And things that are equal to one and the same thing are equal to one another, and so forth. Yet all such propositions are merely mental constructs; as universals they have no existence outside the mind.
It has therefore become clear that the demonstrative universal propositions whose universality they insist must be granted—and which they employ in their syllogisms—are never applied to any concrete existent. They function only with respect to notional entities. Consequently, demonstrative syllogism cannot yield knowledge of particular, real-world things—and that is precisely what we intended to prove.
No proof obliges them to confine the divisions of being to the ten categories.
Indeed, they possess no certain knowledge of any exhaustive enumeration of the modes of existence. Aristotle restricted the genera of existents to ten categories—substance, quantity, quality, where, when, position, acting, being acted upon, and possession—and someone later gathered them into two lines of verse:
Zaid—the tall, the black, son of Mālik—
Yesterday, within his house, lay reclining;
A sword was in his hand; he drew it, it was drawn—
Behold the ten categories, and naught beside them.
From the moment the First Teacher confined existence to substance and the nine accidents, they themselves conceded that there is no way to verify the soundness of this enumeration; some even reduced the kinds of accidents to three, while others offered different schemes.
Nor do they have any proof for restricting existents to five kinds of substance.
When they divided substance into Intellect, soul, matter, form, and body—and then split body into celestial and elemental, further dividing the elemental into the four simple bodies (the elements) and the composites of animal, plant, and mineral—this classification, besides being wrong in what it affirms, offers no certainty that all existents are encompassed by it. They cannot prove that bodies are limited to the celestial and the elemental, and they readily admit the possibility of bodies beyond