An Overview of Second-Order Logical Problems

In rational discourse carried out by irrational beings such as humans, mistakes are a natural occurrence. Collectively, these are known as logical fallacies. A fallacy is a logical structure that may produce false conclusions from true premises. There are a great many fallacious logical structures that one may encounter. Learning to recognize as many of them as possible will both increase one's debating skills and keep one from being led astray by demagogues and charlatans. But when opposition to these fallacies goes too far, further fallacies and sub-optimal behaviors can result. Let us examine the most common examples of this behavior in an effort to counter such second-order problems.

Affirming the Consequent/Denying the Antecedent

Affirming the consequent takes the form

1. If A, then B.
2. B, therefore A.

Denying the antecedent takes the form

1. If A, then B.
2. Not A, therefore not B.

These are rather common errors that are important to avoid. However, there is a non-fallacious logical form that looks similar:

1. If A, then B.
2. Not B, therefore not A.

This is called a contrapositive, and proving the contrapositive is a valid alternative to proving the original statement because they have identical truth tables. Taking the above two fallacies too far can lead one to overlook or even oppose this type of valid argument.

Argumentum ad Antiquitatem (Appeal to antiquity, appeal to common practice, appeal to tradition)

An appeal to tradition can take the form

1. X has always been done by method P, not by method Q.
2. Therefore, method P is superior to method Q.

or the form

1. Idea A was discovered earlier than idea B.
2. Therefore, A is superior to B.

The obvious manner in which opposition to this fallacy can go too far is the commission of the argumentum ad novitatem (appeal to novelty, chronological snobbery) fallacy, which would conclude that method Q is superior to method P and idea B is superior to idea A. A more subtle point is that although tradition is not the end of wisdom, it is the beginning. People keep traditions because they work well enough to avoid abandonment. Over time, this forms a collection of best practices which provide a useful starting point. Ignoring this received wisdom is generally unwise.

Argumentum ad Baculum (Appeal to the cudgel, appeal to force, appeal to the stick, appeal to threat)

An appeal to force has the general form

1. If X accepts P as true, then Q.
2. X acts to prevent Q and succeeds, so Q is false.
3. Therefore, P is false.

The fallacy is in resorting to force rather than using reason to support a position. But there is a valid construct with a similar form:

1. If X accepts P as true, then Q.
2. X does not want Q and will act to prevent it.
3. Therefore, X will reject P.

Note the difference between X subjectively denying P and the objective claim that P is false. It is important to remember the difference between those who believe because they freely choose to and those who feign belief because they must.

Argumentum ad Consequentiam (Appeal to consequences)

An appeal to consequences takes the form

1. A has desirable/undesirable consequences.
2. Therefore, A is true/false.

This is an emotional appeal rather than a rational argument, as the truth value of A is objective while the desirability of its consequences is subjective. But the opposite behavior of rejecting all consideration of consequences is detrimental to long-term decision making and some theories of abstract ethics. It is important to assess the likely consequences of an action while remembering that this is independent of its truth value.

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