By John J. Cleary
John Cleary the following explores the position which the mathematical sciences play in Aristotle's philosophical idea, in particular in his cosmology, metaphysics, and epistemology. He additionally thematizes the aporetic approach through which he offers with philosophical questions about the rules of arithmetic. the 1st chapters think of Plato's mathematical cosmology within the mild of Aristotle's severe contrast among physics and arithmetic. next chapters learn 3 simple aporiae approximately mathematical items which Aristotle himself develops in his technology of first philosophy. What emerges from this dialectical inquiry is a unique perception of substance and of order within the universe, which provides precedence to physics over arithmetic because the cosmological technological know-how. inside of this diverse world-view, we will greater comprehend what we now name Aristotle's philosophy of arithmetic.
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Additional info for Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics
For instance, when compared with the thumb the index finger appears to be large but, at the same time, it appears to be small compared with the middle finger. Similarly Socrates finds that the same thing often appears to be both hard and soft, and so he concludes that the senses by their very nature must deal with such opposites. With reference to the ascent of the soul, therefore, it is only such sensory impressions that provoke the soul to reflect on the true nature of the things perceived. In the case of touch, for instance, Socrates says (524A) that the soul must be puzzled (a1tope'iv) as to what perception means by hard if the same thing also appears to be soft.
27 So the remark may be seen as a dialogical fiction, 28 since Socrates uses the occasion to outline (528B) two major reasons for the neglect of stereometry; namely, lack of support within the city and lack of guidance for such research. Therefore, one should interpret this digression on stereometry in the light of Plato's proposal to reform the mathematical sciences from the viewpoint of their theoretical foundations. The lack of support for stereometry among the ordinary citizens is consistent with their low estimation of all theoretical disciplines, but this one is particularly neglected because it does not appear to have any of the practical uses of arithmetic and geometry.
2. Geometry and astrononry as propaideutic The issue is clarified further by Socrates' leading question (526E 1~2) as to whether geometry makes it easier for the soul to behold the Form of the Good. Since that goal is promoted by whatever compels (avaYKasn) the soul to orient itself towards true Being, he adopts (526E5) this as a criterion for any discipline to quality as propaideutic. In examining the contemporary practice of geometry, therefore, Socrates finds (527 A~B) an internal conflict between its real purpose and the way in which geometricians talk.