Logically Fallacious: The Ultimate Collection of Over 300 Logical Fallacies (Academic Edition) (Dr. Bo's Critical Thinking Series)

by Bo Bennett

Illicit Contraposition New Terminology: Illicit: Forbidden by the rules, or in our cases, by the laws of logic. Contraposition: Switching the subject and predicate terms of a categorical proposition, and negating each. Description: A formal fallacy where switching the subject and predicate terms of a categorical proposition, then negating each, results in an invalid argument form. The examples below make this more clear. This is a fallacy only for type “E” and type “I” forms, or forms using the words “no” and “some,” respectively. Logical Forms: No S are P. Therefore, no non-P are non-S. Some S are P. Therefore, some non-P are non-S. Example #1: No Catholics are Jews. Therefore, no non-Jews are non-Catholics. (contraposition) Explanation: By definition, no Catholics are Jews (using type “E” form here)—clear enough. Now let’s take the contraposition of that proposition by switching the placement of “Catholics” and “Jews,” and negating each, and we can see we have a false proposition. “No non-Jews are non-Catholics” clearly does not mean the same thing as “No Catholics are Jews.” In this example, the premise is true but the conclusion is false (I am a non-Jew and a non-Catholic, and statistically speaking, you probably are too.) Example #2: Some dogs bark. Therefore, some non-barking things are non-dogs. (contraposition) Explanation: We now see the type “I” form in action, stating, “Some” dogs bark. This is true, but that really does not matter in determining what form of ...