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In logic, a contradiction consists of a logical incompatibility between
two or more propositions. It occurs when the propositions, taken together,
yield two conclusions which form the logical inversions of each other.
Illustrating a general tendency in applied logic, Aristotle?s law of
noncontradiction states that ?One cannot say of something that it is and
that it is not in the same respect and at the same time.?
By extension, outside of formal logic, one can speak of contradictions
between actions when one presumes that their motives contradict each other.
Contradiction in formal logic In formal logic, particularly in
propositional and first-order logic, a proposition varphi is a
contradiction if and only if varphivdashbot. Since for contradictory varphi
it is true that vdashvarphirightarrowpsi for all psi (because
varphirightarrowbotrightarrowpsi
