The Continuous and the Discrete presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion. Professor White connects the Aristotelian model, which represents spatial magnitude, time, and motion as infinitely divisible and continuous, with the standard ancient geometrical conception of extended magnitude: it is a model which represents the marriage of physical theory and mathematical orthodoxy. In the second half of the book the author discusses two ancient alternatives to the Aristotelian model: 'quantum' models, and a Stoic model according to which limit entities such as points, (one-dimensional) edges, and (two-dimensional) surfaces do not exist in (physical) reality. Both these alternative models deny the applicability of standard 'Euclidean' ancient geometry to the physical world. A unique feature of the book is the discussion of these ancient models within the context of later philosophical, scientific, and mathematical developments.
A basic assumption of the author's approach is that such a contemporary perspective can deepen our understanding not only of ancient philosophy, physics, and mathematics, but also of later developments in the content and methodology of these disciplines.
The Continuous and the Discrete presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion. Professor White connects the Aristotelian model, which represents spatial magnitude, time, and motion as infinitely divisible and continuous, with the standard ancient geometrical conception of extended magnitude: it is a model which represents the marriage of physical theory and mathematical orthodoxy. In the second half of the book the author discusses two ancient alternatives to the Aristotelian model: 'quantum' models, and a Stoic model according to which limit entities such as points, (one-dimensional) edges, and (two-dimensional) surfaces do not exist in (physical) reality. Both these alternative models deny the applicability of standard 'Euclidean' ancient geometry to the physical world. A unique feature of the book is the discussion of these ancient models within the context of later philosophical, scientific, and mathematical developments.
A basic assumption of the author's approach is that such a contemporary perspective can deepen our understanding not only of ancient philosophy, physics, and mathematics, but also of later developments in the content and methodology of these disciplines.
I. Spatial magnitude, time, and motion: An Aristotelian model:
Aristotle: The formal analysis of spatial magnitude and locomotion;
Aristotle on time and locomotion: Physics and metaphysics;
Aristotelian kinematics and non-locomotive Kineseis; Aristotle and
the mathematicians, ancient and modern; II. Spatial magnitude,
time, and motion: Alternatives to Aristotelianism; The quantum
model: Spatial magnitude; The quantum model: Time and locomotion;
The Stoic model;
Peroration.
`He is well aware of, and admirably avoids, the temptations and
pitfalls inherent in this kind of approach. When he deals with the
post-Aristotelian philosophers, his clarity and good judgement in
regard to the scanty and treacherous evidence are particularly
welcome ... A merit of this book is that it forces the reader to
ask fundamental questions.'
Times Higher Education Supplement
'an unusually productive approach to the history of philosophy, one
that combines historical reconstruction through detailed technical
analysis from within the perspective of the ancient theories ...
One obvious conclusion of the book, built from many rigorous,
subtle, and suggestive analyses, is that the principles of the
continuous and the discrete have a wide range of significance for
ancient and modern physical and mathematical analysis ... White
has
not disguised the intrinsically technical nature of his material,
but he has explicated it clearly and usually succinctly, A modest
amount of logical and mathematical notation is used, and his
rigorous
analysis is supported by a scattering of geometrical drawings and
graphs.'
Dirk D. Held, Connecticut College, Bryn Mawr Classical Review 3.6
(1992)
'Scholarly, provocative, and persuasive, this work is thoroughly
professional'
choice, January 1993
'This is a fascinating story, and White tells it well. White's
reading of Aristotle is admirably sensitive to the detail of his
problems, his methods and his solutions.'
Nicholas Denyer, Trinity College, Cambridge, Mind, Vol. 102, No.
408, Oct '93
'This is an important book ... it is well argued and White displays
good knowledge of modern literature on the matter.'
Leo J. Elders, Institut voor Wysbegeerte en Theologie, Review of
Metaphysics, March 1994
'His discussion reveals the conceptual assumptions underlying each
position, and his conjectures ... are thought-provoking.'
S. Leggatt, University of Reading, The Classical Review, Vol.
XLIII, No. 2, 1993
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