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)
“The conviction that the best way to prepare children for a harsh, rapidly changing world is to introduce formal instruction at an early age is wrong. There is simply no evidence to support it, and considerable evidence against it. Starting children early academically has not worked in the past and is not working now.”
—David Elkind (20th century)
“It is the logic of our times,
No subject for immortal verse—
That we who lived by honest dreams
Defend the bad against the worse.”
—Cecil Day Lewis (1904–1972)