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. Thus the Aristotelian model is presented as 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.
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