A fallacy is an error in reasoning that undermines an argument's support for its conclusion. In academic usage, the term usually applies to arguments, although it is sometimes used more broadly for errors in reasoning in explanations, definitions, questions, or other forms of discourse. A fallacious argument may nevertheless have a true conclusion; the defect lies in the inadequate reasoning offered in support of it. Fallacies are commonly divided into formal and informal fallacies. A formal fallacy is a defect in an argument's logical form that makes a deductive argument invalid. Informal fallacies cannot ordinarily be identified from form alone, since their assessment depends on such factors as content, evidence, context, and the purpose of the argument. They are often grouped under headings such as relevance, ambiguity, presumption, faulty generalization, and faulty causal reasoning, although the classification and boundaries of individual fallacies vary among authors. Fallacies may be used deliberately to persuade, but they can also arise unintentionally through cognitive bias, ambiguity, or faulty inference. In deductive reasoning, a formal fallacy renders an argument invalid. In non-deductive reasoning, fallacious reasoning may make an argument weak, irrelevant, insufficiently supported, or otherwise inadequate without making its conclusion false.
Formal fallacies
A formal fallacy, or non sequitur, is an error in the argument's form.
Appeal to probability – taking something for granted because it would probably be the case (or might possibly be the case). 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. Base rate fallacy – making a probability judgement based on conditional probabilities, without taking into account the effect of prior probabilities. Conjunction fallacy – the assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them. Masked-man fallacy (illicit substitution of identicals) – the substitution of identical designators in a true statement can lead to a false one.
Propositional fallacies 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. 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. 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.
Quantification fallacies 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.
Syllogistic fallacies Logical fallacies that occur in categorical 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. Fallacy of four terms (quaternio terminorum) – a categorical syllogism that has four terms. Illicit major – a categorical syllogism that is invalid because its major term is not distributed in the major premise but distributed in the conclusion. Illicit minor – a categorical syllogism that is invalid because its minor term is not distributed in the minor premise but distributed in the conclusion. Negative conclusion from affirmative premises (illicit affirmative) – a categorical syllogism has a negative conclusion but affirmative premises. Fallacy of the undistributed middle – the middle term in a categorical syllogism is not distributed. Politician's syllogism 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
Informal fallacies – arguments that are logically unsound for lack of well-grounded premises.
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