It has thus become clear that the universal demonstrative propositions they employ in their syllogisms, whose universality must be known with certainty, are not applied to anything that actually exists, but only to things posited in the mind. They therefore cannot acquire knowledge of existing things through demonstrative syllogism. This is precisely the point to be established. For this reason, they have no knowledge of an exhaustive classification of everything that exists. Indeed, when Aristotle confined the genera of existing things to the “ten categories”—substance, quantity, quality, place, time, position, acting, being acted upon, possession, and relation—they agreed that there is no way to establish that this classification is exhaustive.

The second argument:

One may say: If every syllogism must contain a universal proposition, then that universal proposition must ultimately be known without a syllogism; otherwise, circularity and infinite regress would necessarily follow. Since they must therefore have universal propositions known without syllogism, we say:

Whenever our natural understanding knows a universal proposition about existing things without a syllogism, its knowledge of the particular instances falling under that proposition is stronger than its knowledge of the universal proposition itself. Examples include our statements: “One is half of two,” “A body cannot be in two places,” and “Two contraries cannot coexist.” Our natural understanding knows more firmly that this particular one is half of two than that every one is half of every two. The same applies to whatever individual instances may be supposed.

Thus, we say: the purpose of these universal propositions is either to acquire knowledge of what exists in external reality