Kant claims that Aristotle’s logic is complete. He defends this claim from the nature of a strictly scientific logic, and rejects as futile the attempts by some modern philosophers at extending it. I analyse what it means for Kant to regard Aristotle’s (formal) logic as complete, explain the historical and philosophical considerations that commit him to proving the completeness claim and sketch the proof based on materials from his logic corpus. The proof will turn out to be an integral part of Kant’s larger reform of formal logic in response to a foundational crisis facing it.