Editing Rule of inference (section)

== Formal fallacies ==
{{main|Formal fallacy}}
While rules of inference describe valid patterns of deductive reasoning, formal fallacies are invalid argument forms that involve [[Fallacy|logical errors]]. The premises of a formal fallacy do not properly support its conclusion: the conclusion can be false even if all premises are true. Formal fallacies often mimic the structure of valid rules of inference and can thereby mislead people into unknowingly committing them and accepting their conclusions.<ref>{{multiref | {{harvnb|Copi|Cohen|Flage|2016|pp=46–47, 227}} | {{harvnb|Cook|2009|p=123}} | {{harvnb|Hurley|Watson|2018|pp=125–126, 723}} }}</ref>

The formal fallacy of [[affirming the consequent]] concludes <math>P</math> from the premises <math>P \to Q</math> and <math>Q</math>, as in the argument "If Leo is a cat, then Leo is an animal. Leo is an animal. Therefore, Leo is a cat." This fallacy resembles valid inferences following ''modus ponens'', with the key difference that the fallacy swaps the second premise and the conclusion.<ref>{{multiref | {{harvnb|Copi|Cohen|Flage|2016|pp=224, 439}} | {{harvnb|Hurley|Watson|2018|pp=385–386, 720}} }}</ref> The formal fallacy of [[denying the antecedent]] concludes <math>\lnot Q</math> from the premises <math>P \to Q</math> and <math>\lnot P</math>, as in the argument "If Laya saw the movie, then Laya had fun. Laya did not see the movie. Therefore, Laya did not have fun." This fallacy resembles valid inferences following ''modus tollens'', with the key difference that the fallacy swaps the second premise and the conclusion.<ref>{{multiref | {{harvnb|Copi|Cohen|Flage|2016|pp=46, 228, 442}} | {{harvnb|Hurley|Watson|2018|pp=385–386, 722}} }}</ref> Other formal fallacies include [[affirming a disjunct]], the [[existential fallacy]], and the [[fallacy of the undistributed middle]].<ref>{{multiref | {{harvnb|Copi|Cohen|Flage|2016|pp=443, 449}} | {{harvnb|Hurley|Watson|2018|pp=723, 728}} | {{harvnb|Cohen|2009|p=[https://books.google.com/books?id=4aGIsKmkODgC&pg=PA254 254]}} }}</ref>