PreMaT #2 – The 14th Century (original) (raw)

SP.2H3 / ESG.SP2H3 Ancient Philosophy and Mathematics, Fall 2006

Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry.

Between Reality and Mentality -Fifteenth Century Mathematics and Natural Philosophy Reconsidered

Why did the members of the Samarqand Observatory School stand closer to the science of kalām for metaphysical principles in the fifteenth century and reserve more space to Mathematics in the description of the nature? When we look at the works circulating among scientists and emerging terms in this period, we observe some relative advancement in mathematical sciences used for quantitative certainty, also problematization of the ontology of mathematical entities and of epistemological values of mathematical knowledge, and discussions on the legitimacy of mathematical models on the nature. We examine the roots of these questions in Islamic tradition of philosophical sciences and especially developments post-Marāgha Observatory School; and analyze the posed ideas in relation to the concept of nafs al-amr (fact of the matter), which relies at the center of all research and discussions.

Mathematical and Metaphysical Space in the Early Fourteenth Century

Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, 2018

Medieval philosophers did not unequivocally support the Aristotelian doctrine of container-place, that is, that the place of a thing is the first immobile surface of what contains the thing. John Duns Scotus (d. 1308) famously developed a theory that tried to resolve the problems of container-place through an appeal to a notion of equivalence. Peter Auriol (d. 1322) took the radical step of reducing place to the category of position, understood with relation to the three-dimensional extension of the universe. Auriol called this "place according to metaphysical consideration" and contrasted it with "place according to physical consideration." This division evoked one in another thinker, Nicholas Bonet (fl. 1333), who in his Philosophia naturalis distinguished between mathematical and natural senses of place. Rather than being influenced by Auriol, Bonet developed Scotus' doctrine of equivalent place into a doctrine of mathematical place and time. To support his position, Bonet drew upon the Aristotelian notion of abstraction and selectively read Averroes as explicitly supporting his position.