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IN MEMORIAM John J. Cleary

Disciplines

Ancient Philosophy | Classics | Continental Philosophy | Epistemology | History of Philosophy | Logic and Foundations | Logic and foundations of mathematics | Philosophy of Science

Abstract

In the history of science perhaps the most influential Aristotelian division was that

between mathematics and physics. From our modern perspective this seems like an unfortunate deviation from the Platonic unification of the two disciplines, which guided Kepler and Galileo towards the modern scientific revolution. By contrast, Aristotle’s sharp distinction between the disciplines seems to have led to a barren scholasticism in physics, together with an arid instrumentalism in Ptolemaic astronomy. On the positive side, however, astronomy was liberated from commonsense realism for the conceptual experiments of Aristarchus of Samos, whose heliocentric hypothesis was not adopted by later astronomers because it departed so much from the ancient cosmological consensus. It was only in the time of Newton that convincing physical arguments were able to overcome the legitimate objections against heliocentrism, which had looked like a mathematical hypothesis with no physical meaning.

Thus from the perspective of the history of science, as well as from that of Aristotelian scholarship, it is important to examine the details of Aristotle’s philosophy of mathematics with particular attention to its relationship with the physical world, as

reflected in the so-called ‘mixed’ sciences of astronomy, optics and mechanics. Furthermore, we face a deep hermeneutical problem in trying to understand Aristotle’s

philosophy of mathematics without drawing false parallels with modern views that were

developed in response to the foundational crisis at the end of the 19th century. On the

one hand, it is an inescapable fact about our mode of understanding that we cannot jump

over our own shadow, as it were; so that we cannot avoid asking whether Aristotle was

a platonist, or an intuitionist, or a logicist, or a formalist, or some kind of quasiempiricist.

When pursued in this way, the attempt to grapple with Aristotle’s philosophy of mathematics is reduced to asking how well his view matches one of the standard modern views that were developed within an entirely different problem-situation in the history of philosophy. But, on the other hand, one wonders whether it is even possible to recover the original problem-situation in which Aristotle’s views about mathematics

were developed.