Consequentia mirabilis
Pattern of reasoning in propositional logic / From Wikipedia, the free encyclopedia
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Consequentia mirabilis (Latin for "admirable consequence"), also known as Clavius's Law, is used in traditional and classical logic to establish the truth of a proposition from the inconsistency of its negation.[1] It is thus related to reductio ad absurdum, but it can prove a proposition using just its own negation and the concept of consistency. For a more concrete formulation, it states that if a proposition is a consequence of its negation, then it is true, for consistency. In formal notation:
- .
Weaker variants of the principle are provable in minimal logic, but the full principle itself is not provable even in intuitionistic logic.