Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics

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BRILL, 1995 - 558 sivua
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John Cleary here explores the role which the mathematical sciences play in Aristotle's philosophical thought, especially in his cosmology, metaphysics, and epistemology. He also thematizes the aporetic method by means of which he deals with philosophical questions about the foundations of mathematics.
The first two chapters consider Plato's mathematical cosmology in the light of Aristotle's critical distinction between physics and mathematics. Subsequent chapters examine three basic aporiae about mathematical objects which Aristotle himself develops in his science of first philosophy.
What emerges from this dialectical inquiry is a different conception of substance and of order in the universe, which gives priority to physics over mathematics as the cosmological science. Within this different world-view, we can better understand what we now call Aristotle's philosophy of mathematics.
 

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Sisältö

The Academic Background
1
Platos mathematical cosmology
23
Aristotles Criticism of Platos
71
The eternality of the universe
86
The problem of movement and rest
101
Problems about Mathematical Objects
143
The paradigm for demonstrative knowledge
172
Aristotles Dialectical Method
199
The refutation of opponents
278
Difficulties become objections
288
The Perfection of the Cosmos
345
Aristotles Philosophy of Mathematics
424
Conclusion
490
Bibliography
505
Index Locorum
529
General Index
546

Some metaphysical aporiae
205
Aporetic conclusions
264

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John J. Cleary, Ph.D. (1982) in Philosophy, Boston University, is lecturer at Maynooth College and associate professor at Boston College. He has published widely on ancient philosophy.

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