A logical fallacy is a mistake in reasoning. The premises of good arguments support the conclusion, so that in the case of deductive arguments, if the premises are true, the conclusion must also be true. In the case of inductive arguments, true premises make the conclusion more likely. Deductively valid argument forms can be defined as those in which true premises never lead to a false conclusion, no matter what content is presented in that form. In logic, arguments and argument forms are studied and a system of rules is created to systematically distinguish between valid and invalid arguments. Invalid argument types that appear frequently and that seem to be especially deceptive have been categorized and given names. The study of logic and the naming of logical fallacies began with Aristotle (384–322 b.c.e.), and standard Latin names of fallacies have been inherited from the Middle Ages, so "logical fallacy" is not a concept that has changed much with time. However, the teaching of logical fallacies has been revived with the popularity of courses entitled "critical thinking" rather than "logic'" in order to highlight their emphasis on natural language and informal fallacies, rather than on formal logical systems.
It is standard practice to distinguish formal and informal fallacies. Formal fallacies break one or more of the rules of a system of logic and can be seen when an argument is presented in either schematic form or in a natural language. Informal fallacies, by contrast, can often only be seen when the argument is presented in natural language, since they depend often on ambiguity or some other misuse of language. Other common fallacies that do not clearly break a rule of logic are also classified as informal, even when they do not depend on misuse of language.
In traditional Aristotelian logic, a set of rules can be established for the formation of valid arguments. Because breaking any one of the rules results in an invalid argument, there is a logical fallacy corresponding to each rule. Examples of such fallacies include excluded middle, illicit major, illicit minor, etc. One important formal logical fallacy is affirming the consequent, which can be given schematically as an argument of the form "If P, then Q. Q. Therefore, P." The logic of conditional statements has been thought to be essential to the testing of scientific theories, since predictions are written in conditional form. A fact such as "Water freezes at 32° F" can be written as the conditional "If (pure) water is below 32° F, then it will freeze." However, as Karl Popper (1902–1994) emphasized, one cannot claim to prove anything if one obtains a positive result, and indeed would be committing the formal logical fallacy of affirming the consequent if this reasoning is used to support one's claim. Suppose someone had claimed that they have a magic box that freezes water, and that water always freezes when it is put into the box. One should not be impressed if this prediction comes true, not even if this experiment is repeated multiple times. What is needed is a way of isolating the different factors that may be relevant to the change of state that water undergoes—is it being in the box, or being in the dark, or being in the cold that is the crucial factor? This problem of scientific reasoning is highlighted by the fallacy of affirming the consequent. A conditional statement can properly be rejected if a negative result is obtained, but nothing can be concluded deductively from a positive result.
The multitude of names given to informal fallacies can be more confusing than helpful, but nevertheless, the names of logical fallacies are important terms of art in any kind of argumentative writing or speech. Informal logical fallacies can be classified in different ways, but it is common to put them into groups such as fallacies of relevance, weak induction, ambiguity, and presumption.
Fallacies of relevance.
Slippery slope, red herring, and straw person are fallacies that change the issue under discussion to something that is easier to attack. An ad hominem argument attacks the person, rather than the issue. The fact that someone is untrustworthy, for example, does not guarantee that the conclusion of their argument is wrong or that their argument is invalid. The question of whether or not such information is relevant can, however, be rather subtle, because a person's trustworthiness would legitimately lead to questioning what they say. "Tu quoque" means "you too" and is a fallacious argument used in a debating situation to try to undermine the criticism of an opponent, but without actually presenting evidence in one's own defense. Appeal to the popularity of an idea (ad populum ), to force, and to pity are further examples of arguments that present irrelevant evidence and draw attention away from the issue being debated.
Fallacies of weak induction.
Premises may present relevant information without justifying the claim made in the conclusion. A hasty generalization, for example, makes use of either too few cases or unrepresentative cases to make a broad claim. An appeal to ignorance attempts to justify a positive claim by rejecting the evidence on the other side as insufficient. To say, for example, that there is no intelligent life except on Earth, because there is no evidence of such life, is too strong a claim. However, the burden of proof is generally on those who make a positive claim, so it would be legitimate to say that there is no reason to believe in extraterrestrial intelligence. Appeal to authority is also a fallacy of weak induction. Although people constantly rely on information given to them by others, the opinions of experts alone are insufficient to justify a controversial opinion. Experts must have some reasons by which they were convinced of their beliefs and these should be communicated to others.
Fallacies of ambiguity.
The fallacy of equivocation describes an argument in which a word is used in two different senses. Such an argument can be thought of as formally invalid, but since only subtle changes of meaning are misleading, this fallacy is considered to be informal. Amphiboly is the name given to an argument that relies on ambiguity, but involving the grammar of the sentence rather than the meaning of an individual word. Composition and division are a pair of fallacies, in which an illicit inference is made from the properties of individuals in a class to the class itself, or from the class to the individuals. No one would be taken in by an argument that the concept "mammal" must be hairy because all mammals are hairy, but arguments that have seemed very compelling to many people may be of the same form. For example, some versions of the argument from design argue that the order and purpose found in every object in the universe implies that the universe as a whole has a purpose and a designer.
Fallacies of presumption.
Using the conclusion of the argument as a premise or otherwise assuming what is being claimed in the conclusion is called "begging the question." Circular reasoning appears to be formally valid, since the conclusion really does follow from the premises (P, therefore P ). However, if it is assumed that P is controversial and therefore requires some kind of justification, it is clear that a circular argument will not advance the discussion. "That begs the question" is a phrase that is changing its meaning, at least in colloquial usage, to simply mean "that raises the question." This dubious usage loses any connection to the idea of logical fallacy, since the phrase is no longer being used to evaluate an argument. Begging the question is usually classified as an informal fallacy because it relies on tricking the reader into not noticing that the subject of controversy is being assumed.
See also Logic ; Rhetoric .
Aristotle. Aristotle on Fallacies; or, the Sophistici Elenchi. Translated by Edward Poste. New York: Garland, 1987.
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Fearnside, W. Ward. Fallacy: The Counterfeit of Argument. Englewood Cliffs, N.J.: Prentice-Hall, 1959.
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David J. Stump