Aristotle's arguments about the void present special interests and problems because of their long history in Aristotle's commentators. A full accounting of the responses to these arguments lies beyond the scope of my analysis, although some special cases will be taken up. One point however has been crucial for interpretations of these arguments: Euclidean geometry requires a three-dimensional infinite space. Euclid flourished (probably) one generation after Aristotle, and his geometry was enormously influential. Because Aristotle defines place as the limit of the first containing body, place was often thought to be both finite and, as we have seen, a two-dimensional surface. Hence on this view, Aristotle's notion of place fails on both counts to meet the requirements of Euclidean geometry. Taken together, the requirements of Euclidean geometry and the apparent failure of Aristotle's account of place to meet them often motivated first a commitment to the void and then criticism of Aristotle's arguments rejecting the void. Therefore, these criticisms derive from the conjunction of Euclidean geometry and a common misunderstanding of Aristotle's account of place. My interest lies in a direct analysis of the arguments concerning the void in Physics IV.

Place has not been established as the exclusive answer to the question “where are things?” because void [κενόν, i.e., “empty”] presents an alternate answer. Consequently, void must be examined, and, Aristotle says, the same questions must be posed for it as for place, namely, “if it is or not, and how it is and what it is.”

Before turning to Aristotle's arguments on place and void, we must consider the structure of Physics IV as a logos and its relation to the other books of the Physics, especially Physics II and III. In Physics II, 1, Aristotle defines nature as a source of motion and rest (192b14); Physics III, 1, opens with the claim that in order to understand nature, we must also understand motion (200b12–14). In effect, Physics III starts from the subject of physics established in Physics II. In short, motion and nature are coextensive, they are found together, and they, and those things required by them, form the primary subject matter of physics as a science. Hence, Aristotle concludes, it is clear that universal and common things must be examined first, namely, motion and those things without which motion seems to be impossible, including the infinite, place, void, time, and the continuous.

The Structure of the Arguments

Aristotle proceeds accordingly. First, “motion” is defined (Physics III, 1-3), and then “the infinite” (Physics III, 3–8). “Place,” “void,” and “time” occupy Physics IV, while “the continuous” along with the related notions “in contact” and “in succession,” “points,” and “lines” occupy Physics V and VI. These terms follow motion and nature not only rhetorically – they are next in the text – but also logically. That is, the examination of them presupposes the definition of motion that he has just established. Hence, place and void are considered, defined, and evaluated in terms of Aristotle's definitions of motion and ultimately nature.

With this account of “the where” – place, not void – I turn to the De Caelo and its topics, particularly the elements. As a topic, the elements present a problem: the elements – themselves unquestionably “things that are by nature” – appear in the Physics only within the examination of other topics, but are never themselves examined as a topic. A direct examination of them appears in the De Caelo. But historically the coherence of the De Caelo as a set of logoi, the definition of its topic (s), and the relation of its arguments to those of the Physics have been problematic. A consideration of the Physics and the De Caelo as topical investigations solves both problems, substantive and historical.

The Topic of the De Caelo

In the Physics, Aristotle investigates strictly defined topics. Physics II, 1, identifies things that are by nature: animals, their parts, plants, and the elements earth, air, fire, and water (192b9–11). Nature is a principle of “being moved and being at rest in that to which it belongs in virtue of itself” (192b21–22); consequently, Aristotle asserts at Physics III, 1, we must know motion if we are to understand nature, and he lists the “common and universal things” without which motion seems to be impossible (200b20–23). The investigation of proper things, he says, will come later because universal things, including the continuous, the infinite, place, void, and time should be investigated first (200b23–25).

THE FRUITS OF PHILOSOPHY

[Philosophia] animam format et fabricat, vitam disponit, actiones regit, agenda et omittenda demonstrate sedet ad gubernaculum et per ancipitia fluctuantium derigit cursum.

(‘Philosophy shapes and constructs the soul, arranges life, governs conduct, shows what is to be done and what omitted, sits at the helm and directs our course as we waver amidst uncertainties.’) Seneca

It is central to the ancient Greek conception of philosophy that it provides human beings with the way to lead a better life. A significant part of the philosophy of both Plato and Aristotle is concerned with laying out the framework for human fulfilment. For Plato (in some of his writings) the good life turns out actually to consist in philosophical theorizing, while Aristotle vacillates between this conception and a more down-to-earth vision of ordinary ‘practical wisdom’, in which, nonetheless, the achievement of the good life depends, at its deepest level, on the systematic exercise of reason.

