Fallacies

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Formal fallaciesEdit

Main article: Formal fallacy

A formal fallacy is an error in the argument's form.^[2] All formal fallacies are types of non sequitur.

• Appeal to probability – a statement that takes something for granted because it would probably be the case (or might be the case).^[3][4]
• Argument from fallacy (also known as the fallacy fallacy) – the assumption that, if a particular argument for a "conclusion" is fallacious, then the conclusion by itself is false.^[5]
• Base rate fallacy – making a probability judgment based on conditional probabilities, without taking into account the effect of prior probabilities.^[6]
• Conjunction fallacy – the assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them.^[7]
• Non-sequitur fallacy - where the conclusion does not logically follow the premise.^[8]
• Masked-man fallacy (illicit substitution of identicals) – the substitution of identical designators in a true statement can lead to a false one.^[9]

Propositional fallaciesEdit

A propositional fallacy is an error that concerns compound propositions. For a compound proposition to be true, the truth values of its constituent parts must satisfy the relevant logical connectives that occur in it (most commonly: [and], [or], [not], [only if], [if and only if]). The following fallacies involve relations whose truth values are not guaranteed and therefore not guaranteed to yield true conclusions.
Types of propositional fallacies:

• Affirming a disjunct – concluding that one disjunct of a logical disjunction must be false because the other disjunct is true; A or B; A, therefore not B.^[10]
• Affirming the consequent – the antecedent in an indicative conditional is claimed to be true because the consequent is true; if A, then B; B, therefore A.^[10]
• Denying the antecedent – the consequent in an indicative conditional is claimed to be false because the antecedent is false; if A, then B; not A, therefore not B.^[10]

Quantification fallaciesEdit

A quantification fallacy is an error in logic where the quantifiers of the premises are in contradiction to the quantifier of the conclusion.
Types of quantification fallacies:

• Existential fallacy – an argument that has a universal premise and a particular conclusion.^[11]

Formal syllogistic fallaciesEdit

Syllogistic fallacies – logical fallacies that occur in syllogisms.

• Affirmative conclusion from a negative premise (illicit negative) – a categorical syllogism has a positive conclusion, but at least one negative premise
• Fallacy of exclusive premises – a categorical syllogism that is invalid because both of its premises are negative.[11]
• Fallacy of four terms (quaternio terminorum) – a categorical syllogism that has four terms.[12]
• Illicit major – a categorical syllogism that is invalid because its major term is not distributed in the major premise but distributed in the conclusion.[11]
• Illicit minor – a categorical syllogism that is invalid because its minor term is not distributed in the minor premise but distributed in the conclusion.[11]
• Negative conclusion from affirmative premises (illicit affirmative) – a categorical syllogism has a negative conclusion but affirmative premises.[11]
• Fallacy of the undistributed middle – the middle term in a categorical syllogism is not distributed.[13]
• Modal fallacy – confusing necessity with sufficiency. A condition X is necessary for Y if X is required for even the possibility of Y. X does not bring about Y by itself, but if there is no X, there will be no Y. For example, oxygen is necessary for fire. But one cannot assume that everywhere there is oxygen, there is fire. A condition X is sufficient for Y if X, by itself, is enough to bring about Y. For example, riding the bus is a sufficient mode of transportation to get to work. But there are other modes of transportation – car, taxi, bicycle, walking – that can be used.
• Modal scope fallacy – a degree of unwarranted necessity is placed in the conclusion.
• Informal fallacies
• Edit
• Main article: Informal fallacy
• Informal fallacies – arguments that are logically unsound for lack of well-grounded premises.[14]

Argument to moderation (false compromise, middle ground, fallacy of the mean, argumentum ad temperantiam) – assuming that a compromise between two positions is always correct.[15]

Continuum fallacy (fallacy of the beard, line-drawing fallacy, sorites fallacy, fallacy of the heap, bald man fallacy, decision-point fallacy) – improperly rejecting a claim for being imprecise.[16]

Correlative-based fallacies

Suppressed correlative – a correlative is redefined so that one alternative is made impossible (e.g., "I'm not fat because I'm thinner than John.").[17]

Definist fallacy – defining a term used in an argument in a biased manner (e.g., using "loaded terms"). The person making the argument expects that the listener will accept the provided definition, making the argument difficult to refute.[18]

Divine fallacy (argument from incredulity) – arguing that, because something is so incredible or amazing, it must be the result of superior, divine, alien or paranormal agency.[19]

Double counting – counting events or occurrences more than once in probabilistic reasoning, which leads to the sum of the probabilities of all cases exceeding unity.

Equivocation – using a term with more than one meaning in a statement without specifying which meaning is intended.[20]

Ambiguous middle term – using a middle term with multiple meanings.[21]

Definitional retreat – changing the meaning of a word when an objection is raised.[22] Often paired with moving the goalposts (see below), as when an argument is challenged using a common definition of a term in the argument, and the arguer presents a different definition of the term and thereby demands different evidence to debunk the argument.

Motte-and-bailey fallacy – conflating two positions with similar properties, one modest and easy to defend (the "motte") and one more controversial (the "bailey").[23] The arguer first states the controversial position, but when challenged, states that they are advancing the modest position.[24][25]

Fallacy of accent – changing the meaning of a statement by not specifying on which word emphasis falls.