 These constructions require, of course, that one dispense at least with that principle of Boolean logic ex contradictione quodlibet (ECQ) (from a contradiction every proposition may be deduced, also called explosion). In passing, C.I.Lewis showed that ECQ follows by a simple argument from the principle disjunctive syllogism (DS) (from A-or-B and not-A deduce B). So DS has to go too. Obviously, ECQ trivialises any inconsistent theory (triviality = every sentence is provable). Non-triviality should be regarded as a constraint on interesting theories: a trivial theory is useless for mathematical calculation, since a trivial theory does not distinguish principles in the theory from their negations. Similarly, considerable debate (Burgess 1981, Mortensen 1983), made it clear that dispensing with DS was not so counter-intuitive, especially when a plausible story emerged about the special conditions under which DS continues to hold.