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. (shrink)

A collection of essays from major scholars in the field as well as from people in a wide range of other disciplines to which the Timaeus and its reception have been of relevance, from architecture and film studies to physics.

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. (shrink)

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. (shrink)

This paper aims to show that—and how—Plato’s notion of the receptacle in the Timaeus provides the conditions for developing a mathematical as well as a physical space without itself being space. In response to the debate whether Plato’s receptacle is a conception of space or of matter, I suggest employing criteria from topology and the theory of metric spaces as the most basic ones available. I show that the receptacle fulfils its main task–allowing the elements qua images of the Forms (...) to exist as sensible things by being that in which the elements appear, change and move–in virtue of being pure continuity. All further qualifications required for a full notion of space are derived solely from the content of the receptacle. (shrink)

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. (shrink)

It is usually supposed that, with his dichotomy paradox, Zeno gave birth to the modern so-called supertask debate – the debate of whether carrying out an infinite sequence of actions or operations...

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)