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.

Argumentum ad Ignorantium (Argument from ignorance)

An argument from ignorance assumes that a claim is true/false because it has not been or cannot be proven false/true. The problem with opposing this fallacy too strongly is that it can lead one to reject the concept of performative contradiction. A performative contradiction occurs when the content of an argument is opposed to the presuppositions of advancing the argument. For example, the statement “I cannot communicate with you” is a performative contradiction because communicating it implies the negation of the statement. Performative contradictions cannot be rationally advanced in argument, and they render some statements unprovable. By the law of excluded middle, such statements are false because they cannot be proven true, and there is no other truth value besides true or false. This is a powerful concept that allows one to detect falsehoods at the beginning of many ideologies. The idea of argument from ignorance should not take this tool out of one’s logical toolbox.

Argumentum ad Populum (Appeal to the majority, appeal to the people, appeal to widespread belief, bandwagon fallacy)

An appeal to the masses takes the form

  1. Many people believe that A is true or good.
  2. Therefore, A.

It is important to be skeptical of popular opinion, as the truth value of a proposition is an objective matter that does not depend on subjective opinion. Therefore, the following is an equally fallacious logical structure that must also be avoided:

  1. Many people believe that A is true or good.
  2. Therefore, not A.

Argumentum ad Temperantiam (Golden Mean Fallacy)

The golden mean fallacy assumes that the compromise between two extremes is always correct. However, opposing this fallacy can lead one to believe that such a compromise is never correct. For many controversial issues, there are sound arguments on multiple sides. It is possible that arguments from different sides could be combined into a true compromise that produces a valid and sound argument. These new arguments must be evaluated on a case-by-case basis, not automatically accepted or rejected. Otherwise, preventable conflicts will occur and continue.

Argumentum ad Verecundiam (Appeal to authority, appeal to accomplishment)

An appeal to authority takes the form

  1. An authority figure or subject matter expert advocates A.
  2. Therefore, A.

The truth value of A is independent of the authority (or lack thereof) of any person advocating it. That being said, most people who are well-accomplished and/or are in positions of authority are there not by chance, but because they have repeatedly demonstrated good judgment in evaluating propositions. In many cases, one simply lacks the time to become a master of all subjects and must therefore rely upon the wisdom of experts. Sometimes they are wrong, but they are less likely to be wrong than the layperson.

Association Fallacy (Guilt by association, honor by association)

An association fallacy takes the form

  1. A is in group B.
  2. A is also in group C.
  3. Therefore, all Bs are Cs.

This faulty reasoning is used to judge an individual or group by associating them with another group, especially when that group is perceived as negative. This behavior should be avoided, but that should not lead one to ignore the fact that choosing one’s associates carefully is important, as they play an important part in shaping one’s life.

Circulus in Probando (begging the question, circular reasoning, circulus in demonstrando, petitio principii)

This fallacy occurs when the conclusion of an argument is also a starting premise. The simplest example takes the form

  1. A, therefore B.
  2. B, therefore A.

Longer examples may include any number of steps, as long as the last step leads back to the first step. This type of structure cannot prove anything because it presents no evidence to support the conclusion; it only restates the conclusion after a series of steps. That said, opposing this fallacy too strongly can lead one to ignore the existence of feedback loops. There exist causes and effects which are mutually reinforcing, leading to results that spiral out of control. These tend to be destructive in the long-term, so it is best to identify and address such structures instead of ignoring them.

Courtier’s Reply

A courtier’s reply is the inverse of argumentum ad verecundiam, in that it takes the form

  1. The person advocating A lacks sufficient credentials, knowledge, or training to comment on the subject matter.
  2. Therefore, not A.

Again, the truth value of A is independent of the authority (or lack thereof) of any person advocating it. However, this should not keep one from pointing out instances in which a person who is clearly ignorant on a topic is spouting nonsense. One must simply remember not to stop with a simple accusation when doing so, and refute the nonsense as well.

Definitional Retreat/Equivocation

A definitional retreat involves changing the meaning of a word to deal with an objection, while an equivocation uses a particular word or phrase in multiple senses to mislead. Though definitional retreat can be a deceitful tactic, it can also be a method of clarifying what one means when the original use of a word was ambiguous. Some problems really can be defined out of existence, and this is a good thing to do whenever it is legitimate. Equivocation is frequently confused with definitional retreat, especially when it seems to be done in anticipation of criticism.

Ecological Fallacy

This fallacy occurs when individuals are judged solely based on their group identity and statistical averages concerning it. This is the erroneous basis for much bigotry and hate, but one must be careful not to reject demographic data entirely. People are not exactly the same at an individual or collective level, but overzealous opposition to the ecological fallacy can lead one to accept such egalitarian nonsense.

Ergo Decedo (Then go off, therefore leave, traitorous critic fallacy)

An ergo decedo occurs when a critic is dismissed as having an affiliation with an out-group and thus not a relevant commentator on the issue. This occurs most frequently in political debates. While responding to an argument by telling someone to go live in another country is not a valid rebuttal, there are cases in which exercising the right of exit is the best resolution of a dispute. Opposing ergo decedo too strongly can lead one to overlook this.

