The High Price of Contradiction

One cool factoid I picked up from my philosophy of religion lectures:

I'm used to formal logic being very picky about finding contradictions in starting assumptions. However, I didn't realize how important it was. According to the formal rules of logic, if two contradictory premises are allowed in an arguement ("P" and "Not P"), then all possible conclusions can be shown to be true. A single contradiction can thus completely invalidate everything that follows, not because it fails to make sense but because it makes exactly whatever sense we want it to make.

It almost seems unfair, like the Devil has the deck stacked against us. A single error can spawn an infinite number of lies.