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The Scholastic philosophers defined a person as "an individual substance of a rational nature" (e.g., Boethius, Aquinas).
I understand how an individual could not be a substance (it would be an individual accident). But how could a substance not be an individual? Aren't substances, at least according to Aristotle, always individual entities?
Substance is a common terminology in metaphysics which have many different versions belonging to different schools of thought. If restricted to Aristotle's hylomorphic version, substance can be classified as primary substance and secondary substance according to reference here:
A substance—that which is called a substance most strictly, primarily, and most of all—is that which is neither said of a subject nor in a subject, e.g. the individual man or the individual horse. The species in which the things primarily called substances are, are called secondary substances, as also are the genera of these species. For example, the individual man belongs in a species, man, and animal is a genus of the species; so these—both man and animal—are called secondary substances.
Aristotle thinks that in addition to primary substances (which are particulars), there are secondary substances (δεύτεραι οὐσίαι), which are universals (Categories 2a11–a18).
So you're right when you say "Aren't substances, at least according to Aristotle, always individual entities?", in the sense of Aristotle's primary substance. However, he admits there're secondary substance, so if an individual man is his primary substance, then the genus of his species, both man and animal, are his secondary substances which are universals not particulars any more...