Etymological Fallacy/Genetic Fallacy/Intentional Fallacy

These three related fallacies all claim that original or historical meaning takes precedence over current meaning. The etymological fallacy applies such a claim to the meaning of a word or phrase, the intentional fallacy applies such a claim to the meaning of an expression or work, and the genetic fallacy applies such a claim more generally, but all three ignore the importance of continual reinterpretation of history and the socially constructed nature of language. However, one should not take this understanding so far as to engage in eisegesis, for this leads to a litany of errors.

False Dilemma (black-or-white fallacy, fallacy of bifurcation, false dichotomy)

A false dilemma presents a choice between two options when there are really more than two. More generally, there is a false n-lemma fallacy when the number of choices actually exceeds n. But true n-lemmas do exist, both in an absolute sense (a plant can live or die; there is no other alternative) and a relative sense (there might be ten candidates on an election ballot, but perhaps only three have any significant chance of winning). One must learn to recognize true choices from false ones and act accordingly.

Furtive Fallacy

This fallacy asserts without proof that hidden misconduct, malfeasance, and wrongdoing of leaders is to blame for negative outcomes. While it is wrong to insist on hidden deeds and motivations, it is not wrong to consider such possibilities. The furtive fallacy overestimates the role of secret conspiracies, covert agencies, and subversive activities, but dismissing all such concerns as furtive fallacies risking underestimating their role.

Gambler’s Fallacy

The gambler’s fallacy is the belief that independent random events can alter the probability of other random events. For instance, one may believe that choosing a particular number on a roulette wheel is wise because the ball has not landed there for a long time, and is thus “due” to land there. But taking this reasoning too far can lead one to ignore cases in which games of chance and other supposedly random events have been rigged. If an event is not truly random and one reasons as though it is, then one will be swindled by unfair games.

Ignoratio Elenchi (irrelevant conclusion, missing the point)

This is not actually a fallacy in an objective sense, in that it may make a valid argument. The problem is only that it addresses an issue other than the one in question. Of course, who is missing the point or making an irrelevant conclusion may itself be a matter of debate, as a person engaging in this behavior likely believes that the other side is guilty of this fallacy. It is therefore best to tread carefully when considering whether to accuse someone of ignoratio elenchi.

No True Scotsman

A no true Scotsman fallacy attempts to make a generalization true by altering it to exclude a counterexample. The form will look something like this:

  1. Person A: “No Scotsman puts sugar on his porridge.”
  2. Person B: “But my uncle Angus is a Scotsman and he puts sugar on his porridge.”
  3. Person A: “Ah yes, but no true Scotsman puts sugar on his porridge.”[1]

This reasoning goes too far when it is used to claim that there are no defining characteristics of a Scotsman, and thus it means nothing to be a Scotsman. It is important to remember that words must have meanings in order for rational discourse to occur, and that litmus tests are necessary in order to define categories.

Psychogenetic Fallacy (Appeal to motive, Bulverism)

Psychogenetic fallacies are a type of ad hominem that take the form

  1. N is advocated by Person A.
  2. Person A has some bias or psychological issue.
  3. Therefore, not N.

It is fallacious to assume that a proposition is false because the person advocating it has some inherent bias or mental issue, as the truth value of a proposition is objective while personal issues are subjective. However, it is important to attempt to understand why people think and believe as they do, and taking opposition to this fallacy outside of the philosophical realm can interfere with scientific research.

Quantitative Fallacy (McNamara fallacy)

The quantitative fallacy discounts all considerations other than quantitative observations when taking decisions. This faulty logic is responsible for strong, anti-rational empiricism among scientists as well as political autism among economists. However, one must be careful not to go in the opposite direction and reject quantitative observations. Sometimes it is necessary to be non-empirical, but one should never be anti-empirical.

Slippery Slope

A slippery slope asserts that taking one action will lead to a series of events that culminates in some undesirable result. Though this is commonly regarded as a fallacy and is in many cases, true slippery slopes exist and vociferously opposing any such reasoning can blind one to real problems that take a long time and many steps to fully develop.

Thought-Terminating Cliché

A thought-terminating cliché is a phrase that is used to end a debate prematurely without addressing all important points. While this can be a fallacy, it is also employed to avoid dealing with a point that has already been refuted a thousand times, to end an engagement when one no longer feels like participating, or simply because the cliché is a true proposition that applies to the subject being discussed. It is important to distinguish between proper and improper uses so that one does not incorrectly accuse others of using logical fallacies.

Tu Quoque (Appeal to hypocrisy, you too)

This fallacy contends that a position is false or otherwise worth dismissing because it is advocated by a hypocrite. While true statements can be advocated by those who practice their opposite, and dismissing universal arguments for this reason is fallacious, it is not fallacious to point out that the optics of practicing the opposite of what one preaches are not good. Furthermore, hypocrisy is a relevant reason to reject certain subjective moral claims. For instance, a murderer who claims that he should not be executed because he has a right to life should have his claim dismissed because his actions demonstrate that he does not have a consistent belief in a right to life.

References:

  1. Goldman, David P. (2006, Jan. 31). “No true Scotsman starts a war”. Asia Times.

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