# Subalternation

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 or originally, No S is P ) and O (Some S are not P or originally, Not every S is P) categorical propositions of the traditional square of opposition and the original square of opposition.[3] 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, as well as if O is false, then E is 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 E proposition is false, that will not tell us anything about the truth value of the O proposition.

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

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

## References

1. ^ Hurley, Patrick (1991). A Concise Introduction to Logic 4th edition. Wadsworth Publishing. p. 192.
2. ^ Copi, Irving M.; Cohen, Carl (2005). Introduction to Logic. Prentice Hall. p. 189.
3. ^ Parsons, Terence (2012). "The Traditional Square of Opposition". In Edward N. Zalta (ed.). The Stanford Encyclopedia of Philosophy (Fall 2012 ed.). 3-4.