 Finally, a “necessary” inference is one which can be reduced to a categorical or hypothetical syllogism via a necessary auxiliary assumption or “middle” (per medium necessarium) ([Soph] soph. 2 [1494: fol. 83rb]). Similarly, two sentences are assumed to be logically equivalent (convertantur) if they imply each other formally via a necessary middle ([RSS] 1494: fol. 15rb–va [1988b:  461–462]).[20]  This represents the view of validity as reducibility to paradigmatically valid  syllogisms.[21]