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.

Argument from incredulity – when someone can't imagine something to be true, and therefore deems it false, or conversely, holds that it must be true because they can't see how it could be false. Argument to moderation (false compromise, middle ground, fallacy of the mean, ) – assuming that a compromise between two positions is always correct. 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. Correlative-based fallacies Suppressed correlative – a correlative is redefined so that one alternative is made impossible (e.g., "I am not fat because I am thinner than John."). Divine fallacy (argument from incredulity) – arguing that, because something is so phenomenal or amazing, it must be the result of superior, divine, alien or paranormal agency. Doorman fallacy – Reducing a role to its most basic visible/on-paper task without considering the full scope of tangible and intangible value that exists just under the surface, and use that to determine efficiency, cost, and redundancy. Coined by behavioral economist Rory Sutherland in his 2019 book Alchemy. A variant of Chesterton's fence. 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. Ecological fallacy – inferring about the nature of an entity based solely upon aggregate statistics collected for the group to which that entity belongs. Equivocation – using a term with more than one meaning in a statement without specifying which meaning is intended. Ambiguous middle term – using a middle term with multiple meanings. Definitional retreat – changing the meaning of a word when an objection is raised. 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"). The arguer first states the controversial position, but when challenged, states that they are advancing the modest position. Fallacy of accent – changing the meaning of a statement by not specifying on which word emphasis falls. Persuasive definition – purporting to use the "true" or "commonly accepted" meaning of a term while, in reality, using an uncommon or altered definition.

Etymological fallacy – assuming that the original or historical meaning of a word or phrase is necessarily similar to its actual present-day usage. Fallacy of composition – assuming that something true of part of a whole must also be true of the whole. Fallacy of division – assuming that something true of a composite thing must also be true of all or some of its parts. False attribution – appealing to an irrelevant, unqualified, unidentified, biased or fabricated source in support of an argument. Fallacy of quoting out of context (contextotomy, contextomy; quotation mining) – selective excerpting of words from their original context to distort the intended meaning. False authority (single authority) – using an expert of dubious credentials or using only one opinion to promote a product or idea. Related to the appeal to authority. False dilemma (false dichotomy, fallacy of bifurcation, black-or-white fallacy) – two alternative statements are given as the only possible options when, in reality, there are more. False equivalence – describing two or more statements as virtually equal when they are not. Feedback fallacy – believing in the objectivity of an evaluation to be used as the basis for improvement without verifying that the source of the evaluation is a disinterested party. Goomba fallacy - treating separate statements of opinion made by different members of a group as if they were collectively held by that group, especially if the statements are contradictory. Often used with reference to fallacious collective attribution of hypocrisy, inconsistency, or flip-flopping to groups, especially online communities. The Goomba fallacy is a subset of the association fallacy. Historian's fallacy – assuming that decision-makers of the past had identical information as those subsequently analyzing the decision. This is not to be confused with presentism, in which present-day ideas and perspectives are anachronistically projected into the past. Historical fallacy – believing that certain results occurred only because a specific process was performed, though said process may actually be unrelated to the results."The Reflex Arc Concept in Psychology", John Dewey, The Psychological Review, Vol. III. No. 4. July 1896. p. 367 Baconian fallacy – supposing that historians can obtain the "whole truth" via induction from individual pieces of historical evidence. The "whole truth" is defined as learning "something about everything", "everything about something", or "everything about everything". In reality, a historian "can only hope to know something about something". Homunculus fallacy – using a "middle-man" for explanation; this sometimes leads to regressive middle-men. It explains a concept in terms of the concept itself without explaining its real nature (e.g.: explaining thought as something produced by a little thinker – a homunculus – inside the head simply identifies an intermediary actor and does not explain the product or process of thinking). – arguing that, if experts in a field of knowledge disagree on a certain point within that field, no conclusion can be reached or that the legitimacy of that field of knowledge is questionable.Habick, Timothy. "Disinformative Linguistics: Using Linguistic Science for Unethical Purposes.", in The Routledge Handbook of Ethics in Forensic Linguistics. Routledge, 2026. 117-129. If-by-whiskey – an argument that supports both sides of an issue by using terms that are emotionally sensitive and ambiguous. Incomplete comparison – insufficient information is provided to make a complete comparison. Intentionality fallacy – the insistence that the ultimate meaning of an expression must be consistent with the intention of the person from whom the communication originated (e.g. a work of fiction that is widely received as a blatant allegory must necessarily not be regarded as such if the author intended it not to be so). Revised and republished in