A fallacy is the use of invalid or otherwise faulty reasoning in the construction of an argument[1][2] that may appear to be well-reasoned if unnoticed.
Mathematical fallacies are typically crafted and exhibited for educational purposes, usually taking the form of false proofs of obvious contradictions.
[7] 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".
An example is a probabilistically valid instance of the formally invalid argument form of denying the antecedent or affirming the consequent.
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.
Examples in the mass media today include but are not limited to propaganda, advertisements, politics, newspaper editorials, and opinion-based news shows.
[17] 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.
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.
divided fallacies into four Idola (Idols, i.e. False Appearances), which summarize the various kinds of mistakes to which the human intellect is prone.
An ecological fallacy is committed when one draws an inference from data based on the premise that qualities observed for groups necessarily hold for individuals; for example, "if countries with more Protestants tend to have higher suicide rates, then Protestants must be more likely to commit suicide".
[26] The observational interpretation fallacy is a cognitive bias that occurs exclusively in the medical field, leading to the mistaken interpretation of observed associations as causal relationships, negatively impacting medical guidelines, clinical decisions, and healthcare practices, potentially compromising patient safety.
[citation needed] Maarten Boudry[27] and others[28] 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.
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).
[30] Hasty generalization is described as making assumptions about a whole group or range of cases based on a sample that is inadequate (usually because it is atypical or just too small).
Stereotypes about people ("frat boys are drunkards", "grad students are nerdy", "women don't enjoy sports", etc.)
Hasty generalization often follows a pattern such as: While never a valid logical deduction, if such an inference can be made on statistical grounds, it may nonetheless be convincing.
At this point, the actor potentially loses control over the direction of the arguments, thus leading to a ‘fatal’ outcome.
[37] The reason for the straw man argument to be fallacious originates from the problem of how to deal with natural discourse.
The ancient Greek Sophist Protagoras was one of the first thinkers to propose that humans can generate reliable measurements through his "human-measure" principle and the practice of dissoi logoi (arguing multiple sides of an issue).
[43] For example, anchoring fallacies can occur when unwarranted weight is given to data generated by metrics that the arguers themselves acknowledge are flawed.
For example, the limitations of the journal impact factor (JIF) are well documented,[44] and even JIF pioneer Eugene Garfield notes that, "while citation data create new tools for analyses of research performance, it should be stressed that they supplement rather than replace other quantitative and qualitative indicators".
[45] To the extent that arguers jettison the acknowledged limitations of JIF-generated data in evaluative judgments or leave behind Garfield's "supplement rather than replace" caveat, they commit anchoring fallacies.
In any context, including academic debate, a conversation among friends, political discourse, advertising, or comedic purposes, the arguer may use fallacious reasoning to try to persuade the listener or reader, by means other than offering relevant evidence, that the conclusion is true.
Wes Boyer and Samuel Stoddard have written a humorous essay teaching students how to be persuasive by means of a whole host of informal and formal fallacies.
[49] When someone uses logical fallacies intentionally to mislead in academic, political, or other high-stakes contexts, the breach of trust calls into question the authority and intellectual integrity of that person.
[50] According to the pragmatic theory,[51] a fallacy can be either a heuristic error or a ploy used intentionally to unfairly win an argument.
The pragmatic theory finds its roots in the Aristotelian conception of a fallacy as a sophistical refutation but also supports the view that many of the types of arguments traditionally labeled as fallacies are in fact reasonable techniques of argumentation that can be used, in many cases, to support legitimate goals of dialogue.
Hence, under the pragmatic approach, each case needs to be analyzed individually to determine whether the argument is fallacious or reasonable.