Contradiction 

In logic, contradiction is defined much more specifically, usually as the simultaneous assertion of a statement and its negation, also known as its denial. (See: the Law of non-contradiction.) This, of course, assumes that "negation" has a non-problematic definition. (Coming sometime: article on negation.)

In First-order predicate calculus, anything can be derived from a contradiction....

In everyday speech, contradiction can have a much less rigorous feel. For example, if a man condemns the members of his church for not giving the church enough financial support, but then never puts anything in the collection plate when it goes around, it can be said that his actions contradict his words.

...In logic and math, a contradiction is usually taken as a sign that something has gone wrong, that steps need to be retraced. ... a need to "check your premises". ... Proof by contradiction

(ironic: you can't know that correct, formal reasoning will lead to consistent conclusions. (specify in what sense this is true))

Common sense suggests that people do hold many contradictory beliefs, and this is confirmed by psychologists. (?)

Being non-contradictory seems to be central to people's conceptions of what "reason" is, and what it means to be "reasonable".

What to make of it: 1) be very, very careful, so as to not be contradictory. 2) embrace contradiction as part of human nature. 3) ?

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