Logic 101


In response to requests from my logically-sound readers, you can now find links to Logic 102 (which covers the Argumentum ad Baculum, Argumentum ad Hominem, Argumentum ad Ignorantiam, and Argumentum ad Misericordium) and Logic 103 (which covers the rest of the common fallacies) here.

Actual Article Resumes Now:

In the early days of Newsvine (as in, waaay back at the beginning of the year) there was a fair amount of discussion here and there about the nature of the educational system in this country. One of the conclusions reached therein was that our country would be much healthier if logic were taught to all students. More recently, there was an upsurge of folks calling each other out on the use of logical fallacies, most particularly the use of “strawman arguments”. Here in the recent past, I have seen a repeated use of the argument that “if you do not support the extension of my intolerant beliefs into law, you are intolerant.” All of this put together has led me to the conclusion that we may be well overdue for a logic lesson.

Enter my Mom. Both my parents went to school for philosophy. Quite honestly, I tried like hell not to listen to any of it as I was growing up. While most kids were playing Monopoly with their folks, I got to play fun games like this:

“Their are three errors in this sentance.”

My mission was to find them. Good, fun, family times. But I digress…

My Dad died when I was twelve, but my Mom is still alive and kicking. She has never given up on her quest to teach me logic, and now that I have offspring, she is working on him, too. So she seemed the natural place to start when looking to get a grasp of the basics of logic.

This is what my Mom has to say:

When we talk, we usually speak in what we call sentences. For instance,

My hair is brown.

This kind of sentence can be used to give information to someone else.
First, think about that sentence.

Now, if I say that sentence, I am telling the truth: My hair IS brown. But if someone else says the same sentence, he may be lying – because their hair MAY NOT brown, it may be blond, red, black, or blue. So, when a sentence conveys information about the world, what the sentence says can be either TRUE or FALSE.

What’s more, the information is either true or false quite apart from the words you are using to say it. For example, I can say to you

It is raining.

Or, if I were a French lady, I might say,

Il pleut.

Or, if I were a German lady, I would say,

Es regnet.

It doesn’t really matter what language I use, I am still saying the same thing: that it is raining. And, whatever language I say this in, it could still be true or false about the world outside. Is it raining outside? Then, is the sentence true or false?

If we want to talk about the information a sentence is trying to convey, rather than the words or language in which the information is stated, we usually call it not a sentence, but a PROPOSITION. A proposition is just the idea that any particular set of words is trying to pass on to us.

People talk a lot. Often, when they are talking, one person is trying to convince the other to believe what he or she thinks is true. When one person wants to convince another person that something he thinks is really the TRUTH about the world, he will use what we refer to as ARGUMENTS to try to convince the other person he is right. This is what we call a “technical term” and doesn’t usually involve the two people getting angry with each other and raising their voices. An argument, in this technical sense, is a set of propositions that one person offers another because he thinks they are sufficient to prove the truth of what he is arguing for. The thing he is arguing for, we call the CONCLUSION of his argument, and the propositions that are supposed to prove his conclusion, we call the PREMISES.

Let’s look at some examples of arguments:

All people will eventually die. [Premise]

I am a person. [Premise]

Therefore, I will eventually die.[Conclusion]

All mammals have lungs. [Premise]

A cat is a mammal. [Premise]

Therefore, a cat has lungs. [Conclusion]

These are what are called DEDUCTIVE arguments. In a deductive argument, usually a particular conclusion is derived from premises, the first of which is a general or universal proposition.

There is another kind of argument form, called an INDUCTIVE argument. For example:

All cows are mammals and have lungs. [Premise]

All horses are mammals and have lungs. [Premise]

All cats are mammals and have lungs. [Premise]

All whales are mammals and have lungs. [Premise]

All people are mammals and have lungs. [Premise]

Therefore, PROBABLY all mammals have lungs. [Conclusion]

George Washington was elected President when he was over fifty years old. [Premise]

Chester A. Arthur was elected President when he was over fifty years old. [Premise]

Calvin Coolidge was elected President when he was over fifty years old. [Premise]

Abraham Lincoln was elected President when he was over fifty years old. [Premise]

Ronald Reagan was elected President when he was over fifty years old. [Premise]

Jimmy Carter was elected President when he was over fifty years old. [Premise]

George H.W. Bush was elected President when he was over fifty years old. [Premise]

Therefore, PROBABLY all Presidents are over fifty years old. [Conclusion]

Oops! There’s something wrong with this argument, isn’t there? What about Kennedy and Clinton? Were they over fifty when they were elected? But they are Presidents, so this argument is NOT VALID. That is, is doesn’t work. In an inductive argument, we are trying to reach a probable universal conclusion based on a series of either universal or particular propositions for our premises.

As we have seen, it only takes one example of a proposition that is clearly NOT TRUE, to prove that an INDUCTIVE argument is invalid.

By contrast, if a DEDUCTIVE argument is valid, its conclusions follows with the same necessity from its premises no matter what else may be the case in the world.

This is a little confusing, isn’t it? One clear proposition that is true about the world but not in line with the premises leading to its conclusion can overthrow an inductive argument and prove that it is not valid. But a deductive argument remains VALID, even if its premises and its conclusion are false. Because a valid deductive argument simply says that if the premises are true, than the conclusion HAS to be true. It is left to us to figure out whether or not the premises are true. What we can be sure of is that IF the premises are true, then the conclusion is true, too.

Let’s look at another valid deductive argument:

All men are seven feet tall.

Martin Short is a man. Therefore, Martin Short is seven feet tall.

This is a perfectly VALID argument. The problem is that the PREMISE “All men are seven feet tall,” is not TRUE. Therefore, it is not surprising for us to learn that the conclusion is not true, either.

O.K., me again.

So what we have here are a few very simple ideas. There’s a PROPOSITION, which is the idea you are trying to get across. There’s an ARGUMENT, which is a set of propositions you offer up as sufficient proof of your CONCLUSION, and there are the PREMISES, which is the stuff you you put in there (propositions) you think prove your argument.

Then we have the matter of DEDUCTIVE and INDUCTIVE arguments. In deductive arguments, if the premises are true, the conclusion HAS to be true; we go from an overreaching concept to a specific instance. But in inductive arguments, we try to reach a probable conclusion from a basis of generally accepted premises; we go from the specific and try to apply it to the general. So if it turns out that one of our examples in an inductive argument isn’t true, that throws the whole thing out. Got that?

What we have laid out here is the basis for all logical discussion. Tune in next episode, when we unmask the treacherous fallacies and their nefarious schemes for world domination!

2 thoughts on “Logic 101

  1. celestina
    Just thought I’d pop in and puruse around, Hope you don’t mind, I’ll be sure to clean up before I go. Thanks for being you love.

  2. Hey, you! You are welcome to come in here any time. I keep meaning to put more work into it, get up some content not already on Newsvine…but time is hard to wrestle with. It’s slippery. Anyway…I am very glad to see you here, my door is always open.

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