Question

As you are learning about propositions and contradictions, write out a view that you hold on a social issue in propositional form (A, E, I, or O). What is the logical contradiction to your view? Identify a specific group that advocates the contradiction of your viewpoint.

Answer 1

Answer) logical contradiction is the conjunction of a statement S and its denial not-S.   In logic, it is a fundamental law- the law of non contradiction- that a statement and its denial cannot both be true at the same time. Here are some simple examples of contradictions.

1. I love you and I don't love you.
2. Butch is married to Barb but Barb is not married to Butch.
3. I know I promised to show up today, but I don't see why I should come if I don't feel like it.
4. The restaurant opens at five o'clock and it begins serving between four and nine.
5. John Lasagna will be a little late for the party. He died yesterday.
In every statement there is contradictions because they seem either explicitly to state or logically imply a certain statement and its denial. (1) is an explicit contradiction. It's not possible that we love a person and we don't love him/her at the same time. (2) is an implicit contradiction. It depends on the unstated but well known principle: if x is married to y, then y is married to x. (3) is also an implicit contradiction. It depends on the unstated meaning of promising, namely, that whenever you promise to do something you thereby acquire a moral obligation to do it.

Very often contradictions are only apparent. For example someone in a love-hate relationship might utter something like (1), meaning "I love you in some ways, but I hate you in others". This, of course, is not a contradiction at all. (4) also can look like a contradiction, but this may just be the result of unclarity. Perhaps the restaurant opens at 5:00 in the morning. (5) is not literally a contradiction, since a dead person could show up at a party. We call it a contradiction just because the statement "John will be a little late for the party," strongly suggests that John will be alive when he shows up.

When we tell people that they aren't making any sense, it is often because we think that they are saying something contradictory. In a Dilbert cartoon one of Dilbert's office mates is complaining that she hasn't been trained how to use the new computer. The conversation proceeds as follows:

• Dilbert: Why don't you just read the manual?
• Office mate: Right. Who has time to do that?
• Dilbert: You mean you have time to go to a training session, but you don't have time to read the manual? That doesn't add up.

Here Dilbert's point is obviously that she is contradicting herself : She is saying that she has time to learn and she doesn't. Of course she might not really be contradicting herself at all. It may be that she finds computer manuals very hard to understand, so that the time it takes to be trained really is far less than the time it would take to learn from the manual.

This example shows that while it is very important to be logically consistent, it is also important to permit people to be so. When people speak in a way that seems logically contradictory it is often just because they are not speaking completely or clearly. So the point of exposing apparent contradictions is not, ultimately, to criticize peoples views as nonsensical, but rather to make them be clearer about what they are saying.

In order to to identify contradictions properly, consider the following conversational example.

• Mrs. Aanee: You have been absent from class 11 times this month. You fail. Goodbye.
• Butch: What? That's impossible!   The class only meets twice a week.
• Mrs. Beeble: True, but you have missed it 11 times nevertheless.
• Butch: That doesn't make any sense. You can't be absent from a class on days that it doesn't meet.
• Mrs. Beeble: You're saying you weren't absent on those days?
• Butch: That's right..
• Mrs. Beeble: So you were here?
• Butch: No!
• Mrs. Beeble: You are wasting my time. If you weren't here, then you were absent. Goodbye.

Notice here that Butch, while perfectly aware that Mrs. Beeble is talking nonsense, has not successfully identified the contradiction. The closest he comes is to say "You can't be absent from a class on days that it doesn't meet." But this statement can have several different meanings. Butch is trying to say that it is logically contradictory to mark someone absent from a class that doesn't meet. But all he is succeeded in communicating is that it is somehow an unfair or unreasonable requirement, which is open to interpretation. Here then is a better way for Butch to proceed:

• Mrs. Beeble: You have been absent from class 11 times this month. You fail. Goodbye.
• Butch: What? That's impossible!   The class only meets twice a week.
• Mrs. Beeble: True, but you have missed it 11 times nevertheless.
• Butch: So you are saying that I was absent on days that the class didn't meet.
• Mrs. Beeble: That's right.
• Butch: Well, then you have committed a logical error. "X was absent from event Y," logically implies that event Y occurred. So you are saying that on the days that I was absent, the class both met and did not meet. That is nonsense.
• Mrs. Beeble: Sit down and shut up you little bastard.

Actually, the truth is that proper logical analysis does not compel agreement anymore than Butch's first approach. Many people find it tiresome and offensive, but logic doesn't concern itself with things like that.