Contradiction in Formal Logic
- Note: The symbol (falsum) represents an arbitrary contradiction, with the dual tee symbol used to denote an arbitrary tautology. Contradiction is sometimes symbolized by "Opq", and tautology by "Vpq". The turnstile symbol, is often read as "yields" or "proves".
In classical logic, particularly in propositional and first-order logic, a proposition is a contradiction if and only if . Since for contradictory it is true that for all (because ), one may prove any proposition from a set of axioms which contains contradictions. This is called the "principle of explosion" or "ex falso quodlibet" ("from falsity, whatever you like").
In a complete logic, a formula is contradictory if and only if it is unsatisfiable.
Read more about this topic: Contradiction
Famous quotes containing the words contradiction in, formal and/or logic:
“An unconscious consciousness is no more a contradiction in terms than an unseen case of seeing.”
—Franz Clemens Brentano (1838–1917)
“Good gentlemen, look fresh and merrily.
Let not our looks put on our purposes,
But bear it as our Roman actors do,
With untired spirits and formal constancy.”
—William Shakespeare (1564–1616)
“We want in every man a long logic; we cannot pardon the absence of it, but it must not be spoken. Logic is the procession or proportionate unfolding of the intuition; but its virtue is as silent method; the moment it would appear as propositions and have a separate value, it is worthless.”
—Ralph Waldo Emerson (1803–1882)