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The thesis that ‘knowledge is of universals’ is of great importance to Aristotle, as he uses it in different contexts which belong to the heart of his theory of knowledge and his metaphysics. First, he claims that scientific knowledge, as opposed to experience, is knowledge of universals, even though he depicts experience as general knowledge involving universal judgements. Second, he agrees with Plato that ‘knowledge is of universals’, but he disagrees when Plato infers that there are therefore independently existing universals, the Platonic Forms. Third, he himself holds that substances are knowable and definable, but also that no universal is a substance – while still ‘knowledge is of universals’. The challenge is thus to understand Aristotle’s thesis that ‘knowledge is of universals’ in such a way that scientific knowledge is more than just knowledge involving universal judgements, while it has at the same time for him minimal ontological consequences. I propose to do this by understanding the claim in the context of Aristotle’s account of scientific proof, and specifically of its logical structure: in a scientific proof an arbitrary individual is introduced for which the theorem is proved. I show that on the basis of this conception of proof Aristotle’s thesis can be understood as demanding in terms of the content of what is known and as undemanding in terms of what ontology is required in order that there be an object for knowledge. In between I show that if one presupposes this conception of proof, one can see the force of Aristotle’s argument against Platonism from the logical complexity of some theorems in mathematics.