Discussion of the Aristotelian syllogistic over the last sixty years has arguably centered on the question whether syllogisms are inferences or implications. But the significance of this debate at times has been taken to concern whether the syllogistic is a logic or a theory, and how it ought to be represented by modern systems. Largely missing from this discussion has been a study of the few passages in the Prior Analytics where Aristotle provides explicit guidance on how to individuate syllogisms. (...) I argue that syllogisms are individuated by unordered premise pairs and so may be fruitfully thought of as multi-succedent sequents. I conclude by drawing a few consequences for the representation of the syllogistic. (shrink)