Chapter 1: The Method of Economics 9

•LUDWIG VON MISES FAVORED MINIMUM WAGE RATES

•THEREFORE, MISES FAVORED A GOVERNMENT POLICY THAT LEADS TO UNEMPLOYMENT

Here, the conclusion is false: how false you will discover later in the book. But the argument is valid. Then, our rule tells us that at least one of the premises is false. In this case, it is the second premise. Mises, who is one of this book’s heroes, opposed minimum wage laws. But the first premise is true; and by the end of the book, you will be able to explain why. Thus, our rule does not say that in a valid argument with a false conclusion, both premises are false. It says that at least one is false. And if in fact just one premise is false, the rule doesn’t tell us which one it is.

1.Show, using diagrams, that the argument about Mises is valid.

2.	Give examples of a valid argument with a false conclusion	?

that has (a) one false premise and one true premise; (b) two false premises.

3.Suppose you have an invalid argument with a false conclusion. What can you tell about the truth of the premises?

DEDUCTION EXTENDED

The type of argument that we have been discussing so far is called a categorical syllogism. It has two premises, both statements of (alleged) fact, and a conclusion. But not all valid arguments take this form: it was discussed here because you can easily grasp what validity means if you take examples of this kind. But premises can also be

10 An Introduction to Economic Reasoning

hypothetical. For example, the statement: “If wishes were dollars, Social Security would be financially sound” does not claim either that wishes are dollars or that Social Security is financially sound. All that the statement claims is that if wishes were dollars, then Social Security would be sound. A syllogism can have either one or two hypothetical premises.

1.Give examples of syllogisms with (a) one and (b) two hypothetical premises.

?2. Can you show how to convert a hypothetical premise into a categorical one? That is, show how an “if-then” statement can be changed into another statement about a matter of fact. If you can answer this, you will have no difficulty getting an “A” in the course. In fact, you are probably in the wrong class.

DEDUCTION FURTHER EXTENDED

We have just a little bit more technical machinery to get through. Unfortunately, this is the most difficult section of the chapter. Fortunately, it isn’t very long. Some premises are stronger than mere factual claims. Let’s return to a variant of an old friend: “Some communists are two-headed monsters.” This (false) premise does not say that some communists have to be two-headed monsters, i.e., that they couldn’t possibly be anything else. It just says that they are in fact two-headed monsters.

Contrast this statement with the following: “No one can be his own father.” This does not just say that no one is in fact his own father: it makes the stronger claim that no one possibly could be his own father. No matter how we change features of the actual world,

Chapter 1: The Method of Economics 11

this statement is always true. It’s part of the nature of being a father that you can’t be your own father.

Necessarily true propositions (but not the one about fathers) play an important part in economics, and you would be well-advised to reread the preceding paragraph carefully. (Instructors should police students at this point to make sure students understand what a necessary proposition is. If necessary, mild electric shocks may be administered.)

Now for the hard part: In a categorical syllogism, one that does not contain necessarily true premises, the conclusion need not itself be necessarily true, even though it follows of necessity from the premises. Got that? Let’s have another look. Consider this case:

•SOME ECONOMISTS ARE STUPID

•NO AUSTRIAN ECONOMISTS ARE STUPID

•THEREFORE, SOME ECONOMISTS ARE NOT AUSTRIAN

The initial premise is (alas!) true. The truth of the second premise is a matter for discussion. But neither premise is necessary: it could have turned out, however unlikely, that all economists are intelligent. And though difficult to conceive of, it might have been the case that there are stupid Austrian economists. And the conclusion is also not necessarily true. All economists might have turned out to be Austrian economists. (Austrian economics is the foundation for this book. See page 19 for an explanation.)

Nevertheless, the conclusion necessarily follows from the premises. If the premises are true, then it must be the case that the conclusion is true. Given our two premises, it must be the case that some economists are not Austrians.

Then why is it wrong to say that the conclusion is necessary? If it must be the case that some economists are not Austrians, isn’t this just what it means to say that, necessarily, some economists are not

12 An Introduction to Economic Reasoning

Austrians? Yes; but, remember we are not asserting that it must be the case that some economists are not Austrians. We are saying that if the premises are true, then some economists are not Austrians.

One more complication, and then we are out of the woods (at least for now). A syllogism with two premises that are not necessarily true can turn out to have a conclusion that is necessarily true. All that we’ve been trying to show is that it does not have to turn out this way. Here is an example of a valid syllogism with two non-nec- essary premises. (The technical term for “non-necessary” is “contingent.”)

•SOME FATHERS ARE PROFESSIONAL FOOTBALL PLAYERS

•ALL PROFESSIONAL FOOTBALL PLAYERS ARE MALE

•SOME FATHERS ARE MALE

Although the conclusion follows from two contingent premises, it itself is necessarily true. (Why? Because it follows directly from the necessarily true “All fathers are male.” There is a complication here [having to do with “existential import”] that we can ignore. Some logicians don’t think “All fathers are male” entails “some fathers are male.” Why not? In their view, “all fathers are male” means “if x is a father, x is male.” This does not entail that there are any fathers. But “some fathers . . .”does entail that there are fathers. See, I told you we should ignore this.)

We’re now over the hard part. It was important to look at necessary propositions, as they play a key role in economics.

And there is one further extension we need to look at. Not all valid deductive arguments are syllogistic. Putting that into English, a valid argument doesn’t have to have two premises. Suppose we start with this premise: “All socialists are subversives.” From this, we may at once deduce: “All fatheaded socialists are fatheaded subversives.” No intermediate premises are needed.