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Logical fallacy

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A logical fallacy is an error in logical argument which is independent of the truth of the premises. It is a flaw in the structure of an argument as opposed to an error in its premises. When there is a fallacy in an argument it is said to be invalid. The presence of a logical fallacy in an argument does not necessarily imply anything about the argument's premises or its conclusion. Both may actually be true, but the argument is still invalid because the conclusion does not follow from the premises using the inference principles of the argument. By extension, an argument can have a logical fallacy even if the argument is not a purely logical one; for instance an argument that incorrectly applies principles of probability or causality can be said to have a logical fallacy.

Recognizing fallacies in practical arguments may be difficult since arguments are often structured using rhetorical patterns that obscure the logical connections between assertions. As we illustrate with various examples, fallacies may also exploit the emotions or intellectual or psychological weaknesses of the interlocutor. Having the capability of recognizing logical fallacies in arguments will hopefully reduce the likelihood of such an occurrence.

A different approach to understanding and classifying fallacies is provided by argumentation theory; see for instance the van Eemeren, Grootendorst reference below. In this approach, an argument is regarded as an interactive protocol between individuals which attempts to resolve a disputed proposition. The protocol is regulated by certain rules of interaction and violations of these rules are fallacies. Many of the fallacies in the list below are best understood as being fallacies in this sense.

Examples of fallacious arguments

In the strictest sense, a logical fallacy is the incorrect application of a valid logical principle or an application of an nonexistent principle:

  1. Some acts of killing human beings are legal in this state.
  2. Some acts of killing human beings are illegal in this state.
  3. Therefore some acts of killing human beings are both legal and illegal in this state.

This is fallacious. Indeed, there is no logical principle which states

  1. For some x, P(x).
  2. For some y, Q(y).
  3. Then for some z, P(z) and Q(z).

The easiest way to show the above inference is invalid is by using Venn diagrams. In logical parlance, the inference is invalid, since under at least one interpretation of the predicates it is not validity preserving.

Unfortunately, few fallacious arguments are as clear cut as the above example suggests. A great many arguments involve causality, which is certainly not part of formal logic. Others involve psychological ploys such as use of power relationships between proposer and interlocutor, appeals to patriotism and morality, appeals to ego etc., to establish necessary intermediate (explicit or implicit) premises for an argument. Indeed, fallacies very often lay in unstated assumptions or implied premises in arguments that are not always obvious at first glance. One way to obscure a premise is through enthymeme.

We now give a few examples illustrating common errors in reasoning. Note that providing a critique of an argument has no relation to the validity of the conclusion. The conclusion could very well be valid, while the argument itself is unsound. See argument from fallacy.

In the following, we view an argument as a dialogue between a proposer and an interlocutor.

Example 1

James argues:

  1. Application of the death penalty is killing a human being.
  2. Killing a human being is wrong.
  3. Therefore, application of the death penalty is wrong.

This argument claims to prove the death penalty is wrong. This particular argument has the form of a categorical syllogism. Any argument must have premises as well as a conclusion. In this case we need to ask what the premises are, that is the set of assumptions the proposer of the argument can expect the interlocutor to grant. The first assumption is almost true by definition: the death penalty is the killing of a criminal who has been duly convicted under a process of law. The second assumption is less clear as to its meaning. Since the assertion has no quantifiers of any kind, it could mean any one of the following:

  • Every act of killing a human being is wrong.
  • Most acts of killing a human being are wrong.
  • All acts of killing a human being are wrong, except those that are carried out for some legitimate purpose such as deterring serious crime.
  • Some acts of killing a human being are wrong.

The third interpretation for example would be those of individuals who accept the Fifth Commandment under a common interpretation in Judeo-Christian theology. In that interpretation, the above syllogism would then fail to have validated its second premise. James may try to assume that his interlocutor believes every act of killing is wrong; if the interlocutor grants this then the argument is valid. In this case, the interlocutor is essentially conceding the point to James. However, the interlocutor is more likely to believe some acts of killing are not wrong, for instance those carried out in self defense or in legitimate warfare; and in this case James is not much better off than he was before he formulated the argument, since he now has to prove the assertion that the death penalty is not a legimate form of killing, which is a disguised form the original thesis. From the point of view the interlocutor, James commits the logical fallacy of begging the question.

Example 2

Barbara argues:

  1. Andre is a good tennis player.
  2. Therefore, Andre is 'good', that is to say a morally good person.

Here the problem is that the word good has different meanings, which is to say that it is an ambiguous word. In the premise, Barbara says that Andre is good at some particular activity, in this case tennis. In the conclusion, she says that Andre is a morally good person. These are clearly two different senses of the word "good". The premise might be true but the conclusion can still be false: Andre might be the best tennis player in the world but a rotten person morally. Appropriately, since it plays on an ambiguity, this sort of fallacy is called the fallacy of equivocation, that is, equating two incompatible terms or claims.

Example 3

A humorous variant of the fallacy of ambiguity is as follows. Ramesh argues:

  1. Nothing is better than eternal happiness.
  2. Eating a hamburger is better than nothing.
  3. Therefore, eating a hamburger is better than eternal happiness.

This argument has the appearance of an inference which applies transitivity of the two-placed relation is better than, which in this critique we grant is a valid property. The argument is an example of syntactic ambiguity. In fact, the first premise semantically does not predicate an attribute of the subject, as would for instance the assertion

A potato is better than eternal happiness.

In fact it is semantically equivalent to the following universal quantification:

Everything fails to be better than eternal happiness.

So instantiating this fact with eating a hamburger, it logically follows that

Eating a hamburger fails to be better than eternal happiness.

Note that the premise A hamburger is better than nothing does not provide anything to this argument. This fact really means something such as

Eating a hamburger is better than eating nothing at all.

Fallacies in the media and politics

Fallacies are used frequently by pundits in the media and politics. When one politician says to another, "You don't have the moral authority to say X", this could be an example of the argumentum ad hominem or personal attack fallacy; that is, attempting to disprove X, not by addressing validity of X but by attacking the person who asserted X. Arguably, the politician is not even attempting to make an argument against X, but is instead offering a moral rebuke against the interlocutor. For instance, if X is the assertion:

The military uniform is a symbol of national strength and honor.

Then ostensibly, the politician is not trying to prove the contrary assertion. If this is the case, then there is no logically fallacious argument, but merely a personal opinion about moral worth. Thus identifying logical fallacies may be difficult and dependent upon context.

In the opposite direction is the fallacy of argument from authority. A classic example is the Ipse dixit—"He himself said it" argument—used throughout the Middle Ages in reference to Aristotle. A modern instance is "celebrity spokespersons" in advertisements: a product is good and you should buy/use/support it because your favorite celebrity endorses it.

An appeal to authority is always a logical fallacy though it can be an appropriate form of rational argument if, for example, it is an appeal to expert testimony. In this case, the expert witness must be recognized as such and all parties must agree that the testimony is appropriate to the circumstances. This form of argument is common in legal situations.

By definition, arguments with logical fallacies are invalid, but they can often be (re)written in such a way that they fit a valid argument form. The challenge to the interlocutor is, of course, to discover the false premise, that is the premise which makes the argument unsound.

A list of fallacies

Please note that this list is not exhaustive.

See also

References

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