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Line 1: − + + + + + + + + + + + + + + − * For all of us, there is a disparity between the actions we engage in and those we claim we are engaging in. [http://www.transparencynow.com/news/disguises.htm]
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A '''contradiction''' indicates an error in an argument. In a [[proof]], if two contradictory [[inference]]s can be drawn from the same [[premise]], this indicates that the premise is false.
A '''contradiction''' is the simultaneous acceptance and denial of a proposition or statement. "It was the best of times and the worst of times" is a, poetic, example: the contradiction being used to enhance the poetic nature of the piece.
In a [[proof]], if two contradictory [[inference]]s can be drawn from the [[premise]], this indicates either that a premise is false or that the argument is invalid.
It is often held that from a contradiction anything can be inferred. This can be demonstrated:
1. Take any contradiction, “A” and “Not A”, and take it to be true.
2. Take anything that you want to prove, “P”
3. Now because “A and Not A” is true, “A” is true, by virtue of the simplification rule.
4. “A or P” is true just so long as not both A and P are false.
5. So, As “A” is true, “A or P” must be true.
6. If “A or P” is true, then one of “A” or “P” must be true.
7. As “Not A” is true then “A” is false which means that the remaining term in “A or P” must be true.
8. “P”, absolutely anything you like, is true.
[[category:logic]]
[[category:logic]]