Subalternation[1][2] is an immediate inference which is only made between A (All S are P) and I (Some S are P) categorical propositions and between E (No S are P) and O (Some S are not P) categorical propositions of the traditional square of opposition. If the A proposition is true we may immediately infer that I is true. If the E proposition is true we may immediately infer that O is true. Conversely, If the I is false, we can immediately infer that A is also false. However, if the A proposition is false that will not tell us anything about the truth value of the I proposition. Similarly, if the I proposition is false, that will not tell us anything about the truth value of the E proposition.

An example of a superalternation is "If all leopards are mammals, then some leopards are mammals."

When the inference is misapplied, the syllogistic fallacy is called an illicit subalternation.

Reference

  1. ^ Hurley, Patrick (1991). A Concise Introduction to Logic 4th edition. Wadsworth Publishing. p. 192. ((cite book)): Cite has empty unknown parameter: |coauthors= (help)
  2. ^ Copi, Irving M.; Cohen, Carl (2005). Introduction to Logic. Prentice Hall. p. 189. ((cite book)): Invalid |ref=harv (help)