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In logic and philosophy, a **formal fallacy**^{[a]} 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.^{[2]} It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion.^{[3]} Thus, a formal fallacy is a fallacy in which 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.

"Some of your key evidence is missing, incomplete, or even faked! That proves I'm right!"^{[4]}

"The vet can't find any reasonable explanation for why my dog died. See! See! That proves that you poisoned him! There’s no other logical explanation!"^{[5]}

In the strictest sense, a logical fallacy is the incorrect application of a valid logical principle or an application of a nonexistent principle:

- Most Rimnars are Jornars.
- Most Jornars are Dimnars.
- Therefore, most Rimnars are Dimnars.

This is fallacious.

Indeed, there is no logical principle that states:

- For some x, P(x).
- For some x, Q(x).
- Therefore, for some x, P(x) and Q(x).

An easy way to show the above inference as invalid is by using Venn diagrams. In logical parlance, the inference is invalid, since under at least one interpretation of the predicates it is not validity preserving.

People often have difficulty applying the rules of logic. For example, a person may say the following syllogism is valid, when in fact it is not:

- All birds have beaks.
- That creature has a beak.
- Therefore, that creature is a bird.

"That creature" may well be a bird, but the conclusion does not follow from the premises. Certain other animals also have beaks, for example: an octopus and a squid both have beaks, some turtles and cetaceans have beaks. Errors of this type occur because people reverse a premise.^{[6]} In this case, "All birds have beaks" is converted to "All beaked animals are birds." The reversed premise is plausible because few people are aware of any instances of *beaked creatures* besides birds—but this premise is not the one that was given. In this way, the deductive fallacy is formed by points that may individually appear logical, but when placed together are shown to be incorrect.

In everyday speech, a non sequitur is a statement in which the final part is totally unrelated to the first part, for example:

Life is life and fun is fun, but it's all so quiet when the goldfish die.

—West with the Night, Beryl Markham^{[7]}

- List of fallacies – List of faulty argument types
- Apophasis – Stating something by saying the opposite
- Cognitive bias – Systematic pattern of deviation from norm or rationality in judgment
- Demagogue – Politician or orator who panders to fears and emotions of the public
- Fallacies of definition – Ways in which a term may be poorly defined
- False statement – Statement contradicted by facts and reality
- Mathematical fallacy, also known as Invalid proof – Certain type of mistaken proof
*Modus tollens*– Rule of logical inference- Paradox – Statement that apparently contradicts itself
- Relevance logic – mathematical logic system that imposes certain restrictions on implication
- Scientific misconceptions – False beliefs about science
- Sophist – Teacher in ancient Greece (5th century BC)
- Soundness – Term in logic and deductive reasoning
- Subverted support – Logical fallacy of explanation

**^**Barker, Stephen F. (2003) [1965]. "Chapter 6: Fallacies".*The Elements of Logic*(6th ed.). New York, NY: McGraw-Hill. pp. 160–169. ISBN 0-07-283235-5.**^**Gensler, Harry J. (2010).*The A to Z of Logic*. Rowman & Littlefield. p. 74. ISBN 9780810875968.**^**Labossiere, Michael (1995). "Description of Fallacies". Nizkor Project. Retrieved 2008-09-09.**^**"Master List of Logical Fallacies".*utminers.utep.edu*.**^**Daniel Adrian Doss; William H. Glover Jr.; Rebecca A. Goza; Michael Wigginton Jr. (17 October 2014).*The Foundations of Communication in Criminal Justice Systems*. CRC Press. p. 66. ISBN 978-1-4822-3660-6. Retrieved 21 May 2016.**^**Wade, Carole; Carol Tavris (1990). "Eight". In Donna DeBenedictis (ed.).*Psychology*. Laura Pearson (2 ed.). New York: Harper and Row. pp. 287–288. ISBN 0-06-046869-6.**^**Quoted in Hindes, Steve (2005).*Think for Yourself!: an Essay on Cutting through the Babble, the Bias, and the Hype*. Fulcrum Publishing. p. 86. ISBN 1-55591-539-6. Retrieved 2011-10-04.

- Bibliography

- Aristotle, On Sophistical Refutations,
*De Sophistici Elenchi*. - William of Ockham,
*Summa of Logic*(ca. 1323) Part III.4. - John Buridan,
*Summulae de dialectica*Book VII. - Francis Bacon, the doctrine of the idols in
*Novum Organum Scientiarum*, Aphorisms concerning The Interpretation of Nature and the Kingdom of Man, XXIIIff Archived 2020-02-14 at the Wayback Machine. - The Art of Controversy |
*Die Kunst, Recht zu behalten – The Art Of Controversy*(bilingual), by Arthur Schopenhauer - John Stuart Mill, A System of Logic – Raciocinative and Inductive. Book 5, Chapter 7, Fallacies of Confusion.
- C. L. Hamblin,
*Fallacies*. Methuen London, 1970. - Fearnside, W. Ward and William B. Holther, Fallacy: The Counterfeit of Argument, 1959.
- Vincent F. Hendricks,
*Thought 2 Talk: A Crash Course in Reflection and Expression*, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8 - D. H. Fischer,
*Historians' Fallacies: Toward a Logic of Historical Thought*, Harper Torchbooks, 1970. - Douglas N. Walton,
*Informal logic: A handbook for critical argumentation*. Cambridge University Press, 1989. - F. H. van Eemeren and R. Grootendorst,
*Argumentation, Communication and Fallacies: A Pragma-Dialectical Perspective*, Lawrence Erlbaum and Associates, 1992. - Warburton Nigel,
*Thinking from A to Z*, Routledge 1998. - Sagan, Carl,
*The Demon-Haunted World: Science As a Candle in the Dark*. Ballantine Books, March 1997 ISBN 0-345-40946-9, 480 pp. 1996 hardback edition: Random House, ISBN 0-394-53512-X

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