A fallacy is the use of invalid or otherwise faulty reasoning in the construction of an argument that may appear to be well-reasoned if unnoticed. The term was introduced in the Western intellectual tradition by the Aristotelian De Sophisticis Elenchis.
Fallacies in reasoning may be invoked intentionally to manipulate or persuade by deception, unintentionally because of human limitations such as carelessness, cognitive or social biases and ignorance, or potentially due to the limitations of language and understanding of language. These delineations include not only the ignorance of the right reasoning standard but also the ignorance of relevant properties of the context. For instance, the soundness of legal arguments depends on the context in which they are made.
A fallacy does not necessarily lead to a false conclusion: it may accidentally be a result of invalid reasoning. An example is the fallacy of affirming the consequent.
Fallacies are commonly divided into "formal" and "informal". A formal fallacy is a flaw in the structure of a deductive argument that renders the argument invalid, while an informal fallacy originates in an error in reasoning other than an improper logical form. Arguments containing informal fallacies may be formally valid, but still fallacious.
A special case is a mathematical fallacy, an intentionally invalid mathematical proof with a concealed, or subtle, error. Mathematical fallacies are typically crafted and exhibited for educational purposes, usually taking the form of false proofs of obvious contradictions.
Overview Fallacies are types of erroneous reasoning that render arguments logically unsound. According to The New Handbook of Cognitive Therapy Techniques, they include "unsubstantiated assertions that are often delivered with a conviction that makes them sound as though they are proven facts". Informal fallacies, in particular, are frequently found in mass media such as television and newspapers. Understanding fallacies may allow one to recognize them in either one's own or others' writing. Avoiding fallacies may help improve one's ability to produce sound arguments.
It can be difficult to evaluate whether an argument is fallacious, as arguments exist along a continuum of soundness and an argument that has several stages or parts might have some sound sections and some fallacious ones. Moreover, whether a specific argument is fallacious often depends on the content rather than the form of the argument. An example is a probabilistically valid instance of the formally invalid argument form of denying the antecedent or affirming the consequent. Thus, "fallacious arguments usually have the deceptive appearance of being good arguments, because for most fallacious instances of an argument form, a similar but non-fallacious instance can be found". Evaluating an instance of an argument as fallacious is therefore often a matter of evaluating the context of the argument.
Recognizing fallacies in everyday arguments may be difficult since arguments are often embedded in rhetorical patterns that obscure the logical connections between statements. Informal fallacies may also exploit the emotional, intellectual, or psychological weaknesses of the audience. Recognizing fallacies can develop reasoning skills to expose the weaker links between premises and conclusions to better discern between what appears to be true and what is true.
Argumentation theory provides a different approach to understanding and classifying fallacies. In the pragma-dialectical theory, for instance, an argument is regarded as an interactive protocol between individuals who attempt to resolve their disagreement on the merits of a case. The protocol consists of normative rules of interaction, and violations of these rules are considered fallacies because they frustrate the attempt at resolving the disagreement.
Fallacies are used in place of valid reasoning to communicate a point with the intention to persuade. Examples in the mass media today include but are not limited to propaganda, advertisements, politics, newspaper editorials, and opinion-based news shows.
Systems of classification Fallacies are generally classified strictly by either their structure or their content, such as by classifying them as formal fallacies or informal fallacies, respectively. The classification of informal fallacies may be subdivided into categories such as linguistic, relevance through omission, relevance through intrusion, and relevance through presumption. Alternatively, fallacies may be classified by the process by which they occur, such as material fallacies (content), verbal fallacies (linguistic), and formal fallacies (error in inference). In turn, material fallacies may be placed into the more general category of informal fallacies. Verbal fallacies may be placed in either formal or informal classifications: Compare equivocation, which is a word- or phrase-based ambiguity, to the fallacy of composition, which is premise- and inference-based ambiguity.
Greek logic The Greek philosopher Aristotle (384–322 BC) was the first to systematize logical errors into a list to make it easier to refute an opponent's thesis and thus win an argument. Aristotle's Sophistical Refutations () identifies thirteen fallacies. He divided them up into two major types: linguistic fallacies and non-linguistic fallacies, some of which depend on language and others that do not. These fallacies are called verbal fallacies and material fallacies, respectively. A material fallacy is an error in what the arguer is talking about, while a verbal fallacy is an error in how the arguer is talking. Verbal fallacies are those in which a conclusion is obtained by improper or ambiguous use of words. An example of a language dependent fallacy is given as a debate as to who in humanity are learners: the wise or the ignorant. A language-independent fallacy is, for example: "Coriscus is different from Socrates." "Socrates is a man." "Therefore, Coriscus is different from a man."
