OUP (2018) h/b 230pp £45 (ISBN 97-0198779728)

‘Mereology’, the relation of parts to the whole and of the parts to each other within a whole, is not the subject of any Aristotelian treatise in itself. P.’s contention is that Aristotle’s remarks on concepts such as ‘part’, ‘whole’, ‘boundary’, ‘being connected’ and ‘being continuous’, although spread across many different works, do add up to a coherent way of thinking—it might not be a formal system of mereology (or ‘mereotopology’) as such, but it is an internally consistent theory of bodies, complete enough to have constituted an independent treatise if Aristotle had chosen to make it one. 

Moreover, Aristotle, says P., considered the concepts bound up in the theory of bodies to be fundamental to much of his natural philosophy, that is, to his theories of place, movement and action, among others. For him bodies are not merely mathematical or geometrical entities but consist of matter located somewhere: the geometer provides axioms on which the natural scientist draws, but which do not make the natural scientist redundant. Aristotle, unlike his modern counterparts, is only a mereologist insofar as he is a physicist. Overall, P.’s avowed project is to present the Aristotelian doctrine on bodies, and to establish the doctrine’s context in Aristotle’s own thinking, rather than to criticise it or, though he cites Plato and Euclid, to set it in the context of other philosophy contemporary to it or later.

P.’s method of proceeding is to divide his project into two parts: the first deals with the position of Aristotle’s theory of bodies in his own wider philosophy; the second deals with the theory of bodies itself. This might seem an odd way round, but in fact that physical slant which Aristotle takes within the theory is more easily understood after the preliminary ground-clearing. This ground-clearing is, however, laborious: P. states what he is going to do, does it, states what he has done and summarises the conclusions reached so far, a rigour which can seem repetitious when the argument is simple—and when it is applied repeatedly to extracts from various works. Nevertheless, by the end, P.’s view, which he describes as controversial, seems uncontentious.

The second part is more engaging since it explores the conceptual framework which Aristotle erected. For the specialist this provides a comprehensive gathering, and where necessary reconciliation, of Aristotle’s contribution to this subject (gleaned from a wide selection of works, above all the Physics and Metaphysics; Topics Book V is, for some reason, not included). For the non-specialist, this is a revelation of ideas that, if at first they do not seem the stuff of sleepless nights, take on an interest all of their own—Aristotle’s analysis of quantity and magnitude; his discussion of whether the boundary between objects is part of the objects; the definition of a point not as the constituent of a line but the division of a line; and much more. The intensity of Aristotle’s inquiry, and the way he fits it into a larger system, is always deeply impressive. P., despite the scattering of his sources, succeeds very well in capturing this sense of system-building.

There are two appendices: in the first P. discusses Metaphysics V.13 on quantity, plurality and magnitude in detail; in the second, he lists the conclusions from each section of the book, what he terms the ‘propositions’—a useful synopsis of the ground covered. There are three indices to round off a work never less than thorough.

Christopher Tanfield