Aristotle's Metaphysics M3: Realism and the Philosophy of Qua

Abstract

The article provides a new translation and interpretation of Aristotle’s Metaphysics M3, arguing that Aristotle uses there the QUA as a perspective of intellectual action: an operator on actions rather than a filter on objects. Instead of Aristotle’s mathematics being a science of “Objects QUA mathematical”, we should consider it as a science whose manner of action is “QUA mathematical”. A discussion follows as to Aristotle’s view that his QUA account salvages a realist reading of mathematics without invoking special mathematical objects. This view depends on the deceptively compelling assumption that a statement which is true QUA X is also true simpliciter. If this assumption is false – as I believe the experience of modern science suggests – then Aristotle was wrong and we must indeed either deny the reality of mathematics, or invoke special mathematical objects.