Changes

The '''Law of Non-Contradiction''' can be formulated as follows: Two truths cannot contradict one another.<ref>{{cite web |author=Galileo Galilei |title=Letter to the Grand Duchess Christina of Tuscany| year=1615, 1998 |publisher= Internet History Sourcebooks Project, Paul Halsall, [The Jesuit] Fordham University [of New York]|url= http://www.fordham.edu/halsall/mod/galileo-tuscany.asp |accessdate=June 10, 2013}}</ref>

The '''Law of Non-Contradiction''' can be formulated as follows: Two truths cannot contradict one another.<ref>{{cite web |author=[[Galileo Galilei]] |title=Letter to the Grand Duchess Christina of Tuscany| year=1615, 1998 |publisher= Internet History Sourcebooks Project, Paul Halsall, [The Jesuit] Fordham University [of New York]|url= http://www.fordham.edu/halsall/mod/galileo-tuscany.asp |accessdate=June 10, 2013}}</ref>

On the other hand, for any pair of contradictory premises, one must be true and the other false. The Law of Non-Contradiction prevents both premises being true, while the [[Law of Excluded Middle]] points out that a pair of contradictory premises exhausts all possibilities. Another way of putting it is: a [[proposition]] must be either true or false—not both true and false, nor in some limbo state in between [[truth]] and falsity. This can be useful in listing all possible alternatives and refuting all of them but the correct one.<ref>{{cite web |title=Loving God with all your mind: logic and creation|author=Jonathan D. Sarfati|publisher=CMI|url=http://creation.com/loving-god-with-all-your-mind-logic-and-creation|accessdate=June 10, 2013}}</ref>

On the other hand, for any pair of contradictory premises, one must be true and the other false. The Law of Non-Contradiction prevents both premises being true, while the [[Law of Excluded Middle]] points out that a pair of contradictory premises exhausts all possibilities. Another way of putting it is: a [[proposition]] must be either true or false—not both true and false, nor in some limbo state in between [[truth]] and falsity. This can be useful in listing all possible alternatives and refuting all of them but the correct one.<ref>{{cite web |title=Loving God with all your mind: logic and creation|author=Jonathan D. Sarfati|publisher=CMI|url=http://creation.com/loving-god-with-all-your-mind-logic-and-creation|accessdate=June 10, 2013}}</ref>