## Wednesday, September 14, 2005

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.”
“Why?”
“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."]

Next: Meaning and the necessity of the law of non-contradiction

At 9/14/2005 3:31 PM ,  Steve said...

I think the law of non contradiction works, but not as well in real life.

I am Stationary
I am not Stationary

Using Einstein's theory of relativity, I can say they are both stationary and not stationary at the same time.

Lets take a train. If someone is standing on the train with me (doors closed), I appear to the person as being stationary, even though the train is moving at 80 MPH.

But If another person is at a nearby platform, watching the train pass, it appears to them that I am NOT stationary, I am traveling at 80MPH.

Here is a perfect example of how things can be true or not true depending on your point of view and perspective.

Moreover, we are rarely in a position to conclusively determine whether something is or is not true.

The problem is there SOMETIMES exists a third explanation that permits the possibility that explains things.

In a contradiction, you have something true or not true and by definition it cannot both be true. However, that contradiction doesn't tell you anything about the relationship and meaning between the two ideas.

You are either a master, or a nonmaster (according to Hegel, that makes you a slave). But is it possible, that we can be both a master and a nonmaster (a slave). A Prince who is master of others, but a slave to the king?

Anyways... logic can be true but it can also be "not true" if you know what i mean ;)

At 9/14/2005 5:52 PM ,  ephphatha said...

Steve, you equivocated twice in your response and confused ontology with epistemology once.

The first equivocation was with your "I am/am not stationary" explanation. The law of contradiction states that two propositions that contradict each other cannot both be true at the same time and in the same sense. If I am stationary with respect to one point of reference but not to another point of reference, then the two statements are talking about being stationary in different senses and therefore don't actually contradict.

The second equivocation was about being a master/nonmaster. If I am a master over one person but somebody else is a master over me, then I am not a master in the same sense that I am a nonmaster. Again, equivocation only gets you out of an actual contradiction. It does not invalidate the law of non-contradiction.

At 9/14/2005 6:06 PM ,  daleliop said...

Sam,

I was reading Paul's blog and I saw you made a comment saying that it's too bad Anthony Flew died because you would have wanted to hear his thoughts.

But Anthony Flew is alive! Where did you get that information?

(Ironically, the topic was about the resurrection. I guess Flew kinda "resurrected", eh?)

At 9/14/2005 6:07 PM ,  ephphatha said...

Really? I heard that he died. I don't remember where I heard it, though.

At 9/14/2005 6:27 PM ,  Paul said...

Yes, I meant to ask you about that one. BTW, the response to steve was nicely addressed.

At 9/15/2005 1:14 AM ,  Vman said...

how can you argue agains't the law of non contradiction?

At 9/15/2005 1:59 AM ,  ephphatha said...

Vman, people usually do it by trying to come up with counter-examples. But as I said in the post and also in my response to Steve, most of these examples turn out to be cases of equivocation, not real counter-examples.

At 9/15/2005 2:20 AM ,  daleliop said...

Isn't denying the law of non-contradiction self-refuting?

At 9/15/2005 2:21 AM ,  ephphatha said...

Yes, but if you deny it, a little thing like inconsistency isn't going to bother you. That's why it's impossible to prove the law of non-contradiction. You have to assume it to prove it, and that's circular reasoning.

At 9/15/2005 2:26 AM ,  ephphatha said...

I was just thinking about what I said to Vman. When people try to disprove the law of non-contradiction by coming up with counter-examples, they are assuming the law of non-contradiction. Their argument only works if the law of non-contradiction is valid. A counter-example would be something that contradicts the law of non-contradiction. If you deny the law of non-contradiction, then you can't deny it on the basis that there are counter-examples. Counter-examples can only disprove something if you assume the validity of the law of non-contradiction.

At 9/22/2005 8:35 PM ,  Paul said...

Is it even possible to argue against the law of non-contradiction? It seems to me that one would then be implying that it is not true and that something else is true. But then you are arguing that either the law of NC is true or this other thing is true -- either/or, one or the other, this not that. Sounds like an affirmation of the law of NC to me.

At 9/23/2005 3:56 AM ,  ephphatha said...

I agree Paul, and I appreciate you giving me one more way of putting it. Sometimes you have to explain something in a dozen different ways before it clicks for somebody.

At 2/21/2013 12:08 PM ,  Mrs. Beck said...

..."I appear..." This does not violate the law of contradiction; it shows that reality and perception are not necessarily the same.

At 5/27/2013 9:10 PM ,  Steve2 said...

Mmm. What about quantum superposition? For example, a photon can be in a superposition of two different spin-states, spin-up and spin-down, at the same time and place and in the same sense. It settles into one state or the other when it is observed, but until then it is in both states at the same time. We now have the first quantum computer that uses that principle.

At 5/27/2013 10:34 PM ,  Sam said...

Steve2, I don't know enough physics to response specifically to quantum superposition, but I can promise you with absolute confidence that there are no violations of the law of non-contradiction in nature. Any model of quantum physics that contains a contradiction cannot possibly accurately represent the reality of the situation, though it may be a useful model for explaining observed phenomena.

At 10/03/2016 6:25 AM ,  Vivie Xie said...

I just want to say, Thank you for this explanation of law of noncontradiction!

At 12/24/2016 1:51 AM ,  The Skipper said...

Very well put and in neat everyday terms. I like it!

At 12/24/2016 1:54 AM ,  The Skipper said...

Unless you open the cookie jar and have a look...

At 5/13/2018 8:30 AM ,  Maina Patrick Samuel Junior said...

The law of non contradiction I think requires approval from the other party.

At 5/28/2018 1:58 PM ,  Anonymous said...

This is an old post, but will leave a thought anyway.

Have an issue with Steve's post. First, Einstein's theory of relativity centers on the context of quantum physics, not to anyone standing either on a moving train or not. Bad analogy.

Secondly, Steve says:
"Moreover, we are rarely in a position to conclusively determine whether something is or is not true."

Begs the question. Either this statement itself is true or it is not. If it is true, how does Steve know whether or not he is in the rare position to conclusively determine whether his statement is true or not? If it is false, then it is nonsense.

Subjective relativity cannot stand against the objectivity inherent in the laws of non-contradiction. Every time you try to clobber them, they clobber you. It is inevitable.

Cheers.