6.2 Subalternates and the Square of Opposition - From "The Reasonable Person" by Mark Grannis

Continuing with completing the square of opposition we need to add, what are called, "subalternates". These are the relations between A and I, as well as E and O. Grannis defines them as:

"... any two propositions that have the same subject and predicate and the same quality but differ in quantity." 

And so A and I share an affirmative property, but differ in quantity, while E and O share a negative property, but differ in quantity. 

With subalternates they "never imply opposite truth values; they either imply nothing at all or else they imply identical truth values." 

Dictum De Omni

Between A and I. "Whatever is affirmed universally of a certain concept is affirmed of every inferior within the extension of that concept." 

Dictum De Nullo

Between E and O. "Whatever is denied universally of a certain concept is denied of every inferior within the extension of that concept." 

What's common here is that "we can only imply truth from the universal to the particular, not from the particular to the universal." 

Going the other direction we can say: "A true I proposition might not imply anything about its subalternate, but a false I proposition, like 'Some ducks speak Latin,' does imply that the subalternate A proposition, 'All ducks speak Latin,' must also be false." 

From a negative particular we can draw a negative universal. 

All the Relations in the Square

Here's a summary: 

"Contradictories always contradict

True contraries falsify

False subcontraries verify

Subalternates descend with truth and rise with falsity"