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False Conversion Summary

(also known as: illicit conversion, [illicit] inductive conversion)

New Terminology:

Type “A” Logical Forms: A proposition or premise that uses the word, “all” or “every” (e.g., All P are Q)

Type “E” Logical Forms: A proposition or premise that uses the word, “none” or “no” (e.g., No P are Q)

Type “I” Logical Forms: A proposition or premise that uses the word, “some” (e.g., Some P are Q)

Type “O” Logical Forms: A proposition or premise that uses the terms, “some/not” (e.g., Some P are not Q)

Description: The formal fallacy where the subject and the predicate terms of the proposition are switched (conversion) in the conclusion, in a proposition that uses “all” in its premise (type “A” forms), or “some/not” (type “O” forms).

Logical Form:

All P are Q.

Therefore, all Q are P.

Some P are not Q.

Therefore, some Q are not P.

Example #1:

All Hollywood Squares contestants are bad actors.

Therefore, all bad actors are Hollywood Squares contestants.

Example #2:

Some people in the film industry do not win Oscars.

Therefore, some Oscar winners are not people in the film industry.

Explanation: It does not follow logically that just because all Hollywood Squares contestants are bad actors that all bad actors actually make it on Hollywood Squares.  Same form problem with the second example — but we used “some” and “are not”.

Exception: None, but remember that type “E” and type “I” forms can use conversion and remain valid.

No teachers are psychos.

Therefore, no psychos are teachers.

What Now: Remember that formal fallacies are often obscured by unstructured rants. Creating a formal argument from such rants is both an art and a science.

References:

Welton, J. (1896). A Manual of Logic. W. B. Clive.