Indian logic Indian logicians took great pains to identify fallacies in arguments. An influential collection of texts on logic and reason, the Nyāya Sūtras, attributed to Aksapada Gautama, variously estimated to have been composed between the 6th century BCE and the 2nd century CE, lists in its theory of inference five such reasons used in an argument that was further developed by later logicians.
Asiddha: It is the unproved reason that results in this fallacy. [Paksadharmata] Savyabhichara: This is the fallacy of irregular reason. Satpratipaksa: Here the reason is contradicted by another reason. If both have equal force, then nothing follows. 'Sound is eternal, because it is audible', and 'Sound is non-eternal, because it is produced'. Here 'audible' is counterbalanced by 'produced' and both are of equal force. Badhita: When another proof (as by perception) definitely contradicts and disproves the middle term (reason). 'Fire is cold because it is a substance'. Viruddha: Instead of proving something it is proving the opposite. 'Sound is eternal because it is produced'.
Whately's grouping English scholar and theologian Richard Whately (1787–1863) defines a fallacy broadly as, "any argument, or apparent argument, which professes to be decisive of the matter at hand, while in reality it is not".
Whately divided fallacies into two groups: logical and material. According to Whately, logical fallacies are arguments where the conclusion does not follow from the premises. Material fallacies are not logical errors because the conclusion follows from the premises. He then divided the logical group into two groups: purely logical and semi-logical. The semi-logical group included all of Aristotle's sophisms except ignoratio elenchi, petitio principii, and non causa pro causa, which are in the material group.
Other systems of classification Other famous methods of classifying fallacies 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. J. S. Mill discussed the subject in book five of his Logic, and Jeremy Bentham's Book of Fallacies (1824) contains valuable remarks.
Formal fallacy
A formal fallacy, deductive fallacy, logical fallacy or non sequitur (Latin for "it does not follow") is a flaw in the structure of a deductive argument that renders the argument invalid. The flaw can be expressed in the standard system of logic. Such an argument is always considered to be wrong. The presence of the formal fallacy does not imply anything about the argument's premises or its conclusion. Both may actually be true or may even be more probable as a result of the argument, but the deductive argument is still invalid because the conclusion does not follow from the premises in the manner described.
Even non-deductive arguments can be said to be fallacious: for example, an inductive argument that incorrectly applies principles of probability or causality. But "since deductive arguments depend on formal properties and inductive arguments don't, formal fallacies apply only to deductive arguments".
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 error or logical fallacy similarly invalidates the deductive guarantee. Both the argument and all its premises must be true for a conclusion to be true.
The term non sequitur denotes a general formal fallacy, often meaning one that does not belong to any named subclass of formal fallacies, like affirming the consequent.
Fallacy fork Maarten Boudry and others have argued that formal, deductive fallacies rarely occur in real life and that arguments that would be fallacious in formally deductive terms are not necessarily so when context and prior probabilities are taken into account, thus making the argument defeasible and/or inductive. Boudry coined the term fallacy fork. For a given fallacy, one must either characterize it by means of a deductive argumentation scheme, which rarely applies (the first prong of the fork), or one must relax definitions and add nuance to take the actual intent and context of the argument into account (the other prong of the fork). To argue, for example, that one became nauseated after eating a mushroom because the mushroom was poisonous could be an example of the post hoc ergo propter hoc fallacy.
Informal fallacy
In contrast to a formal fallacy, an informal fallacy originates from a reasoning error other than a flaw in the logical form of the argument. A deductive argument containing an informal fallacy may be formally valid, but still remain rationally unpersuasive. Nevertheless, informal fallacies apply to both deductive and non-deductive arguments.
Though the form of the argument may be relevant, fallacies of this type are "types of mistakes in reasoning that arise from the mishandling of the content of the propositions constituting the argument".
Faulty generalization A special subclass of the informal fallacies is the set of faulty generalizations, also known as inductive fallacies. Here, the most important issue concerns inductive strength or methodology (for example, statistical inference). In the absence of sufficient evidence, drawing conclusions based on induction is unwarranted and fallacious. With the backing of sufficient amounts of the right type of empirical evidence, however, the conclusions may become warranted and convincing (at which point the arguments are no longer considered fallacious).
Hasty generalization