Plotinus’ outline of his method on inquiry on eternity and time in 3.7(45).1.4 includes a reference to ‘concentrated apprehensions of thought’ ([…] ταῖς τῆς ἐννοίας ἀθροωτέραις ἐπιβολαῖς […]). Scholars sometimes argue that Plotinus is here referring to the Epicurean notion of ἀθρόα ἐπιβολή (Epic., Ep. Hdt. 35.9; PHerc. 346, col. 4.24–28). I suggest instead that Gal., mm x.38 Kühn provides the closest parallel to Plotinus’ passage. Further parallels between 3.7 and Galens’ lost On Demonstration suggest that Galen, not Epicurus, is (...) Plotinus’ immediate source. (shrink)

Frege argues that number is so unlike the things we accept as properties of external objects that it cannot be such a property. In particular, (1) number is arbitrary in a way that qualities are not, and (2) number is not predicated of its subjects in the way that qualities are. Most Aristotle scholars suppose either that Frege has refuted Aristotle's number theory or that Aristotle avoids Frege's objections by not making numbers properties of external objects. This has led some (...) to conclude that Aristotle's accounts of arithmetical and geometrical objects differ substantially. I close this supposed gap by showing that Aristotle's arithmetical objects, like geometrical objects, are just certain sensible things qua certain properties they in fact possess. Specifically, numbers are pluralities qua quantitative or relational properties like ten units or ten. I show that this view is resistant to the Fregean concerns about arbitrariness and numerical predication. (shrink)