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In logic and rhetoric, a fallacy is usually an improper argumentation in reasoning often resulting in a misconception or presumption. Literally, a fallacy is "an error in reasoning that renders an argument logically invalid".^[1] By accident or design, fallacies may exploit emotional triggers in the listener or participant (appeal to emotion), or take advantage of social relationships between people (e.g. argument from authority). Fallacious arguments are often structured using rhetorical patterns that obscure any logical argument.

Though an argument is not "logically valid", it is not necessarily the case that the conclusion is incorrect. It simply means that the conclusion cannot logically be arrived at using that argument.

Though often used unintentionally, fallacies can be used purposefully to win arguments regardless of the merits. Among such devices, discussed in more detail below, are: "ignoring the question" to divert argument to unrelated issues using a red herring, making the argument personal (argumentum ad hominem) and discrediting the opposition's character, "begging the question" (petitio principi), the use of the non-sequitur, false cause and effect (post hoc ergo propter hoc), bandwagoning (everyone says so), the "false dilemma" or "either-or fallacy" in which the situation is oversimplified, "card-stacking" or selective use of facts, and "false analogy". Another common device is the "false generalization", an abstraction of the argument that shifts discussion to platitudes where the facts of the matter are lost. There are many, many more tricks to divert attention from careful exploration of a subject.^[2]

Fallacies can generally be classified as informal (premises fail to support the proposed conclusion, but the argument is structured properly) or formal (logical structure is flawed).

  Material fallacies

The taxonomy of material fallacies is based on that of Aristotle's body structure Organon (Sophistici elenchi). This taxonomy is as follows:

  Fallacy of accident or sweeping generalization

• Fallacy of accident or sweeping generalization: a generalization that disregards exceptions.
  • Example

    Argument: Cutting people is a crime. Surgeons cut people, therefore, surgeons are criminals.

    Problem: Cutting people is not a crime in certain situations.

    Argument: It is illegal for a stranger to enter someone's home uninvited. Firefighters enter people's homes uninvited, therefore firefighters are breaking the law.

    Problem: The exception does not break nor define the rule; a dicto simpliciter ad dictum secundum quid (where an accountable exception is ignored).^{[clarification needed]}

  Converse fallacy of accident or hasty generalization

• Converse fallacy of accident or hasty generalization: argues from a special case to a general rule.
  • Example

    Argument: Every person I've met has ten fingers, therefore, all people have ten fingers.

    Problem: Those who have been met are not a representative subset of the entire set.

  • Also called reverse accident, destroying the exception, a dicto secundum quid ad dictum simpliciter

  Irrelevant conclusion

• Irrelevant conclusion: diverts attention away from a fact in dispute rather than addressing it directly.
  • Example

    Argument: Billy believes that pigs can fly, therefore pigs can fly.

    Problem: Billy can be wrong. (In particular this is an appeal to authority.)

  • Special cases:
    • purely personal considerations (argumentum ad hominem),
    • popular sentiment (argumentum ad populum—appeal to the majority; appeal to loyalty.),
    • fear (argumentum ad baculum),
    • conventional propriety (argumentum ad verecundiam—appeal to authority)
    • to arouse pity for getting one's conclusion accepted (argumentum ad misericordiam)
    • forwarding the proposition under dispute without any certain proof (argumentum ad ignorantiam)
    • assuming a perceived defect in the origin of a claim discredits the claim itself (genetic fallacy)
  • Also called Ignoratio Elenchi, a "red herring"

  Affirming the consequent/Denying the antecedent

• Affirming the consequent and Denying the antecedent: draws a conclusion from premises that do not support that conclusion by confusing necessary and sufficient conditions.
  • Affirming the consequent Example:

    Argument: If people have the flu, they cough. Torres is coughing. Therefore, Torres has the flu.

    Problem: Other things, such as asthma, can cause someone to cough. The argument treats having the flu as a necessary condition of coughing; in fact, having the flu is a sufficient condition of coughing, but it is not necessary to have the flu for one to cough.

    Argument: If it rains, the ground gets wet. The ground is wet, therefore it rained.

    Problem: There are other ways by which the ground could get wet (e.g. someone spilled water).

• Denying the antecedent Example

  • Argument: If it is raining outside, it must be cloudy. It is not raining outside. Therefore, it is not cloudy.

    Problem: Rain is a sufficient condition of cloudiness, but cloudy conditions do not necessarily produce rain.

