Subalternation

Subalternation refers to the relationship between universal and particular propositions. The truth of the universal proposition implies the truth of the particular. The inverse of a proposition changes the quality of the statement instead of changing its quantity.

Example

If E is true, O has to be true. If E is false, nothing can be inferred about O. The inference has to originate from the truth of the particular proposition, and a subalternate proposition cannot be inferred from an untrue particular proposition.

The contrapositive of the universal proposition "all English majors are good writers" is "all non-good writers are English majors." This statement is the contrapositive of the universal proposition because the subject is replaced with the predicate. (See: naming propositions).

"All dogs are pets" is a universal proposition that does not bear the same meaning as the particular proposition "some dogs are pets." Despite this, the two statements are not contrapositives.

Traditional and modern squares of opposition

``` (t) (f)

 A---E
 |\ /|
 | X |
 |/ \|
 I---O

(t) (f) ```

Practice

Identifying subalternate propositions is essential to quantifying the formal logic of a proposition and, in turn, identifying logical fallacies.

It is most useful for a proposition to be written in standard form for identifying contrapositives.