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Among the many, many different mitzvot that appear in our Parshah, the Torah commands us, מדבר שקר תרחק -- "distance yourself from words of falsehood." (23:7) While we know that God prohibits us from lying outright, what does the Torah mean by commanding us to "distance" ourselves from falsehood?
The gemara in Shavuos (30b) explains, that this verse makes greater demands than simply telling the truth. Rather, the verse teaches us, "that if a inherently judge knows that the case is corrupt, he may not say, 'Since the witnesses are testifying, I'll just adjudicate the case and the responsibility [for the miscarriage of justice] will lie with them!' It's not enough to simply tell the truth. The Torah demands that each of us uphold the truth, whether we actually speak the words or not.
Perhaps that's the intention of the oath to tell not only the truth, but "the whole truth." A witness might himself be telling the truth, but withhold further information that would complete the picture and change the nature of the case. That, the Torah tells us, isn't telling the truth. And no amount of self-justification can absolve us from that responsibility.
If only our elected officials followed suit.