  Begging the question

• Begging the question: demonstrates a conclusion by means of premises that assume that conclusion.
  • Example

    Argument: Aspirin users are at risk of becoming dependent on the drug, because aspirin is an addictive substance.

    Problem: The premise and the conclusion have the same meaning. If one has already accepted the premise, there is no need to reason to the conclusion. Obviously the premise is not logically irrelevant to the conclusion, for if the premise is true the conclusion must also be true. It is, however, logically irrelevant in proving the conclusion.

  • Also called Petitio Principii, or assuming the answer. Begging the question does not preclude the possibility that the statement is incorrect, and it is not sufficient proof in and of itself.
  • A related fallacy is Circulus in Probando, arguing in a circle, or circular reasoning. This is when two (or more) conclusions are used as premises to support each other, but unless one accepts one of them as true at the outset, there is no reason to accept the conclusions.

  Fallacy of false cause

• Fallacy of false cause or non sequitur: incorrectly assumes one thing is the cause of another. Non Sequitur is Latin for "It does not follow."
  • Example

    Argument: I hear the rain falling outside my window; therefore, the sun is not shining.

    Problem: The conclusion is false because the sun can shine while it is raining.

  • Special cases
    • post hoc ergo propter hoc: believing that temporal succession implies a causal relation.
      • Example

        Argument: It rained just before the car broke down. The rain caused the car to break down.

        Problem: There may be no connection between the two events. Two events co-occurring is not an indication of causation.

    • cum hoc ergo propter hoc: believing that correlation implies a causal relation.
      • Example

        Argument: More cows die in the summer months. More ice cream is consumed in summer months. Therefore, the consumption of ice cream in the summer months is killing cows.

        Problem: No premise suggests the ice cream consumption is causing the deaths. The deaths and consumption could be unrelated, or something else could be causing both, such as summer heat.

        Also called causation versus correlation.

  Fallacy of many questions

• Fallacy of many questions or loaded question: groups more than one question in the form of a single question.
  • Example

    Argument: Have you stopped beating your wife?

    Problem: A yes or no answer will still be an admission of guilt to beating your wife at some point. (See also Mu.)

  • Also called Plurium Interrogationum and other terms

  Straw man

• Straw man: A straw man argument is an informal fallacy based on misrepresenting an opponent's position so as to more easily refute it.^[3]
  • Example

    Person A: Sunny days are good.

    Person B: If all days were sunny, we'd never have rain, and without rain, we'd have famine and death. Therefore, you are wrong.

    Problem: B has misrepresented A's claim by falsely suggesting that A claimed that only sunny days are good, and then B refuted the misrepresented version of the claim, rather than refuting A's original assertion.

  Verbal fallacies

Verbal fallacies are those in which a conclusion is obtained by improper or ambiguous use of words. They are generally classified as follows.

  Magisterial fallacy (Engineer's Resolve)

• "Wherein we think and speak as if our outsider status and lengthy education have given us the authority of a high-court judge to decide what is true." (p. 320)^[4]

Magic Robe fallacy

Wherin we believe that a high-court judge is always more apt than the outsider at deciding what is true.

  Equivocation

• Equivocation consists in employing the same word in two or more senses, e.g. in a syllogism, the middle term being used in one sense in the major and another in the minor premise, so that in fact there are four not three terms. Often this happens when the two meanings are similar despite being distinctly different.

Example Argument: All heavy things have a great mass; Jim has a "heavy heart"; therefore Jim's heart has a great mass.

Problem: Heavy describes more than just weight. (Jim is sad.)

  Connotation fallacies

• Connotation fallacies occur when a dysphemistic word is substituted for the speaker's actual quote and used to discredit the argument. It is a form of attribution fallacy.

  Apophasis and argument by innuendo

• Argument by innuendo involves implicitly suggesting a conclusion without stating it outright. For example, a job reference that says a former employee "was never caught taking money from the cash box" In this example the overly specific nature of the innuendo implies that the employee was a thief, even though it does not make (or justify) a direct statement of accusation.^[5]

  Amphiboly

• Amphiboly is the result of ambiguity of grammatical structure.

Example: The position of the adverb "only" in a sentence starting with "He only said that" results in a sentence in which it is uncertain as to which of the other three words the speaker is intending to modify with the adverb.

