The law of non-contradiction
The law of non-contradiction is one of the most obvious laws of logic, but one of the most frequently denied. It states that for any two propositions, if they contradict each other, they cannot both be true. Whenever I argue with people about the law of non-contradiction, they almost always resort to equivocation to get around it, but two statements can only contradict each other if they are talking about the same thing at the same time and in the same sense. Take the following two statements for example:
1. It is raining outside.
2. It is not raining outside.
A person who wants to argue against the law of non-contradiction may point out that both of these statements can be true provided that one is referring to Phoenix and the other is referring to Tallahassee. It may be raining in Tallahassee but not in Phoenix. But if we are talking about different places, then the statements don’t contradict each other, and consequently, they can both be true. If, however, they are both talking about the same thing, then they cannot both be true at the same time. Equivocation only gets you out of an actual contradiction; it doesn’t get you past the law of non-contradiction.
The law of non-contradiction is important because it’s how we tell the truth from a lie. Without it, there’s no such thing as a lie. A lie is that which contradicts the truth. After our lively discussion last Tuesday, I was all jazzed, so I went to work that night and talked to my co-worker, Julie, to get it off my chest. I said,
“Julie, let’s suppose I tell you that my sister is pregnant, and then five minutes later, you come to me and ask, ‘Does your sister know the sex of her unborn baby?’ I then reply, ‘My sister is not pregnant.’ What would you conclude from that?”
Julie said, “I’d say you’re crazy.”
“Because one minute you said your sister was pregnant, and the next minute, you said she wasn’t.”
“Would you assume I was lying?”
“Well yeah, duh!”
“But why would you assume that?”
She just looked at me like I had two heads, so I let her off the hook. I said,
“My sister is either pregnant or she’s not pregnant, right? She can’t be both pregnant and not pregnant at the same time and in the same sense, can she?”
Julie understood what I was getting at. It was something so obvious to her that she couldn’t deny it. If I say that my sister is pregnant, and yet she’s not, then I’ve told a lie. On the other hand, if I says she’s not pregnant, and yet she is, then I’ve told a lie. The reason for that is the law of non-contradiction. Both statements cannot simultaneously be true because they contradict each other. Whenever you encounter a contradiction, you can know for an undeniable fact that you are in the midst of error.
[Ronald Nash has a chapter in Worldviews in Conflict where he gives two arguments for the law of non-contradiction. One is basically the same as mine. Significant speach is impossible without the law of non-contradiction, because nothing we say means anything unless it excludes the negation of what we say. But he also argues that significant action is impossible without the law of non-contradiction. We cannot pay our taxes if there is no difference between paying our taxes and not paying our taxes. Nash gives a funny scenario in which the IRS confronts a guy who didn't pay his taxes. I don't have the book with me, but the guy said something like, "I learned in my philosphy classes in college that logic is not universally valid, so there's no difference between paying my taxes and not paying my taxes." The IRS responded, "Then there's no difference between going to jail and not going to jail."]