A contradiction is something that purports to be a and not-a at the same time in the same sense. The law of noncontradiction is fundamental to reasoning and logic. This law states that nothing asserting both of these things at the same time and in the same sense is true. For instance, if I said to you “I’m on my way to the store right now,” then turned to your friend with you and said “I am not on my way to the store right now,” then I have uttered a contradiction.
Contradictory terms cannot both be true. However, neither can they both be false. One of them absolutely must be true. This is called the law of excluded middle (where there truly is no third option). This law points out between a and not-a there is no option. The principle of bivalence says either a or not-a is true. Both are in use within contradictories. Either I am going to the store right now or I am not. Why is this important? So you do not confuse “contradictories” with “contraries.”
Contraries are statements which both cannot be true in the same time and the same sense, yet could possibly both be false. An easy example is this: “Mary got an A on her test,” and “Mary got a D on her test.” While both cannot be true these are not contradictory. It could be that Mary got a C on her test, and thus both options are false.
In summary, in a contradiction one can be true and the other false, or the reverse. In a contrary, one may be true and the other false, or the reverse, or they may both be false. How can this distinction manifest itself in discussions with atheists, agnostics, or even other Christians?
It could be said of Jesus’ body in the Resurrection, “either the disciples stole his body, or he was buried in another tomb!” But why can’t we point out this is only a contrary, and thus it is possible (even plausible) that neither are true? Remember, in a contrary, excluding one option does nothing to prove the truth of the other. Sometimes showing the only two options helps to narrow the conversation. “Either Jesus was God or he wasn’t.” Showing a contradictory pair of statements forces an evaluation of both; if one is false the other is true of necessity.