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One of the main controversies of the Logic Schools of the 12th century centered on the question: What follows from the impossible? In this paper arguments for two diametrically opposed positions are examined. The author of the ‘Avranches Text’ who probably belonged to the school of the  Parvipontani  defended the view that from an impossible proposition  everything  follows (‘Ex impossibili quodlibet’). In particular he developed a proof to show that by means of so-called ‘disjunctive syllogism’ any arbitrary proposition  B  can be logically derived from a pair of contradictory propositions  A  and Not- A . The author of the  Ars Meliduna  instead argued that  nothing  follows from an impossible proposition (‘ex falso nihil sequitur’). This view is supported by various counterexamples which aimed to show that the admission of impossible premises would give rise to inconsistent conclusions. Upon closer analysis these inconsistencies do not, however, have the formal structure of a real contradiction like  A  and Not- A , but rather the structure of two rivalling  conditionals  like ‘If  B  then  A ’ and ‘If  B  then Not- A ’. Hence these counterexamples rather have to be considered as refutations of the basic principles of ‘connexive logic’.

What Follows from the Impossible: Everything or Nothing? (An Interpretation of the ‘Avranches Text’ and the Ars Meliduna )