David Gordon - Economic Reasoning Chapter 1 - The Method of Economics

Dr. David Gordon begins his book with the following statement;

"In economics, we operate with deductive logic."

In this first chapter of his book Dr. Gordon explains why deductive logic is a powerful tool, and some of its basic rules.

What makes deductive logic so powerful? Starting from premises one knows to be true, the rules of deductive logic deliver conclusions that must be true.

Dr. Gordon begins with a simple example to illustrate; if all of a class A are part of a class B, and all of a class B are part of a class C, then all of A are part of C.

(It is after this example the reader comes upon the first of Dr. Gordon's 'thought starter's -I'll call them- that are found throughout his book. I appreciate his adding of these questions. They forced me to think more about what I had read. I list these questions at the end of each Chapter and attempt to answer them if Dr. Gordon has not answered them already.)

In the next section he continues the discussion with Aristotle' Laws of Reality (sometimes misnamed the 'Laws of Thought);

Aristotle's Laws of Reality:
1) A=A: The Law of Identity
2) Not (A and not A): The Law of Non-Contradiction
3) A or not A: The Law of Excluded Middle

The first rule, restated, says a thing is what it is. For example; a ball is ball, not something else.

The second rule, restated, says that a thing cannot be a thing and not a thing at the same time. For example, a thing cannot be a ball and not a ball.

The third rule, a bit trickier, says that a thing is either something or not something. For example, a thing is either red or non-red. It cannot be neither, or both.

The next section is on validity. Dr. Gordon now reviews the implications of an argument based on false premises. An argument based on true premises that follows the rules of logic yields a true conclusion every time. What about an argument beginning with false premises? Does it yield a false conclusion if it too, follows the rules? No. It may, but it also may not. Examples are given showing this to be the case.

An argument yields a true conclusion only if its premises are true and it is valid. It is valid if it follows the rules of logic. An argument resting on true premises that does not follow the rules of logic may also yield a false conclusion.

The next section, Deduction Extended, adds the hypothetical syllogism as another argument type. Up to this point Gordon discusses arguments of the type known as the categorical syllogism which has two factual premises and a conclusion. A hypothetical syllogism consists of premises that are not factual and yield non factual conclusions. An argument if X then Y does not say X or Y is a fact, only that if X is a fact then Y is a fact. Hypothetical syllogisms can have one or two premises that yield a conclusion.

Deduction Further Extended discusses the nature of certain premises. All premises are meant as facts, but their factual ‘nature’ fall under two different categories. In the first category, a premise is a fact, but does not necessarily have to be a fact. The statement ‘A communist is a two-headed monster’ does not say a communist must be a two headed monster; a communist could be something else.

Under the other category, a premise is necessarily a fact. That is, it cannot be anything else but what it is. The statement ‘No one can be their own father’ is a necessarily true statement. It must be the fact that no one can be their own father. Propositions of this nature are very important in economics.

Furthermore a categorical syllogism containing premises that are not necessarily true can yield a conclusion that it also not necessarily true even though the conclusion must necessarily follow from the premises. (If the premises are true, then the conclusion is true. This is not the same as saying that the conclusion must be true).

On the other hand, it is possible for premises that are not necessarily true to yield conclusions that are necessarily true. For example, some fathers are football players, all football players are males, from which it follows some fathers are males; the conclusion is necessarily true, though the premises are not.

(Note that some logicians argue the following; all X are Y means if X, then Y, which does not mean X exists. At the same time, they maintain that some X is Y means that there is at least one X that is Y, which implies the existence of X. This was discussed in Logic and Scientific Method by Cohen).

A final extension of deduction is that not all deductive arguments are syllogistic. For example, one can deduce all fathead socialists are fatheaded subversives from all socialists are fatheads alone. This inference is especially important in Austrian Economic Theory as several non syllogistic inferences are drawn from the concept of action, which is central to Austrian Theory.

