This analysis is also the basis for showing that suneches is conceptualized very differently in Parmenides’ poem and Aristotle’s Physics because of different starting points and different understandings of what we would call the principle of sufficient reason.

This paper has two main goals: first, it reconstructs Aristotle’s account of measurement in his Metaphysics and shows how it connects to modern notions of measurement. Second, it demonstrates that Aristotle’s notion of measurement only works for simple measures, but leads him into a dilemma once it comes to measuring complex phenomena, like mo-tion, where two or more different aspects, such as time and space, have to be taken into account. This is shown with the help of Aristotle’s reaction to one of the problems Zeno’s dichotomy paradox raises: Aristotle implicitly employs a complex measure of motion when solving this problem, while he explicitly characterizes the measure of motion as a simple measure in his Physics.

This paper argues that the problem of how to act in the face of radical contingency is of central importance in Musil’s novel and intimately connected to what Musil calls the sense of possibility. There is a variety of different strategies by which individuals, and the state of Kakania as a whole, deal with contingency, and they all involve a claim to a kind of grounding or necessity; for example, the Parallel Campaign is one big attempt to ground Kakania in what can be perceived as a form of metaphysical necessity. With the figure of Ulrich, Musil radicalizes the problem by showing the consequences of viewing even the relationship one has to one’s own self as contingent – the ultimate outcome of which is self-alienation.

This paper argues that processes in the sensible realm can be in accord with reason in the Timaeus, since rationality is understood here as being based on regularity, which is conferred onto processes by time. Plato uses two different temporal structures in the Timaeus, associated with the contrast there drawn between Greek and Egyptian approaches to history. The linear order of before and after marks natural processes as rational and underlies the Greek treatment of history. By contrast, a bidirectional temporal structure is the basis for the Egyptian approach to historical processes: present actions are not only determined by preceding ones in the past, but can also be influenced by the future (plans, aims). This latter temporal structure is shown to be necessary for learning from history, which makes human actions more regular.

The paper demonstrates that Parmenides’ monism is a logical consequence of his criteria for philosophy, in conjunction with the logical operators he uses, and their holistic connection. Parmenides, I argue, is the first philosopher to set out explicit criteria for philosophy, establishing as criterion not only consistency, but also what I call rational admissibility, the requirement when giving an account of something that the account be based on rational analysis and can withstand rational scrutiny. I give a detailed account of the logical operators Parmenides uses in his argument and of the way in which his notion of being is tailored to fit both them and his criteria for philoso-phy.

Zeno’s Moving Rows paradox is the only paradox among his four paradoxes of motion that is usually skipped over as being of no philosophical interest. This paper aims to give a new diagnosis of the Moving Rows paradox, a diagnosis that allows us to see it as raising a philosophically interesting problem concerning the relationship of time, space, and motion. It shows the consequences of confusing time’s dependence on the space covered in a motion with time’s dependence on the motion performed. I argue that, to date, the paradox has not been given the correct analysis – usually being reconstructed either as a mere oversight, or as some confusion about the relativity of motion, or as a very different atomistic paradox.

This is part of a two-paper project to show in detail in ways that have not been attempted before that, in the Symposium, Plato uses the language and metaphors of the Eleusinian Mysteries as a template for the ascent to the Form of Beauty; and also to explain why he might have chosen to do so. The standard accounts of the Eleusinian Mysteries come from sources that have themselves been influenced by Plato and hence are unsuitable to demonstrating the extent of his exploitation of the Mysteries. This first paper offers a reconstruction of what can be known about the Eleusian Mysteries with the help of Pre-Platonic sources, by looking at material culture, archaeological remains, and pre-Platonic literature.

The much-anticipated anthology on Plato’s_Timaeus_—Plato’s singular dialogue on the creation of the universe, the nature of the physical world, and the place of persons in the cosmos—examining all dimensions of one of the most important books in Western Civilization: its philosophy, cosmology, science, and ethics, its literary aspects and reception. Contributions come from leading scholars in their respective fields, including Sir Anthony Leggett, 2003 Nobel Laureate for Physics. Parts of or earlier versions of these papers were first presented at the _Timaeus_ Conference, held at the University of Illinois at Urbana–Champaign in September of 2007._ To this day, Plato’s _Timaeus_ grounds the form of ethical and political thinking called Natural Law—the view that there are norms in nature that provide the patterns for our actions and ground the objectivity of human values. Beyond the intellectual content of the dialogue’s core, its literary frame is also the source of the myth of Atlantis, giving the West the concept of the “lost world.” From Platonic space to Presocratic vortices, from Philosopher-Kings to Craftsman-Gods and from modern physics to the myth of Atlantis, _One Book, The Whole Universe_ presents in one volume the most up-to-date and penetrating scholarship on Plato’s _Timaeus_ by some of the greatest minds alive today. Contributors__ _Ann Bergren Gábor Betegh Sean Carroll Alan Code Zina Giannopoulou Verity Harte Thomas Kjeller Johansen Charles H. Kahn Anthony J. Leggett Anthony A. Long Stephen Menn Richard D. Mohr Kathryn A. Morgan Alexander P.D. Mourelatos Ian Mueller Thomas M. Robinson Barbara M. Sattler Allan Silverman Jon Solomon Anthony Vidler Matthias Vorwerk Donald Zeyl