Aristotle offers arguments that resolve the valid syllogisms to various first figure syllogisms (Prior Analytics I.7). He further argues that the particular first figure forms, both negative and affirmative (i.e. "Darii" and "Ferio") can be resolved to the universal negative of the first figure ("Celarent") by contradiction and reductio. Thus, of the fourteen valid forms, ten resolve directly or indirectly to "Celarent" and two resolve to "Barbara" (they are both negative: "Baroco" and "Bocardo"). However, there seems to be no resolution of "Celarent" to "Barbara." However, one can offer the following arguments that the "perfection" of these figures, that the mind can immediately grasp the necessity of the conclusion, by resolving them to the principle of contradiction. Furthermore, perhaps, we have a from these arguments an argument that the negative does resolve to the affirmative universal figure.

The necessity of the conclusion from the "Celarent" form is per se notum because "Celarent" is a form of speech that sets down the negation (not-being) of a predicate whole from a subject whole, which is in turn the predicate whole of a subject part, but such a form appeals to the negative side of the principle of contradiction, which is per se notum. "Celarent" also appeals to the principle that the whole is greater than the part.

The necessity of the conclusion from the "Barbara" form is per se notum because "Barbara" is a form of speech that sets down the affirmation (being) of a predicate whole of a subject whole, which subject whole is predicate to a subject part, but such a form appeals to the positive side of the principle of contradiction, which is per se notum. Likewise, this form utilizes the first principle that the whole is greater than or contains the part.

However, being is prior to non-being in notion, and therefore affirmation (saying of something that it is) is prior to negation (saying of something that it is not) in notion. Thus the necessity of "Celarent" depends upon that of "Barbara."

I apologize for the dirty word in the title. These arguments are actually attempting to be a part of metaphysics.