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Inlogic andphilosophy, aformal fallacy[a] is a pattern ofreasoning renderedinvalid by a flaw in its logical structure.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 adeductiveargument that is invalid. The argument itself could have truepremises, but still have a falseconclusion.[3] Thus, a formal fallacy is afallacy in which deduction goes wrong, and is no longer alogical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic.
While a logical argument is anon 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 amathematical fallacy, an intentionally invalidmathematical 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 obviouscontradictions.
A formal fallacy is contrasted with aninformal fallacy which may have a validlogical form and yet beunsound because one or morepremises 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.
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"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:
This is fallacious.
Indeed, there is no logical principle that states:
An easy way to show the above inference as invalid is by usingVenn 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 followingsyllogism is valid, when in fact it is not:
"That creature" may well be a bird, but theconclusion does not follow from the premises. Certain other animals also have beaks, for example: anoctopus and asquid both have beaks, someturtles andcetaceans 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 ofbeaked 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]
