There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...) continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous. (shrink)

Aristotle explicitly speaks of intelligible matter in three passages only, all from theMetaphysics, in the context of the analysis of definition as the formula that expresses the essence:Metaph.Z10, 1036 a8-11;Metaph.Z11, 1037 a5;Metaph.H6, 1045 a34-36 and 45 b1. In the case of the occurrences of Z10 and Z11, there is almost unanimous consensus that Aristotle uses the expression in a technical way, to indicate the matter of that particular type of objects that are intelligible compounds, of which mathematical objects are paradigmatic (...) instances. By contrast, there is no agreement on how to understand the expression in the case of H6. Here, ‘intelligible matter’ would denote, as stated by some interpreters, the generic element of the definition. The aim of this paper is to show that ὕλη νοητή has the same technical meaning in all the three explicit occurrences in theMetaphisics. Contrary to the interpretation that there is a shift in meaning from Z10-11 to H6, my goal is to illustrate that in both contexts, Aristotle uses the expression ‘intelligible matter’ to designate the matter of mathematical objects insofar as they are paradigmatic intelligible compounds. (shrink)

This article is primarily concerned with Aristotle’s theory of the syllogistic, and the investigation of the hypothesis that logical symbolism and methodology were in these early stages of a geometrical nature; with the gradual algebraization that occurred historically being one of the main reasons that some of the earlier passages on logic may often appear enigmatic. The article begins with a brief introduction that underlines the importance of geometric thought in ancient Greek science, and continues with a short exposition of (...) Aristotle’s views and methods in regard to logic. We then offer an interpretation of syllogisms, as well as of the main proof methods that are utilized by Aristotle, in terms of diagrams that can be seen as analogous to those of Euclidean geometry; where the various proofs proceed by appropriately manipulating an initially drawn diagram, in a way parallel to constructions that occur in Euclid’s Elements. In this way, logic is presented as following, to a large degree, methodological tenets established by the practice of geometry. Finally, we present a diagrammatic decision procedure that allows one to directly read off the validity of syllogisms from a corresponding diagram, in a way such that no further manipulation of it is necessitated. (shrink)