The fifth argument:

Concerning universal syllogistic reasoning—which consists in knowing that a predicate holds of every individual—we say: it is known, and they concede, that knowledge that certain predicates hold of certain individuals must be immediate. For if a conclusion requires two premises, the process must ultimately reach two premises known without recourse to two further premises; otherwise, it would entail circular reasoning or an infinite regress, both of which are invalid.

If two premises are known by the same means, there is no need for a syllogism. Consider, for example, knowing that every human being is an animal and that every animal is capable of sensation and voluntary movement. Knowing that every human being is capable of voluntary movement is clearer and more evident. Thus, if both premises are known by the same means and have already been established, neither needs to be demonstrated. If they are known by different means, someone who does not know one of them needs that premise demonstrated, but does not need a demonstration of the other, which he already knows. This is evident in every case posited. Their logic thus wastes time, multiplies senseless talk, and exhausts minds.

The sixth argument:

There is no doubt that the major premise is more general than the minor premise or equal to it in scope; it cannot be narrower. The conclusion is narrower than the major premise or equal to it in scope, and more general than the minor premise or equal to it; it cannot be narrower than the minor premise.

Sense perception first apprehends particulars, then proceeds from them to general propositions. It observes this human being, then that human being, and each one observed is capable of sensation and voluntary movement. We say, then: either knowledge of a general proposition is attained through a syllogism—in which case the syllogism must itself contain a general proposition. It would follow that a general proposition can be known only through another general proposition, which entails circular reasoning or an infinite regress. The process must therefore ultimately reach a universal proposition