Daniel Maher

Aristotle's treatment of Parmenides in the beginning of Physics argues that it is impossible that being have one sense only, but leaves unstated the relation between one and being. The remainder of Physics A reveals that the practice of counting the principles involves a determination of what those principles are. The analysis of number that is incorporated into Aristotle's account of time in Physics $\Delta$ reveals that a multitude or magnitude can be counted to be a determinate number only by fixing a measure that is or can be taken to be one and that is cognate $ with each part of the amount to be counted. Counting proceeds differently for discrete multitudes and continuous magnitudes because the measures for each are one in different ways. In order to determine more precisely in what sense being is one, the dissertation follows Aristotle's procedure in Metaphysics, beginning with a difficulty cast in terms of the accounts of his predecessors, concerning how being and one are with respect to other natures. Aristotle's solution to the difficulty proceeds by way of explaining how sensible substances are one despite their many parts. Aristotle shows that each determinate sense of being is and is one in virtue of itself, so that one belongs to the first sense of being with an intimacy greater than that between a substance and its accident, or between a definition and its part, or between matter and form, or even between potency and act. Even so, being and one do not have the same account . Aristotle's solution to the aporia involves distinguishing between one in the sense of indivisible and one in the sense of the measure of a class. This distinction enables him to show how there can be different sorts of numbers and to preserve the fundamental difference between what is one in itself and what is many