Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics
BRILL, 1995 - 558 sivua
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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The Academic Background
Platos mathematical cosmology
Aristotles Criticism of Platos
The eternality of the universe
The problem of movement and rest
Problems about Mathematical Objects
The paradigm for demonstrative knowledge
Aristotles Dialectical Method
Some metaphysical aporiae
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Anaxagoras aporia Apostle appear argues argument Aristotle Aristotle says Aristotle's assumption astronomy attributes basic belong bodies Cael Caelo cause claim clear conclusion contrast cosmology cosmos definition Demiurge Democritus dialectical difficulties discussion distinction divisible eivai elements ematical entities essence eternal Euclid's Elements exist explain fact fire Form Numbers geometry grasped implications independent substances indivisible infinite inquiry insists instance intellect intelligible Intermediates ISBN 90 kind logical magnitude math mathematical objects mathematical sciences mathematicians matter means Metaph Metaphysics mode motion nature ontological status parallel Parmenides particular passage perception philosophy philosophy of mathematics physical planes Plato Platonic Forms Platonists position possible Posterior Analytics predication primary principles prior priority problem Proclus Pythagoreans quantity question reason reference sense sensible substances sensible things separated Socrates solids soul Speusippus stereometry suggests supersensible substance Syrianus theory thinkers Timaeus tion triangles units unity universe unmoved mover whereas whole Xenocrates
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