 Chronologically, the development of theories of consequence in the 14th century is thus characterized by an early and rather ‘primitive’ stage (1), then by a stage of further development, in which, nevertheless, topical notions still play a prominent role (2), and then by two further traditions which run more or less parallel, namely the Parisian/continental tradition (3) and the British tradition (4). While they differed in particular in the various definitions given to the formal vs. material consequence distinction, they all agreed that necessary truth-preservation (TP) is a necessary (but perhaps not sufficient) condition for something to count as a (valid) consequence (Dutilh Novaes 2008).