THE PROJECT

Universae philosophiae finis est humana foelicitas (‘The goal of a complete philosophy is human happiness. ’) Eustachius a Sancto Paulo

This ambitious statement, from an early seventeenth-century textbook, the Composite System of Philosophy in Four Parts encapsulates a view of philosophy that was widespread at the time, and had a long ancestry. It has two aspects: the first, the notion of philosophy as a complete system of thought encompassing all aspects of human knowledge – metaphysical, physical and ethical – and, the second, the idea that the ultimate raison d'être of such a system is its ability to provide an authentic blueprint for human flourishing.

But can philosophy really show us how to live? The ancient Greek philosophers certainly thought it could; Descartes, the ‘father of modern philosophy’ strongly maintained as much. But in our own time, confused and conflicting answers have emerged, mostly on the negative side. It is often said that we live in the century of Freud; in the popular intellectual culture of our time, reflected in literature and drama and the media, it is psychoanalytical ideas, rather than philosophical theories, that seem to play an increasingly important role in how we try to understand ourselves and in our attempts to remove the obstacles to fulfilled and happy living.

THE CARTESIAN REVOLUTION: MATHEMATICAL TRANSPARENCY AND ARBITRARY LAW

Le silence éternel de ces espaces infinis m'effraie.

(‘The eternal silence of these infinite spaces terrifies me.’) Blaise Pascal

It is a familiar fact that the seventeenth-century revolution in philosophy profoundly altered our conception not just of the physical universe but of the very nature of scientific understanding. But although that revolution is often presented by historiographers as a purely epistemological and scientific affair, it also subtly and irreversibly altered philosophy's relationship to its age-old task of providing an account of how humans can live fulfilled lives. In order to understand how that shift came about, it will be necessary first to lay out the principal respects in which the new seventeenth-century world-view differed from what had gone before.

The old picture, dominant in the Middle Ages, and broadly based on Platonic and Aristotelian elements incorporated within a Judaeo-Christian metaphysic, was of a benign and intelligible cosmos, with the earth at its centre – a universe made up of substances whose nature could be understood in terms of readily graspable forms and essences (what Aristotle had called ‘formal causes’), and whose behaviour could be understood teleologically, in terms of a progression towards a series of specifically ordered goals or end-states.

THE ECLIPSE OF REASON

L'homme se trouve devant l'irrationnel.

(‘Man stands face to face with the irrational.’) Albert Camus

The traditional project of synoptic ethics aims at the discovery of a rational life-plan for human happiness; its achievement is the jewel in the philosopher's crown, the ultimate accolade set on the activity of philosophizing. For the ancient Greek thinkers, what makes us essentially human is above all our rationality, and the models of well-being they offer are shaped by reason in the light of its best perceptions of what will realize our true nature. The resulting blueprint is either one where rational activity itself is viewed as the supreme good, or else one in which reason is seen as the essential coordinator and controller of the fulfilled life. Many centuries later, we find in Descartes a view of ethics as part of a philosophical system whose structure is illuminated by the ‘light of reason’; the end-point of philosophical knowledge is that we should reach a clear understanding both of the world around us and of our own human nature, and, armed with the power that understanding brings, be able to bring about the conditions for a worthwhile life.

From our contemporary standpoint, we cannot approach the optimistic ethics of the classical and early modern eras without being aware of a powerful challenge to the traditional doctrine of reason as the determiner and realizer of the conditions for the good life.

For non-human animals, life can be wretched or happy, but there is nothing much they can do about how it turns out. For human beings, by contrast, at least those who are fortunate enough to have the material resources to free them from the daily struggle for existence, there is the opportunity to reflect on how life should be lived. Among the educated citizens of the ancient Greek and Roman worlds, many found it natural to turn to philosophy for guidance; as for the philosophers themselves, though few were prepared to offer instant solutions, most saw it as a main part of the purpose of philosophizing to reach a view on how to achieve fulfilment in life. In the centuries that followed, philosophical systems became steadily more complex and elaborate, but their authors held fast to the old aspiration of philosophy to help humans lead happy and worthwhile lives.

Nowadays, things are very different. A good many academic philosophers, for much of our own century, have strenuously resisted the idea that philosophy can help us with how to live. And while others, particularly in more recent times, have addressed questions about happiness and well-being, for the most part they have shrunk from offering direct guidance on these matters to their fellow citizens. This generalization, like most, is subject to notable exceptions; but it remains true that the bulk of philosophical work on ethics is now addressed to those within the specialist confines of the academy.