Jumping into Metaphysics for a short while, we’ve clarified the object of Logic by discussing the difference between real being (i.e., ens reale or mind-independent being) and being of the reason (i.e., ens rationis or mind-dependent being). We saw that beings of the reason, which are understood precisely because of their inability to exist, are of two kinds depending on their opposition to real existence: negation and relation. We saw that some relations of reason have foundations in something insofar as that thing exists in reality, while some relations of reason have foundations in something insofar as that thing exists in intellectual knowledge: these latter we call second intentions, and it is these that we are concerned with in Logic. We said that these second intentions vary according to the different ways that a subject can be known. When it is known by simple apprehension we have such second intentions as definition, term, extension, etc. When it is known by judgment we have such intentions as being the subject of predication, supposition, contradiction, perseity, etc. When it is known by reasoning we have such second intentions as induction and deduction, syllogistic moods and figures, demonstration, dialectics, etc.
With the goal of explaining the various kinds of certitude that a valid syllogism can present, we are ultimately aiming at demonstration; this means that we must begin by looking at those various second intension or logical relations which are necessary in order to construct a demonstrative syllogism. Since definition is always the middle term in demonstration, we must first examine definition; since definition isn’t possible without understanding genus, species, difference, property, and accident we must begin with the relations of the predicables; and since the predicables are the five possible logical relations (second intentions) of the logical universal, we will first begin by examining the logical universal and the ways it can be related to its logical inferiors. Once we’ve examined the perfect process of reason, demonstration, we will examine the various ways that it can fall short of this: scil., dialectics and the lesser degrees of certitude.