Logical Fallacies-Classification & Formal Fallcies

As we saw earlier, logical fallacies are deliberate or inadvertent errors in logical reasoning and argument designed in ways to evoke strong emotional response in the interlocutors clouding out their judgement and destroy the possibility of a civilised argument. While it is strongly advisable to steer away from these at all times, it may be helpful and instructive to be aware of these. Ever since I started studying them, I have been able to notice them in several, or even most, conversations that I enter in, and it brings a wry smile on my face.

Logical fallacies have typically been classified into 2 broad categories:

  • Formal Fallacies, and
  • Informal Fallacies

Formal Fallacies

An argument can be considered as an interactive protocol between the participants with a purpose of resolving disagreements. As a protocol, the argument is governed by a set of rules and norms the violations of which are fallacies.

Formal fallacies are defined to be the ones that do not have anything to do with the content of the argument, which may be perfectly valid and reasonable, but to the forma and the structure of the same. The use of a formal fallacy in an argument renders the deductive argument invalid. Formally, all formal fallacies are special cases of non-sequitur. Non sequitur (Latin for “it does not follow”), in formal logic, is an argument in which its conclusion does not follow from its premises. In a non sequitur, the conclusion can be either true or false, but the argument is fallacious because there is a disconnection between the premise and the conclusion.

On their own, formal fallacies may not be as interesting to a layperson as to a student of formal logic.

Informal Fallacies

Informal fallacies are fallacies based on the arguments content. An informal fallacy is an argument whose stated premises fail to support their proposed conclusion. The deviation in an informal fallacy often stems from a flaw in the path of reasoning that links the premises to the conclusion. Informal fallacies are far more prevalent and would surely be interesting to everyone.

Let’s quickly run through some of the more intriguing formal fallacies, if only for the sake of completeness. I promise that the more exciting informal fallacies shall proceed this immediately.

Formal Fallacies – various types

Appeal to probability

Ironically, Appeal to probability, also known as Appello Probabilitatem, is a fallacy based on a blatant disregard to probability. Appealing to Probability is a logical fallacy where one assumes that a thing is inevitable simply because it is possible. Typical examples of this include Murphy’s Law on one hand (pessimistic extreme), and a financially desperate person sinking all his remaining savings in a lottery on the other hand (optimistic extreme).

Argument from fallacy

This one is indeed a funny one. Remember when we said that the content of the argument may be absolutely valid and reasonable in spite of the argument itself being fallacious. This fallacy precludes that if an argument for some conclusion is fallacious, then the conclusion itself is false. It is also called argument to logic (argumentum ad logicam), fallacy fallacy, or fallacist’s fallacy. Quoting a typical example:

Tom: All cats are animals. Ginger is an animal. This means Ginger is a cat.

Bill: Ah you just committed the affirming the consequent logical fallacy. Sorry, you are wrong, which means that Ginger is not a cat.

As a programmer, I am inclined to imagine one more level of indirection, what if the fallacy IS “Argument from fallacy”. Would the new fallacy be called as “Fallacy Fallacy Fallacy”? For example, let’s continue the discussion in the same vein

Tom: and you have just committed the “argumentum ad logicam” logical fallacy, which implies that Ginger IS a cat.

….. and so forth

Base rate fallacy

The probability of an occurrence is generally expressed as a percentage. However, by definition, a percentage is a ratio dependent upon the population (the denominator in the ratio). It so happens that somehow this gets neglected and 2 possibilities are compared as is. Here’s a real world example, which also happens to be a major issue. Remember that the numbers below are strictly hypothetical and are for illustration only.

Suppose that the incidence of being HIV+ is 40% in sex workers. The incidence in others is a hundredth of this number i.e. 0.4%. Now if a person is detected to be HIV+, what is the probability of him or her being a sex worker? Is it 40%? More? Less? If we assume that the sample size is one million, and 1 person out of every 1000 is a sex worker, there would be one thousand sex workers in the sample, 400 of which are likely to be HIV+. Among the other 999,000 people, 3996 are likely to be so, to give a total number of HIV+ people to be 4396. The probability boils down to merely 0.4396% or about 1 in 200. The stigma that can be attached to HIV+ people can be staggeringly nauseous due to the overestimation of this number, result of a stunning and collective fallacious reasoning.

Conjunction Fallacy

It is a debatable fallacy depicting an assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them. However, the responses have been shown to be dependent on the phrasing of the question.

