This chapter is focused on thirteenth-century logical hylomorphism. It describes an original chapter in the history of logical form, when argument had "substantial forms," namely syllogistic forms, and when logical matter did "matter," as much as logical form, when defining the scope of logic and the essence of the syllogism. Various senses of logical "matter" are distinguished and the idea of a Latin "material logic" is defended. The study of a series of vexing issues, especially puzzles in modal syllogistic, shows how many arguments lingered in a "syllogistic limbo" at that period. The contribution of logical matter was such that the possibility of a logical "salvation" of these arguments, as syllogisms or as a formally valid arguments, remained undecided.