Fallacy

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 may be committed 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.

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.

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.