Fallacy

An informal fallacy is an error in reasoning that does not originate in improper logical form. Arguments committing informal fallacies may be formally valid, but still fallacious. An error that stems from a poor logical form is sometimes called formal fallacy or simply an invalid argument.

There are many different informal fallacies, but a few basic types. For instance, material fallacies is error in what the arguer is talking about, while Verbal fallacies is error in how the arguer is talking.

Fallacies of presumption fail to prove the conclusion by assuming the conclusion in the proof. Fallacies of weak inference fail to prove the conclusion with insufficient evidence. Fallacies of distraction fail to prove the conclusion with irrelevant evidence, like emotion. Fallacies of ambiguity fail to prove the conclusion due to vagueness in words, phrases, or grammar.^[1]

Some fallacies are committed intentionally (to manipulate or persuade by deception), others unintentionally due to carelessness or ignorance.

Formal and material fallacies

Modern logic textbooks use various systems to categorize fallacies. The oldest such categorization is based on Aristotle's "Sophistical Refutations" (De Sophisticis Elenchis), in which he identified thirteen fallacies found in argument.

Aristotle's distinction between fallacies in dictione and fallacies extra dictionem is not the same as [Richard] Whately's division into logical, and non-logical or material. By "logical" fallacies Whately meant those in which "the conclusion does not follow" from the premisses; by "material," those in which the "conclusion does follow" from the premisses. In the former class, the defect of proof lies either in a manifest violation of some of the formal laws of the syllogism--quaternio terminorum, undistributed middle, illicit major, illicit minor, negative premisses, etc., defects which remain even when symbols are substituted for the terms and concepts, and which Aristotle would not regard as sophisms owing to the transparency of the mistake;--or the defect lies in a similar violation masked in ambiguous language. The transparent defects Whately called purely logical, the cloaked defects semi-logical fallacies. The latter he regarded as all alike reducible to ambiguous middle term, including in this class all Aristotle's sophisms except the ignoratio elenchi, the petitio principii, and the non causa pro causa. These three he included in his "material" falacies, by which he understood mistakes due to assuming false or unproven premisses, or premisses which prove the wrong conclusion. Whately's main distinction--between formally inconclusive arguments, and other sources of error--is sound and intelligible. But his nomenclature is objectionable. It is due to his narrow, nominalistic view of the scope of logic. All fallacies are logical, inasmuch as they are violations of logical principles or canons. Then, although most of Aristotle's sophismata, included in Whately's class of "semi-logical" fallacies, do in fact usually lead to formally invalid syllogisms through ambiguous middle terms, yet this is not clear in regard to some; and they certainly may lead to error otherwise as well. Hence the attempt to group them under such a head is unsatisfactory. Finally, on his own view of the scope of logic, Whately should not have dealt at all with what he called "non-logical" or "material" fallacies.

The distinction between a "formal" fallacy and a "material" fallacy is not fixed or clear--any more than that between "formal" and "material" logic. But at all events in a reasoning process, we can distinguish between the narrower "formal" or "consistency" aspect, which is independent of the truth of the premisses and the meaning of the terms used, and the "material" or "truth" aspect. Now, the formal validity of an inference, in this narrow sense, being independent of the subject-matter, i.e. of the meaning of the concepts and terms employed, it is only when the invalidity persists with the symbols, i.e. when some of the formal laws of reasoning are violated, that the fallacy is a formal one. If the fallacy lies in the language, .i.e. in the meaning of the terms employed, in ambiguitites of meaning, then its source is in the subject-matter, in the things for which the terms stand, and the fallacy is a material fallacy. An ambiguous middle term in a syllogism is, therefore, in this sense a material fallacy: when its two distinct meanings are explicitly substituted for it by two distinct terms, we have immediately the formal fallacy of quaternio terminorum. In this meaning of the expression "material fallacy," all Aristotle's sophismata in dictione are, when they enter into an inference, material fallacies; while some of his fallacies extra dictionem are formal in the sense that they can be represented in sysmbols; so that it is a mistake to confound Aristotle's two lists with Whately's semi-logical and material fallacies, respectively: a mistake into which Jevons seems to have fallen.^[2]

—Peter Coffey, The Science of Logic

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 commit a crime.