  Fallacy of composition

• Fallacy of composition "From each to all". Arguing from some property of constituent parts, to the conclusion that the composite item has that property. This can be acceptable (i.e., not a fallacy) with certain arguments such as spatial arguments (e.g. "all the parts of the car are in the garage, therefore the car is in the garage").

Example Argument: All the musicians in a band (constituent parts) are highly skilled, therefore the band itself (composite item) is highly skilled.

Problem: The band members may be skilled musicians but may lack the ability to function properly as a group.

  Division

• Division, the converse of the preceding, arguing from a property of the whole, to each constituent part.

Example Argument: "The university (the whole) is 700 years old, therefore, all the staff (each part) are 700 years old".

Problem: Each and every person currently on staff is younger than 700 years. The university continues to exist even when, one by one, each and every person on the original staff leaves and is replaced by a younger person. See Theseus' Ship paradox.

Example Argument: "This liquid is part of a nutritious breakfast therefore the liquid is nutritious."

Problem: Simply because the breakfast taken as a whole is nutritious does not necessarily mean that each part of that breakfast is nutritious (unless the definition of a nutritious breakfast requires all parts to be nutritious).

  Proof by verbosity

• Proof by verbosity, sometimes colloquially referred to as argumentum verbosum - a rhetorical technique that tries to persuade by overwhelming those considering an argument with such a volume of material that the argument sounds plausible, superficially appears to be well-researched, and it is so laborious to untangle and check supporting facts that the argument might be allowed to slide by unchallenged.

  Accent

• Accent, which occurs only in speaking and consists of emphasizing the wrong word in a sentence. e.g., "He is a fairly good pianist", according to the emphasis on the words, may imply praise of a beginner's progress or insult of an expert pianist.

• "He is a fairly good pianist." This argument places emphasis on the fact that "He", as opposed to anyone else, is a fairly good pianist.
• "He is a fairly good pianist." This is an assertion that he "is" a good pianist, as opposed to a poor one.
• "He is a fairly good pianist." The emphasis on "a" makes this an assertion that while he is a good pianist, there are other good pianists as well.
• "He is a fairly good pianist." This is an assertion that his ability as a pianist is fair, perhaps in need of improvement.
• "He is a fairly good pianist." This is an assertion that he is most certainly a good pianist, perhaps even impressively so.
• "He is a fairly good pianist." This is isolating his ability as only being good in the field of musical instruments, namely, the piano, and possibly excludes the idea that he is good at anything else.
• "I killed my wife?" in response to a police officer asking if he killed his wife. In court, the police officer states his reply to his question was "I killed my wife." This use of accent is demonstrated in the courtroom comedy My Cousin Vinny.

  Figure of Speech

• Figure of Speech, the confusion between the metaphorical or figurative use of a word or phrase and the ordinary or literal use of a word or phrase.

Example: The sailor was at home on the sea.

Problem: The expression 'to be at home' does not literally mean that one's domicile is in that location.

This can happen in conjunction with Equivocation, whereby word or phrase is used literally in one part of an argument but figuratively in another part of the argument.

Example: John lives on a house-boat on the sea. He feels at home on his house-boat. Therefore he is like a sailor because he is at home on the sea.

  Fallacy of misplaced concreteness

• Fallacy of misplaced concreteness, identified by Whitehead in his discussion of metaphysics, this refers to the reification of concepts which exist only in discussion.

  Example 1

Timmy argues:

1. Billy is a good tennis player.
2. Therefore, Billy 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, Timmy says that Billy is good at some particular activity, in this case tennis. In the conclusion, Timmy states that Billy 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: Billy might be the best tennis player in the world but a rotten person morally. However, it is not legitimate to infer he is a bad person on the ground there has been a fallacious argument on the part of Timmy. Nothing concerning Billy's moral qualities is to be inferred from the premise. 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 2

One posits the argument:

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

This argument has the appearance of an inference that 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

Nothing 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 sandwich, it logically follows that

Eating a sandwich fails to be better than eternal happiness.

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

Eating a sandwich is better than eating nothing at all.

Thus this is a fallacy of equivocation.

  Deductive fallacy

In philosophy, the term logical fallacy properly refers to a formal fallacy: a flaw in the structure of a deductive argument which renders the argument invalid.

However, it is often used more generally in informal discourse to mean an argument which is problematic for any reason, and thus encompasses informal fallacies as well as formal fallacies.