In the final section of economics vs. mathematics, Dr Gordon explains economics, like math, is a deductive science. Yet, he continues, it is unlike math in that one cannot just ‘fill in the blanks’ and operate mechanically. For example, the immediate inference all Russian socialists are Russian subversives does not necessarily follow from all socialists are subversives. The Russian socialists could be Bulgarian subversives; wanting to overthrow the Bulgarian government, but not their own. Immediate inference, then, requires judgment as opposed to simple mechanical operations like 2x=10, x=? in mathematics.


Chapter 1 Questions;

p.4

1. Can something be both red and not red?

No. A thing is either red or it is not. It cannot be both at the same time. If a thing is red, then it is not not-red. If a thing is not-red, then it cannot be red.

2. Some philosophers have denied that these laws are always true. Marxists say, e.g., that everything is constantly changing; therefore, the Law of Identity isn’t true. Why is this objection based on a misunderstanding of the Law of Identity?

Saying that everything is constantly changing and that therefore the Law of Identity (a thing is what it is) is not true is a misunderstanding because the Law does not say anything about change. The Law says a thing is what is, not that a thing cannot be something else at some future point in time. For example, a caterpillar is a caterpillar, and not something else, until it becomes a chrysalis.

Also, what about the Law of Identity as it applies to the word ‘change?’ Change is what it is, it cannot be something else.

Questions p. 8

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



2. Give examples of (a) valid arguments w/ true premises (b) valid arguments w/ 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?

a. All dogs are mammals
All mammals are warm-blooded
All dogs are warm blooded

b. All dogs are domesticated mammals
All domesticated mammals are warm-blooded
All dogs are warm blooded

c. Some dogs are trained reptiles
Some trained reptiles are 4-legged
Some dogs are 4-legged

d. Some dogs are trained mammals
Some trained mammals are large
Some dogs are large

As one can see, none of the above arguments leads to a false conclusion, so none of the argument types need lead to a false conclusion. (Valid arguments with true premises always yield a true conclusion. False conclusions derived from valid arguments must have at least one false premise).

Pg 9.

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

a. All dogs are mammals.
All mammals are cats.
All dogs are cats.

b. All dogs are cats
All cats are fish
All dogs are fish

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

You cannot tell anything from an invalid argument. The premises may be true or false. A false conclusion implies a false premise only if the argument is valid.

p. 10

1. Give examples of syllogisms with (a) one and (b) two hypothetical syllogisms
a. If money grew on trees then we would encourage CO2 emissions

b. If money grew on trees then we would encourage CO2 emissions
If we would encourage CO2 emissions then Al Gore would have to find a new job

2. Can you convert a hypothetical premise into a categorical one?

(With help from Cohen)
Hypothetical: If A then B
Categorical version of Hypothetical: All A that exist are B

p. 13

1. How can you find out if a statement is necessarily true?

A statement is necessarily true if by denying it you contradict the nature of the meaning of the subject.

2. If a statement is necessarily true, do you need to test it to find out whether it is true?

You do not need to test a necessarily true statement to determine its truth. You can tell if it’s true by deduction.

p. 14

1. How do we know the rules of mathematics are correct?

I answer first by noting that we cannot expect the rules of mathematics to be correct based on experimentation. We expect 2+2=4 all the time, not only under certain conditions, or until some experiment, test or observation proves that 2+2 could equal 5. The rules of mathematics are logically deduced based on propositions that we understand to be self evident.

2. Would it be a good idea to use symbolic logic in economics, if economics relies on immediate inferences?

It is not a good idea to use symbolic logic in economics because of its reliance on immediate inferences. Immediate inference requires evaluating the terms involved in order to determine if the inference is valid.

3. Is it always best to begin by “defining your terms”? Why or why not?

I argue it is always best to begin by defining your terms. The terms you use must be understood clearly in order to ensure your premises, conclusions and arguments are sound.

Note that certain terms must be assumed to be commonly understood; otherwise one would have to define the terms used to define your terms, and so on, ad infinitum.

4. Deduction only tells us what we already “know.” How might a supporter of the deductive approach reply?

Deduction does not tell us what we already know. The application of deduction uncovers the implication and relationship between certain propositions and conclusions. It tells us what must follow if we assume certain things to be true, or false. Though these relationships have always existed, we only come to know them through the application of deductive logic.