Expertlatin
- What is theorem principle of explosion?
- What is ex falso quodlibet principle?
- What is explosive logic?
What is theorem principle of explosion?
The principle of explosion just says that if a theory contains a single inconsistency, such a theory is trivial—that is, it can prove everything. Therefore, according to the principle of explosion, there is only one inconsistent theory: the trivial theory that has every sentence as a theorem.
What is ex falso quodlibet principle?
Ex falso quodlibet is Latin for “from falsehood, anything”. It is also called the principle of explosion. In logic it refers to the principle that when a contradiction can be derived in a system, then any proposition follows. In type theory it is the elimination rule of the empty type.
What is explosive logic?
A logical consequence relation is explosive if according to it any arbitrary conclusion \(B\) is entailed by any arbitrary contradiction \(A\), \(\neg A\) (ex contradictione quodlibet (ECQ)). Classical logic, and most standard 'non-classical' logics too such as intuitionist logic, are explosive.
