Download Aristotle and Mathematics: Aporetic Method in Cosmology and by John J. Cleary PDF
By John J. Cleary
John Cleary right here explores the position which the mathematical sciences play in Aristotle's philosophical idea, specially in his cosmology, metaphysics, and epistemology. He additionally thematizes the aporetic process by way of which he bargains with philosophical questions about the principles of arithmetic. the 1st chapters examine Plato's mathematical cosmology within the mild of Aristotle's severe contrast among physics and arithmetic. next chapters learn 3 easy aporiae approximately mathematical gadgets which Aristotle himself develops in his technology of first philosophy. What emerges from this dialectical inquiry is a special belief of substance and of order within the universe, which provides precedence to physics over arithmetic because the cosmological technology. inside of this assorted world-view, we will be able to higher comprehend what we now name Aristotle's philosophy of arithmetic.
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Extra info for Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics
As one might expect from a natural philosopher, however, Aristotle makes the problem of change a crucial test for the cosmological views of his predecessors. The Eleatic denial of change is taken to be absurd, while being diagnosed as a failure to distinguish between sensible and intelligible entities. According to Aristotle's account, Plato did not make the same mistake (as Parmenides) of applying the argument from the sciences to the sensible world, though his mathematical cosmology is open to more serious objections.
But all of this has been worked out in elaborate detail by Gaiser (1962) and Kramer (1959 & 1964), who use later neoplatonic reports to develop what are merely 'hints' in the dialogues. Although they remark on how quickly the Platonic project of mathematizing reality is abandoned in the Academy, they tend to overlook Aristotle's radical criticism as a possible cause of this apostasy. Significantly, they concentrate on Metaphysics I and tend to ignore Book III as a source for objections to this project.
While such an account may be reconstructed from Aristotle's reports on the so-called 'unwritten doctrines,' all one finds in the Platonic dialogues are vague hints. 18 But Euclidean geometry does require a plurality of ideal figures which are neither sensible things nor unique Forms. 19 Therefore Burnyeat is right in saying that the precise ontological status of mathematical 15 van der Waerden (1954) 49-50 & 115-16 claims that calculation with fractions probably led to the theory of proportions found in Euclid's Elements Book VII, but he thinks that these fractions were later eliminated because of the theoretical indivisibility of the unit, as shown by Republic 525E.