Formal fallacy

"Logical fallacy" redirects here. For an argument problematic for any reason, see Fallacy.

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.

Common examples

Main article: List of fallacies

Venn diagram showing how axioms of "most animals in this zoo are birds" and "most birds can fly" need not mean that "most animals in this zoo can fly"

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

1. Most animals in this zoo are birds.
2. Most birds can fly.
3. Therefore, most animals in this zoo can fly.

This is fallacious: a zoo could have a large proportion of flightless birds.

Indeed, there is no logical principle that states:

1. For some x, P(x).
2. For some x, Q(x).
3. 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:

1. All birds have beaks.
2. That creature has a beak.
3. 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, such as turtles. Errors of this type occur because people reverse a premise.^[4] 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.

Special example

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.

Non sequitur in everyday speech

Main article: Non sequitur (literary device)

See also: Derailment (thought disorder)

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^[5]

See also

• Philosophy portal
• Psychology portal

• List of fallacies
• 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 – Logically self-contradictory statement
• Relevance logic – A kind of non-classical logic
• Scientific misconceptions – False beliefs about science
• Sophist – Teachers of 5th century BC Greece
• Soundness – Term in logic and deductive reasoning
• Subverted support – Logical fallacy of explanation

Notes

1. Also known as a deductive fallacy, logical fallacy, or a non sequitur (/ˌnɒn ˈsɛkwɪtər/; Latin for 'it does not follow').^[1]