 It is from Boethius that later authors inherited the term ‘consequentia’, but the influence of Boethius is not only terminological. In HS, he focuses on conditionals of the form “If something’s (not) A, then it’s (not) B” (si (non) est A, (non) est B), and lists a number of principles and rules governing the logical behavior of such sentences (Martin 2009, 66–78). Boethius’ considerations are not sufficiently worked-out as to be viewed as a full-fledged ‘theory of consequence’, and indeed there are a number of tensions and inconsistencies in his doctrines. But HS will prove to be an important source for the later development of theories of consequence. For example, in this text Boethius introduces the distinction between natural and accidental consequences, which then remains the main subdivision of consequences up until the beginning of 14th century (when it is surpassed by the distinction between formal and material consequences) (Martin 2018) (Archambault 2018a). For Boethius, both kinds of consequences, natural and accidental, entail inseparability, roughly meaning that the antecedent cannot be true while the consequent is false (i.e. a version of (TP)), but natural consequences entail something more, namely a real causal, metaphysical connection between the items in question.