This paper examines the view held by Francesco Piccolomini (1523-1607) on the relation between prime matter and extension. In his discussion of prime matter in the Libri ad scientiam de natura attinentes Piccolomini develops a theory of prime matter that incorporates crucial elements of the viewpoint adhered to by the Neoplatonist Simplicius. The originality of Piccolomini’s undertaking is highlighted by contrasting it with the ideas found in Jacopo Zabarella’s De rebus naturalibus . The case of Piccolomini shows that, in order (...) to classify early modern metaphysical theories of prime matter, the category ‘prime matter as sheer dimensionality’ is indispensable. (shrink)

The Neoplatonist Proclus, in his commentary on Euclid's Elements, appears to have been the first to systematically cut imagination's exclusive ties with the sensible realm. According to Proclus, in geometry discursive thinking makes use of innate concepts that are projected on imagination as on a mirror. Despite the crucial role of Proclus' text in early modern epistemology, the concept of a productive imagination seems almost not have been received. It was generally either transplanted into an Aristotelian account of mathematics or (...) simply ignored. In this respect, Johannes Kepler is a remarkable exception. By rejecting the traditional meta-mathematical framework, Kepler was the first to incorporate the productive side of imagination within an early modern philosophy of mathematics. Moreover, by securing imagination's sensory input, he transformed Proclean imagination into a tool for cosmic self-knowledge. -/- . (shrink)

© by Journal of the History of Ideas. Federico Commandino can be considered the personification of the renaissance of mathematics in sixteenth-century Italy. Previous scholars have generally reduced the philosophy of mathematics developed by Commandino in the preface to his translation of Euclid’s Elements to a superficial synthesis of Neoplatonic and Aristotelian elements. Until now, no attention has been paid to Commandino’s use of the sixth-century commentary on Aristotle’s De Anima by John Philoponus. In his article I will argue that, (...) in depicting imagination as a mental drawing board for geometrical figures, Commandino directly relies on Philoponus’s concept of mathematical imagination. (shrink)

The metamathematical framework of the early modern period is primarily determined by two presuppositions stemming from the Aristotelian tradition: mathematical objects are abstracted from sensible matter; imagination is a reproductive faculty exclusively connected with the sensible realm. The recovery of the works of the Greek commentators confronted the early modern readers with rivalling philosophical–mathematical views that explicitly called into question some of their previously undisputed assumptions. In this article I will argue that Francesco Piccolomini in his Academicae contemplationes brings about (...) an original fusion of these colliding horizons, by transposing the synthesis established by Simplicius between Aristotelian abstractionism and Neoplatonic innatism into the sixteenth century. (shrink)