Masked man fallacy

This fallacy, also known as illicit substitution of identicals, is a peculiar one because a set of true statements taken together can be shown to lead to an erroneous conclusion. The name says it all, ” “I do not know who the masked man is”, which can be true even though the masked man is Jones, and I know who Jones is.”. The two true statements- I know Jones and- I do not know who the masked man is- combined together lead to an error is deduction.

Propositional fallacies

Propositional fallacies deal with fallacies related to the derivation of complex conclusions of simple statements taken together. This is not a single fallacy but a group of several similar ones. Consider the following simplistic examples to illustrate the point.

Consider a rescue operations directive for a building on fire for preference to women and disabled people

  • If you are a woman or physically disabled, proceed first.
  • Mary came first.
  • Conclusion: Since Mary is a woman, she cannot be disabled.

Those familiar with Boolean algebra shall do well to distinguish between OR and XOR here. The OR is inclusive, you can be both. The assumption here is that since one of the premises is true, the other is automatically false. This fallacy is formally known as Affirming the Disjunct.

Consider another case

  • If you use a cell phone when you drive, you will meet an accident.
  • Andrew met with an accident the other day.
  • Conclusion: He must have been using a cell-phone while driving.

The second statement is a statement of fact which matched the consequence of the action in the first. The conclusion assumes that the fact must have been the consequence of the action in the first statement, denying that the fact may also be a consequence of other actions not stated here. Or in other words, the action in the first statement is one of the several ways leading to the fact in the second, not the only one. This fallacy is formally known as Affirming the Consequent. A related fallacy is the reverse of this, where a fact is taken to be denial of the action in the statement. This is particularly common in scenarios like this:

  • Squatting on the floor is known to cause knee ailments.
  • My grandfather squatted all his life and never had knee ailments.
  • Therefore the first statement is false.

This kind of argument is known as Denying the Antecedent.

Syllogistic Fallacies

A syllogism is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. For example:

  • Major premise: All men are mortal.
  • Minor premise: All Greeks are men.
  • Conclusion: All Greeks are mortal.

Syllogistic fallacies are also a group of fallacies related to the arguments in the form of syllogisms. I shall try to give several examples below:

  • My handwriting is not good.
  • There are several great people whose handwriting was not good.
  • Hence I am great.

This is essentially deriving positive conclusions from a set of negative premises. This is formally known as Affirmative conclusion from a negative premise or Illicit negative.

  • No internal combustion engines are non-polluting power plants, and
  • No non-polluting power plants are safe devices.
  • Therefore, no internal combustion engines are safe devices.”

What a thing is NOT, does not tell you what a thing IS. If I say that something is NOT blue, does it tell you what colour it actually IS? To explain the example above- internal combustion engines are NOT a non-polluting power plant (They are something else that is not specified). Non-polluting power plants are not safe devices (Doesn’t say anything about polluting power plants, or internal combustion engines). At the end, it is still not clear, what internal combustion engines are, or what safe devices are, and hence the premise that they are not safe just seems to be plucked out a hat. This is formally known as Fallacy of exclusive premises.

I have seen this written on T-shirts

  • Nobody is perfect.
  • I am nobody.
  • Hence I am perfect.

The word “nobody” in the example above has two meanings, as presented: “Nobody is perfect” means perfection cannot be attained by anybody; “I am nobody” means that the speaker is not a distinguished person . Therefore, “nobody” acts as two different words in this example, thus creating the fallacy of four terms. Ideally, to connect 4 terms, you must have at least 3 premises. Predictable, this fallacy is known as the Fallacy of Four Terms.

Now see this argument:

  • All cats die.
  • Tom died.
  • Hence, Tom is (was?) a cat.

Now, the fallacy here stems from the fact that the middle premise [die] has not been distributed, i.e. it is assumed that all those who die are cats, whereas cats are a subset of all those who die. This is known as Fallacy of the undistributed middle.

These were the more interesting logical fallacies that I tried to cover in this pretty long post. If you have any more illustrations of the fallacies covered, please let me know in the comments. We shall venture into the more interesting set of informal fallacies next. Stay tuned.

References:

  1. List of Fallacies. Wikipedia, the free encyclopedia. [Online] http://en.wikipedia.org/wiki/List_of_fallacies.
  2. Syllogistic Fallacies. Introduction to Logic. [Online]

    http://philosophy.lander.edu/logic

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