 John Buridan’s treatise on consequence (TC, edited by H. Hubien in 1976, English translation in (Buridan 2015)) quite likely represents the pinnacle of sophistication for (Latin) medieval discussions of the concept of consequence. Its modern editor dates it to the 1330s, thus belonging to the early stages of Buridan’s career. We currently know much less about Buridan’s immediate predecessors than about Burley’s or Ockham’s, so it is not clear who Buridan takes inspiration from or is criticizing. The treatise is composed of four books: Book I presents general considerations on the very notion of consequence; Book II treats of consequences involving modal sentences; Book III treats of syllogisms involving assertoric (i.e. non-modal) sentences; Book IV deals with syllogisms involving modal sentences. Each of them is remarkable in its own way (Book III for example represents a radical subversion of Aristotelian orthodoxy, with the suggestion that third-figure syllogisms are more foundational than first-figure syllogisms), but here we shall focus on the first two books (Book I in particular), given the methodological decision of leaving syllogistic aside in the present analysis.