Abstract This paper addresses alleged contradictions between the use and theory of

Abstract Aristotle’s philosophy of geometry is widely interpreted as a reaction against a Platonic realist conception of mathematics. Here I argue to the contrary that Aristotle is concerned primarily with the methodological question of how universal inferences are warranted by particular geometrical constructions. His answer hinges on the concept of abstraction, an operation of “taking away” certain features of material particulars that makes perspicuous universal relations among magnitudes. On my reading, abstraction is a diagrammatic procedure for Aristotle, and it is through imagined variation of diagrams that one can universalize spatial inferences. In order to shift the discussion of Aristotle’s work on geometry from ontological to methodological questions, I argue in the first section that geometrical properties for Aristotle are necessary accidents of the particulars, canonically diagrams, in which they inhere. I then consider a line of research that shows how diagrams in ancient geometry are not illustrations of the textual proof but are in part constitutive of geometrical inference, an insight I claim can shed light on Aristotle’s philosophical project. Next I substantiate this assertion by giving an alternative interpretation of abstraction according to which it is a diagrammatic procedure that allows a part of a particular diagram to stand in for a universal. In the last section, I consider Aristotle’s account of mathematical cognition, arguing that there is evidence for the view that imagination is necessary both for the construction of figures, and for their presentation as abstractions subject to universal inference.

Abstract Aristotle claims that in some extenuating circumstances, the correct response to the wrongdoer is

Abstract One of the most discussed parts of Cicero’s

Abstract Many commentators have noted how the conflict in Aristotle’s account of human nature in the

Abstract Most scholars of Aristotle’s biology have accepted the view of D. M. Balme and Pierre Pellegrin that the History of Animals is devoid of any systematic classification of animals. I challenge this reading. I show that Aristotle can produce a taxonomy of animals kinds that are found in the essences of atomic species, or, to borrow from Plato, divide nature by the joints. I start from Aristotle’s positive views of division stated in APo. II.13–14 and how they imply a taxonomic order of a genus. I then develop my interpretation of how Aristotle can divide nature by the joints in respect to his criticisms of division in APr. I.31 paired with the methodology developed in APr. I.27–30. I conclude by illustrating that Aristotle employs this methodology to divide the genus animal by its joints in the History of Animals and how he seeks out the taxonomic order of the genus animal in that work.

Abstract This paper argues that the source for a number of chapters of Book I (“On Medicine”) of the

Abstract At