knowledge by deductive reasoning, part 2

These basic syllogism are things we all use every day of our lives. Think of the last time you lost power in your house. How did you know when the power came back on? You probably knew it because maybe your lights came back on or something. When you make that inference, you’re using a syllogism.

1. If the power is not on, the light will not come on.
2. The light is on.
3. Therefore, the power is on.

It is actually almost impossible to think without using these syllogisms. The reason we are not consciously aware that we are doing it is because the first premise is hardly ever stated. It is assumed. Imagine having the following conversation:

Jim: Is the power on?
Bob: Yeah.
Jim: How do you know?
Bob: Because the lights are on.

Do you see how Bob is working with the assumption that If the lights are on, then the power is on? He doesn’t state it explicitly. It’s assumed in his reasoning. But without that assumption, Bob would not be able to conclude that the power was on just because the light was on. Using syllogisms is just a way of making explicit what is already implicit, and it’s useful in analyzing another person’s reasoning.


There is some reasoning we can immediately recognize as fallacious. Steve gave the classic example on our first class session. Suppose I said that Socrates is a man, and the reason I said he was a man was because he’s mortal. Can I really say that Socrates is mortal merely because he is a man? Of course not. The fact that he’s mortal doesn’t necessarily mean he’s a man. He might be a bird. Birds are also mortal. When a person makes an argument where the conclusion does not follow from the premises, that’s an invalid argument. In order for the argument to be valid, you would have to assume the hidden premise to be, “All mortals are humans,” or “If Socrates is mortal, then Socrates is a man.” In that case, the argument would not be sound because the first premise would be false. Those are the two ways a deductive argument can go wrong. If the conclusion does not follow from the premises, the argument is not valid. If one of the premises is false, the argument is not sound.

But in the classic argument, the first premise is that All men are mortal.

1. All men are mortal.
2. Socrates is mortal.
3. Therefore, Socrates is a man.

You can see that the conclusion does not follow. Socrates may in fact be a man, but we cannot know that simply by knowing that he is mortal. However, we can know that if Socrates is a man, then he is mortal, provided the first premise is true.

These syllogisms are one aspect of logic, and they are necessary to think or reason intelligibly. The other aspect is the three basic laws of logic, the law of identity, the law of non-contradiction, and the law of excluded middle. Steve mentions a fourth, which is basically the same thing as the law of identity stated in the negative.

[The best "intro to logic" I've seen is in chapter two of Philosophical Foundations for a Christian Worldview by J.P Moreland and William Lane Craig. It goes into more depth than mine does, and it's far more clearly written.]

Next: The law of identity