The presence of a formal fallacy in a deductive argument does not imply anything about the argument's premises or its conclusion (see fallacy fallacy). Both may actually be true, or even more probable as a result of the argument (e.g., appeal to authority), but the deductive argument is still invalid because the conclusion does not follow from the premises in the manner described. By extension, an argument can contain a formal fallacy even if the argument is not a deductive one; for instance an inductive argument that incorrectly applies principles of probability or causality can be said to commit a formal fallacy.

  Formalisms and frameworks used to understand fallacies

A different approach to understanding and classifying fallacies is provided by argumentation theory; see for instance the van Eemeren, Grootendorst.^[6] In this approach, an argument is regarded as an interactive protocol between individuals which attempts to resolve a disagreement. The protocol is regulated by certain rules of interaction, and violations of these rules are fallacies. Many of the fallacies in the list above are best understood as being fallacies in this sense.

  Other systems of classification

Of other classifications of fallacies in general the most famous are those of Francis Bacon and J. S. Mill. Bacon (Novum Organum, Aph. 33, 38 sqq.) divided fallacies into four Idola (Idols, i.e. False Appearances), which summarize the various kinds of mistakes to which the human intellect is prone. With these should be compared the Offendicula of Roger Bacon, contained in the Opus maius, pt. i. J. S. Mill discussed the subject in book v. of his Logic, and Jeremy Bentham's Book of Fallacies (1824) contains valuable remarks. See Rd. Whateley's Logic, bk. v.; A. de Morgan, Formal Logic (1847) ; A. Sidgwick, Fallacies (1883) and other textbooks.

  See also

Attacking Faulty Reasoning Cognitive distortion Evidence List of cognitive biases Mathematical fallacy

List of fallacies List of paradoxes Sophistry Straight and Crooked Thinking Truth

Logic portal Thinking portal Psychology portal

  References

  Further reading

• C. L. Hamblin, Fallacies, Methuen London, 1970. reprinted by Vale Press in 1998 as ISBN 0-916475-24-7.
• Douglas N. Walton, Informal logic: A handbook for critical argumentation. Cambridge University Press, 1989.
• Hans V. Hansen; Robert C. Pinto (1995). Fallacies: classical and contemporary readings. Penn State Press. ISBN 978-0-271-01417-3. 
• John Woods (2004). The death of argument: fallacies in agent based reasoning. Springer. ISBN 978-1-4020-2663-8. 
• Frans van Eemeren; Bart Garssen; Bert Meuffels (2009). Fallacies and Judgments of Reasonableness: Empirical Research Concerning the Pragma-Dialectical Discussion. Springer. ISBN 978-90-481-2613-2. 

Historical texts

• Aristotle, On Sophistical Refutations, De Sophistici Elenchi. library.adelaide.edu.au
• William of Ockham, Summa of Logic (ca. 1323) Part III.4.
• John Buridan, Summulae de dialectica Book VII.
• Francis Bacon, the doctrine of the idols in Novum Organum Scientiarum, Aphorisms concerning The Interpretation of Nature and the Kingdom of Man, XXIIIff. fly.hiwaay.net
• Arthur Schopenhauer, The Art of Controversy | Die Kunst, Recht zu behalten - The Art Of Controversy (bilingual), (also known as "Schopenhauers 38 stratagems"). gutenberg.net
• John Stuart Mill, A System of Logic - Raciocinative and Inductive. Book 5, Chapter 7, Fallacies of Confusion. la.utexas.edu

  External links

Look up fallacy in Wiktionary, the free dictionary.

• Infographic poster of common logical fallacies
• SEP entry on informal logic has a section on fallacy theory
• Appeal to Authority Appeal to Authority Logical Fallacy
• FallacyFiles.org contains categorization of fallacies with examples.
• 42 informal logical fallacies explained by Dr. Michael C. Labossiere (including examples), nizkor.org
• Humbug! The skeptic’s field guide to spotting fallacies in thinking – textbook on fallacies. scribd.com
• List of fallacies with clear examples, infidels.org
• Interactive Syllogistic Machine A web based syllogistic machine for exploring fallacies, figures, and modes of syllogisms.
• Logical Fallacies and the Art of Debate, csun.edu
• LogicalFallacies.Info
• An Informal Fallacy Primer, acontrario.org
• Stephen Downes Guide to the Logical Fallacies, onegoodmove.org
• "Love is a Fallacy", a short story written by Max Shulman. WebCitation archive.