In logic and philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (ˌnɒn_ˈsɛkwɪtər; Latin for "[it] does not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a formal fallacy is a fallacy where deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic.
While a logical argument is a non sequitur if, and only if, it is invalid, the term "non sequitur" typically refers to those types of invalid arguments which do not constitute formal fallacies covered by particular terms (e.g., affirming the consequent). In other words, in practice, "non sequitur" refers to an unnamed formal fallacy.
A special case is a mathematical fallacy, an intentionally invalid mathematical proof, often with the error subtle and somehow concealed. Mathematical fallacies are typically crafted and exhibited for educational purposes, usually taking the form of spurious proofs of obvious contradictions.
A formal fallacy is contrasted with an informal fallacy which may have a valid logical form and yet be unsound because one or more premises are false. A formal fallacy; however, may have a true premise, but a false conclusion.
Prior Analytics is Aristotle's treatise on deductive reasoning and the syllogism. The standard Aristotelian logical fallacies are:
Fallacy of four terms (Quaternio terminorum);
Fallacy of the undistributed middle;
Fallacy of illicit process of the major or the minor term;
Affirmative conclusion from a negative premise.
Other logical fallacies include:
The self-reliant fallacy
In philosophy, the term logical fallacy properly refers to a formal fallacy—a flaw in the structure of a deductive argument, which renders the argument invalid.
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Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a
An argument is a series of sentences, statements or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion. Arguments are intended to determine or show the degree of truth or acceptability of another statement called a conclusion. Arguments can be studied from three main perspectives: the logical, the dialectical and the rhetorical perspective.
The fallacy of the undistributed middle (non distributio medii) is a formal fallacy that is committed when the middle term in a categorical syllogism is not distributed in either the minor premise or the major premise. It is thus a syllogistic fallacy. In classical syllogisms, all statements consist of two terms and are in the form of "A" (all), "E" (none), "I" (some), or "O" (some not). The first term is distributed in A statements; the second is distributed in O statements; both are distributed in "E" statements, and none are distributed in I statements.
Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the form of the argument, as is the case for formal fallacies, but can also be due to their content and context. Fallacies, despite being incorrect, usually appear to be correct and thereby can seduce people into accepting and using them. These misleading appearances are often connected to various aspects of natural language, such as ambiguous or vague expressions, or the assumption of implicit premises instead of making them explicit.
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