consequentia mirabilis the logical principle that if a statement follows from its own negation it must be true. Strict consequentia mirabilis is the principle that if a statement follows logically from its own negation it is logically true. The principle is often connected with the paradoxes of strict implication, according to which any statement follows from a contradiction. Since the negation of a tautology is a contradiction, every tautology follows from its own negation. However, if every expression of the form ‘if p then q’ implies ‘not-p or q’ (they need not be equivalent), then from ‘if not-p then p’ we can derive ‘not-not-p or p’ and (by the principles of double negation and repetition) derive p. Since all of these rules are unexceptionable the principle of consequentia mirabilis is also unexceptionable. It is, however, somewhat counterintuitive, hence the name (‘the astonishing implication’), which goes back to its medieval discoverers (or rediscoverers). See also IMPLICATION. R.P.