    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 (Since the homeowner did not invite the firefighters, but would want them to enter uninvited, this exception does not actually break the law)

Hasty generalization, or converse fallacy of accident

• Hasty generalization: argues from a special case to a general rule. Inductive logic demands a data set large enough and qualitative enough to warrant a generalization.
  • 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

    Proper Generalization: Every person in this room has ten fingers. Therefore, all people in this room have ten fingers.

Irrelevant conclusion

The irrelevant conclusion diverts the attention away from addressing the claim in a dispute instead of analysing its content. This is also called Ignoratio Elenchi or a "red herring". There are a number of special cases of irrelevant conclusions.

• Appeal to authority (argumentum ad verecundiam)

Claim: Pigs can fly

Argument: Oliver believes that pigs can fly, therefore pigs can fly

Weakness: Oliver can be wrong, even if Oliver is an authority in the topical area of the claim. Oliver may well believe that pigs can fly. Pigs should be able to fly not because of Oliver's beliefs, but because of real ability.

• Purely personal considerations (argumentum ad hominem)

Claim: Taxes should not be raised

Argument: George argues that taxes should be raised. But he is a communist, so taxes shouldn't be raised.

Weakness: George's political affiliation doesn't pertain to the truth of his claim.

In particular George is a communist, therefore taxes shouldn't be raised is another deduction that has to be enquired separately from the claim.

• Appeal to the majority or popular sentiment (argumentum ad populum)

Claim: You should drink Acme Cola

Argument: A thousand cool kids drink Acme Cola: (therefore) you should too!

Weakness(es): You may not be inclined to be a cool kid or to play that role by specifically drinking Acme Cola. Concerning the antecedent A thousand cool kids drink Acme Cola, it could be also argued that each cool kid could be wrong to do so; or even that drinking Acme Cola does not makes any kid cool in the first place.

• Appeal to loyalty
• Appeal to fear (argumentum ad baculum)

Claim: Penguins are mammals

Argument: All penguins are mammals. Disagree with me, and I'll cancel your research funding.

Weakness: The claim is false in the first place. The intimidating threat does not pertain to the truth of the claim. In particular, Disagree with me, and I'll cancel your research funding states an intention that is connected to the condition of penguins only within the scope of threat. The false claim that penguins are mammals, however, may well be a reason to assess who holds this view and conducts research on penguins -- unless the aim of the research is to disprove that penguins are birds.

• Appeal to pity (argumentum ad misericordiam)

Claim: I'm not guilty of speeding

Argument: I'm not guilty of speeding. My mom is sick, my dog just died, and I can't afford a ticket.

Weakness: Such misfortunes do not pertain to the truth of the claim.

This fallacy aims at arousing irrelevant pity for getting one's claim accepted.

• Appeal to ignorance argumentum ad ignorantiam)

This fallacy forwards the proposition under dispute without any certain proof.

• Genetic fallacy

This fallacy assumes a perceived defect in the origin of a claim discredits the claim itself.

Affirming the consequent and 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. Floridi argues that "the two best known formal logical fallacies, namely denying the antecedent (DA) and affirming the consequent (AC) are not just basic and simple errors, which prove human irrationality, but rather informational shortcuts, which may provide a quick and dirty way of extracting useful information from the environment."^[3]
  • Affirming the consequent Example:

    Argument: If people have the flu, they cough. Dax is coughing. Therefore, Dax 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 imply 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 issue is circular reasoning (Circulus in Probando or "arguing in a circle"). Conclusions can be used as the premises for an argument that, itself, concludes with the first argument's premises. When taken together, such viciously circular arguments become unpersuasive because they can no longer provide mutual support.

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 happening one after another is not an indication of causation.

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

        Argument: Ice cream sales increase in summer, the rate of drowning deaths increases in summer. Therefore, ice cream consumption causes drowning.

