As for the “preventer of absence,” it hinges on contradiction and necessary implication, for two contradictories cannot both be absent; hence it blocks the possibility of their simultaneous non-existence. Still, its consequent clause—“the existence of one thing and the non-existence of the other”—is not identical to saying “the existence and non-existence of the same thing.” Now, the existence of one thing alongside the non-existence of another may indeed involve a necessary connection between the two, even though they cannot both be absent; for if they were, both existence and non-existence would disappear together.

The core of reasoning rests on the material content of knowledge, not on the outward form of the syllogism:

In sum, nothing exists without a concomitant that never departs from it, nor without an opposite whose presence negates it. One therefore infers a thing’s existence from the presence of its concomitant, and its non-existence from the disappearance of that concomitant.

Likewise, one infers its non-existence from the presence of its opposite, and its existence from the absence of that opposite—provided the matter is restricted to these two, so that their joint absence is impossible just as their joint presence is impossible.

Such inference arises from knowing a thing’s states, its implicants, and its concomitants. Once the innate disposition apprehends this, it may articulate it through various expressions and cast it into many argumentative molds; none of these is confined to the single form they lay down for the syllogism, much less to what they call “demonstration.” For demonstration, they stipulate a specific material—namely the propositions they list—thereby excluding from the primaries what they label “imaginaries” and what they label “commonly accepted propositions.” Yet the judgment of the innate disposition in favor of these two—especially the so-called “imaginaries”—is stronger than its assent to many of the “certainties” they choose as the material of demonstration.

I have treated this at length, citing their own statements, exposing their contradictions, and showing that what they discard would strip us of the very means by which we attain the noblest sciences, both theoretical and practical. Left in their hands is nothing but constructs devised in the mind, without any reality in the external world. Were this the place to quote their exact words and my rebuttals, I would have done so; but I have set all of that forth in its proper place within the discussions of the universal and divine sciences, for these are the matters truly sought.

As for the present discussion of logic, it only arose because they claimed that it is a legalistic instrument whose careful observance protects the mind from