In medieval theories of consequence, we encounter several criteria of validity. One of these is known as the containment criterion: a consequence is valid when the consequent is contained or understood in the antecedent. The containment criterion was formulated most frequently in the thirteenth and fourteenth centuries, but it can be found in earlier writings as well. In The Tradition of the Topics in the Middle Ages, N.J. Green-Pedersen claimed that this criterion originated with Boethius. In this article, the author shows that a notion of containment is indeed present in Boethius, but is not used to define or describe the relation between antecedent and consequent, i.e., the relation of consequence, as Green-Pedersen asserted. The author then offers two interpretations of the notion of containment that are present in Boethius – a metaphysical and a semantic interpretation – and shows how these relate to the containment criterion.