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

        Also called causation versus correlation.

Loaded question

• A loaded question is a multiple choice question which fails to disclaim the implied suggestion that an exhaustive list of applicable choices is being offered.
  • Example

    Question: Have you quit smoking?

    Problem: A simple 'yes' answer to the aggregated question implies a tacit acknowledgement on the part of the respondent that he or she used to smoke, whereas answering 'no' self-identifies the respondent as an active smoker. Neither choice is applicable for a respondent who has never been a smoker.

  • See also: the fallacy of many questions, (Plurium Interrogationum or "complex question").

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.^[4]
  • 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 falsely suggested that A said it would be good to have only sunny days, then refuted this misrepresentation rather than refuting A's actual assertion.

No true Scotsman

• No true Scotsman: When faced with a counterexample to a universal claim, rather than denying the counterexample or rejecting the original universal claim, this fallacy modifies the subject of the assertion to exclude the specific case or others like it by rhetoric, without reference to any specific objective rule.
  • Example

    Person A: All Scotsmen enjoy haggis.

    Person B: My uncle is a Scotsman, and he doesn't like haggis!

    Person A: Well, all true Scotsmen like haggis.

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.

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

• Apophasis or 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. Examples:
  • "One morning I shot an elephant in my pajamas. How he got in my pajamas I'll never know." (attributed to Groucho Marx. The first sentence leaves unclear whether he was in his pajamas when he shot the elephant or whether the elephant was in his pajamas when he shot it)
  • "Don't let depression kill you--let God help." (The sentence leaves unclear whether God is going to help you not be depressed or whether God is going to help you to die)

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.

Fallacy of division

• Fallacy of 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 verbosium - 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.

Figure of speech

• A figure of speech may not distinguish 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.

Reification or the fallacy of misplaced concreteness

• The fallacy of misplaced concreteness, identified by Whitehead in his discussion of metaphysics, wrongly substantiates concepts meant for discussion purposes only.

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 a 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.

Intentional Fallacies

Sometimes a speaker or writer uses a fallacy intentionally.

In humor, errors of reasoning are used for comical purposes. Groucho Marx used fallacies of amphiboly, for instance, to make ironic statements; Gary Larson employs fallacious reasoning in many of his cartoons. Wes Boyer and Samuel Stoddard have written a humorous essay teaching students how to be persuasive by means of a whole host of informal and formal fallacies.^[6]

In academic debate, in a conversation among friends, political discourse, or advertising, the arguer may use fallacious reasoning in order persuade the listener truth of the conclusion by any other means than offering relevant evidence.

For instance, the speaker or writer might divert the argument to unrelated issues using a red herring; insult someone's character (argumentum ad hominem), assume they are right by "begging the question" (petitio principi); make jumps in logic non-sequitur; identify a false cause and effect (post hoc ergo propter hoc); assert that everyone agrees, the bandwagoning; create a "false dilemma" or "either-or fallacy" in which the situation is oversimplified; selectively use facts or "card-stacking"; make false or misleading comparisons with "false equivalence", and "false analogy"; generalize quickly and sloppily with a "false generalization", and many more.^[7]

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, the same terms are used in informal discourse to mean an argument which is problematic for any reason.

A logical form such as A and B is independent of any particular conjunction of meaningful propositions. Logical form alone can guarantee that given true premises, a true conclusion must follow. However, formal logic makes no such guarantee if any premise is false, the conclusion can be either true or false. Any formal mistake or logical fallacy similarly invalidates the deductive guarantee. The so-called fallacy fallacy is a failure to understand that all bets are off unless the argument is formally flawless and all premises are true.

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

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

• Fallacy at PhilPapers
• Fallacy at the Indiana Philosophy Ontology Project

• Informal logic entry in the Stanford Encyclopedia of Philosophy

• Fallacy entry in the Internet Encyclopedia of Philosophy
• Infographic poster of common logical fallacies
• 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
• Daftar/Tabel -- 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.