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In logic and philosophy, a formal fallacy[a] is a pattern of reasoning with a flaw in its logical structure (the logical relationship between the premises and the conclusion). In other words:
- It is a pattern of reasoning in which the conclusion may not be true even if all the premises are true.
- It is a pattern of reasoning in which the premises do not entail the conclusion.
- It is a pattern of reasoning that is invalid.
- It is a fallacy in which deduction goes wrong, and is no longer a logical process.
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. The term 'logical fallacy' is sometimes used in everyday conversation, and refers to a formal fallacy.
Propositional logic,[2] for example, is concerned with the meanings of sentences and the relationships between them. It focuses on the role of logical operators, called propositional connectives, in determining whether a sentence is true. An error in the sequence will result in 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" is synonymous with "a logical argument 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.
- ^ 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.
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