Chapter 1: The Method of Economics 5

VALIDITY CONTINUED

We now know that if you start with true premises, you will arrive at a true conclusion. A valid argument transmits truth from the premises to the conclusion. What happens if one of the premises is false? Does this make the conclusion false? Not necessarily. All our rule says is that true premises transmit truth: it says nothing about how premises and conclusion are related with a false premise.

In the example already used, the major premise is false. It’s not the case that all communists are two-headed monsters. The conclusion is also false: Marx was not a two-headed monster. But this pattern by no means always holds true. Let’s look at another example:

•ALL SCORPIONS ARE DEMOCRATS

•HILLARY CLINTON IS A SCORPION

•THEREFORE, HILLARY CLINTON IS A DEMOCRAT

Both the premises are false. (Perhaps the falsity of the second premise is arguable!) But the conclusion is true: Hillary Clinton is a Democrat! How can this be?

By now, you should know the answer. The conclusion is true, but the premises don’t make it true. These premises do not transmit truth, since they are false. Just to make things absolutely clear, all the premises must be true for truth to be transmitted. One false premise prevents the rule from applying.

Notice that the rule requires both true premises and a valid argument. This example does not meet our requirement:

•SOME TEXANS ARE TALL

•SOME TALL PEOPLE ARE DEMOCRATS

•SOME TEXANS ARE DEMOCRATS

6 An Introduction to Economic Reasoning

This argument is invalid: the conclusion does not follow from the premises. Can you see why? Let’s resort to diagrams again:

The first premise:

TALL PEOPLE	TEXANS

The first premise says that the classes of tall people and Texans intersect, or have some members in common. It does not say that the class of Texans is included in the class of tall people. (Can you give the premise for which this is the correct diagram?)

TALL PEOPLE

TEXANS

Similarly, the second premise looks like this:

TALL PEOPLE
		DEMOCRATS

It states that these two classes, tall people and Democrats, intersect.

You can now see why the conclusion does not follow. The conclusion, some Texans are Democrats, looks like this:

Chapter 1: The Method of Economics 7

DEMOCRATS	TEXANS

Our premises allow this to be true, but they don’t require it. This is also consistent with our premises:

DEMOCRATS		TEXANS

Both premises will be true, and the conclusion turns out to be false. Can you see how this is possible? Once again, use of a diagram will help. Suppose this was the situation:

		TALL PEOPLE
DEMOCRATS				TEXANS

Here, both of our premises are represented. The diagram shows that some Texans are tall, and also that some tall people are Democrats. But, in this state of affairs, no Texans are Democrats. The tall people who are Texans are different tall people from those who are Democrats.

In fact, of course, both of the premises are true; and so, is the conclusion. Lyndon Baines Johnson, whom most of you won’t recall, was both. (If you do remember LBJ, what are you doing still in school?) Even though premises and conclusions are both true, the premises do not transmit their truth to the conclusion, since the argument is invalid.

8 An Introduction to Economic Reasoning

Can true premises in an invalid argument lead to a false conclusion? Certainly.

•ALL AUSTRIAN ECONOMISTS SUPPORT THE SUBJECTIVE THEORY OF VALUE

•NO AUSTRIAN ECONOMIST LIVED BEFORE THE NINETEENTH CENTURY

•THEREFORE, NO SUPPORTER OF THE SUBJECTIVE THEORY OF VALUE LIVED BEFORE THE NINETEENTH CENTURY

As we shall see later in this book, both of the premises are true, but the conclusion is false.

1.Diagram the argument just given. Show why the conclusion does not follow.

?2. Given examples of (a) valid arguments with true premises;

(b)valid arguments with at least one false premise; (c) invalid arguments with at least one false premise; (d) invalid arguments with true premises. Must any of these types always lead to a false conclusion?

STILL MORE ON VALIDITY

Fortunately, we have only one more rule to cover about transmission of truth. In a valid argument, if the conclusion is false, then at least one of the premises must be false. A valid argument transmits the falsity of the conclusion to at least one premise. Once again, an example:

• MINIMUM WAGE RATES LEAD TO UNEMPLOYMENT