Full Idea
On its modern interpretation, the validity of the inference 'All S are M; All M are P; so All S are P' just expresses the transitivity of the relation 'subclass of'.
Gist of Idea
The universal syllogism is now expressed as the transitivity of subclasses
Source
Hilary Putnam (Philosophy of Logic [1971], Ch.1)
Book Reference
Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.5
A Reaction
A simple point I've never quite grasped. Since lots of syllogisms can be expressed as Venn Diagrams, in which the circles are just sets, it's kind of obvious really. So why does Sommers go back to 'terms'? See 'Term Logic'.