Fallacy

In logic and rhetoric, a fallacy is incorrect reasoning in argumentation resulting in a misconception. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor (e.g. 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 the logical argument, making fallacies more difficult to diagnose. Also, the components of the fallacy may be spread out over separate arguments.

Fallacies
The taxonomy of material fallacies is based on that of Aristotle's 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 only sometimes a crime.
 * 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).

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 speaks English, so it must be true that all people speak English.
 * Problem: Those one has met are a 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 address it directly.
 * Example
 * Argument: Billy believes that war is justifiable, therefore it must be justifiable.
 * 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)
 * proving 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

 * Affirming the Consequent: draws a conclusion from premises that do not support that conclusion.
 * Example:
 * Argument: If people have the flu, they cough. Billy is coughing. Therefore, Billy has the flu.
 * Problem: Other things, such as asthma, can cause someone 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. dew).

Denying the antecedent

 * Denying the antecedent: draws a conclusion from premises that do not support that conclusion.
 * Example
 * Argument: If it is raining outside, it must be cloudy. It is not raining outside. Therefore, it is not cloudy.
 * Problem: There does not have to be rain in order for there to be clouds.

Begging the question

 * Begging the question: demonstrates a conclusion by means of premises that assume that conclusion.
 * Example
 * Argument: Billy always tells the truth, I know this because he told me so.
 * Problem: Billy may be lying.
 * Also called Petitio Principii, Circulus in Probando, arguing in a circle, assuming the answer. Begging the question does not preclude the possibility that the statement in question is correct, but is insufficient proof in and of itself.

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: Taxes fund necessary services such as police, courts, and roads; this demonstrates the necessity of taxation.
 * Problem: The fact that taxes currently fund certain services does not prove that taxation is the only means, or the best means, of funding those services. Although, in all fairness, it is a deductive fallacy to claim that the logical possibility of something (funding public services without taxes) implies its practicality, probability or even existence.
 * Special cases
 * post hoc ergo propter hoc: believing that temporal succession implies a causal relation.
 * Example
 * Argument: After Billy was vaccinated he developed autism, therefore the vaccine caused his autism.
 * Problem: This does not provide any evidence that the vaccine was the cause. The characteristics of autism may generally become noticeable at the age just following the typical age children receive vaccinations.
 * cum hoc ergo propter hoc: believing that correlation implies a causal relation.
 * Example
 * Argument: More cows die in India in the summer months. More ice cream is consumed in summer months.  Therefore, the consumption of ice cream in the summer months is killing Indian cows.
 * Problem: It is hotter in the summer, resulting in both the death of cows and the consumption of ice cream.
 * 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 misrepresentation of an opponent's position.
 * Example
 * Person A claims: Sunny days are good.
 * Argument 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 falsely framed A's claim to imply that A says that only sunny days are good, and has argued against that assertion instead of the assertion A has made.

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.
 * Example Argument: All heavy things have a great mass; this is heavy fog; therefore this fog has a great mass.
 * Problem: Heavy describes more than just weight. In the case of fog, it means that the fog is nearly opaque, not that it has a great mass. In fairness, a heavy fog does have significant mass, but not for the above reason.

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.

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" implies that the employee was a thief, even though it does not make (or justify) a direct negative statement.

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 band members (constituent parts) are highly skilled, therefore the band (composite item) is highly skilled.
 * Problem: The band members may be skilled musicians but 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's Ship paradox.


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

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.

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 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." This is an insult to his ability as a pianist and indicates that many others are better than he.
 * "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 excludes the idea that he is good at anything else.
 * "I killed my wife?" in response to a police officier asking if he killed his wife. In court, the police officier states his reply to his question was "I killed my wife"

Figure of Speech

 * Figure of Speech, the confusion between the metaphorical and ordinary uses 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.

Fallacy of Misplaced Concretion

 * Fallacy of Misplaced Concretion, identified by Whitehead in his discussion of metaphysics, this refers to the reification of concepts which exist only in discussion.

Example 1
Timmy argues:

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

Example 2
One posits the argument:


 * 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 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 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.

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 reference below. 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 below[what list?] 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.