THAT THE DIVINE BEING CANNOT BE DETERMINED BY THE ADDITION OF SOME SUBSTANTIAL DIFFERENCE [Quod divinum esse non potest designari per additionem alicuius differentiae substantialis]
The online annotated edition states, "This and the next chapter go to show that the logical arrangement is inapplicable to God, by which genus and differentia together constitute the species or definition, as animal and rational make up man."
 We can likewise show from what we have said [viz., that God's essence is His own existence and that no incidental attributes exist in Him] that nothing can be added to the divine being to determine it with an essential determination, as a genus is determined by its differences.
 Nothing can be in act unless everything that determines its substantial act of being exists [Impossibile est enim aliquid esse in actu nisi omnibus existentibus quibus esse substantiale designatur]. Thus, there cannot be an actual animal unless it be a rational or an irrational animal. Hence, the Platonists themselves, in positing the Ideas, did not posit self-existing Ideas of genera, which are determined to the being of their species through essential differences; rather, they posited self-existing Ideas solely of species, which for their determination need no essential differences. If, then, the divine being is determined essentially through something else superadded to it, it will be in act only if what is superadded is present. But the divine being, as we have shown, is the divine substance itself. Therefore the divine substance cannot be in act without the presence of something added; from which it can be concluded that it is not through itself a necessary being. But, we have proved the contrary of this proposition above.
The online annotated edition explains, "There is an ideal or typical man in the Platonic scale, but no ideal animal. The former is specific in reference to Socrates, the latter would be generic. The type stops at the species. This piece of Platonism is not formulated in the writings of Plato."
…  Again, that through which a thing derives being in act and is intrinsic to it is either the whole essence of that thing or a part of the essence. But that which determines something in an essential way makes that thing to be in act and is intrinsic to the determined thing [Quod autem designat aliquid designatione essentiali, facit rem esse actu et est intrinsecum rei designatae: alias per id designari non posset substantialiter]; otherwise, the thing could not be determined substantially by it. It must therefore be either the essence itself or a part of the essence. But, if something is added to the divine being, this cannot be the whole essence of God, since it has already been shown that God’s being is not other than His essence. It must, then, be a part of the essence, which means that God will be composed of essential parts. But, we have proved the contrary of this above.
 Furthermore, what is added to a thing to give it a certain essential determination does not constitute its nature but only its being in act [Quod additur alicui ad designationem alicuius designatione essentiali, non constituit eius rationem, sed solum esse in actu]. For rational added to animal gains for animal being in act, but it does not constitute the nature of animal as animal, since the difference does not enter the definition of the genus [nam differentia non intrat definitionem generis]. But, if something is added in God by which He is determined in His essence, that addition must constitute for the being to which it is added the nature of its own quiddity or essence, since what is thus added gains for a thing its being in act. But in God this “being in act” is the divine essence itself, as we have shown above [hoc autem, scilicet esse in actu, est ipsa divina essentia, ut supra ostensum est]. It remains, then, that to the divine being nothing can be added that determines it in an essential way, as the difference determines the genus.
Book I, Chapter 25:
THAT GOD IS NOT IN SOME GENUS [Quod Deus non est in aliquo genere]
 From this we infer necessarily that God is not in some genus.
 Every thing in a genus has something within it by which the nature of the genus is determined to its species; for nothing is in a genus that is not in some species of that genus [nihil enim est in genere quod non sit in aliqua eius specie]. But, as we have shown, this determination cannot take place in God. God cannot, then, be in some genus.
…  Again, whatever is in a genus differs in being from the other things in that genus; otherwise, the genus would not be predicated of many things [Quicquid est in genere secundum esse differt ab aliis quae in eodem genere sunt. Alias genus de pluribus non praedicaretur]. But all the things that are in the same genus must agree in the quiddity of the genus, since the genus is predicated of all things in it in terms of what they are. In other words, the being of each thing found in a genus is outside the quiddity of the genus [Esse igitur cuiuslibet in genere existentis est praeter generis quidditatem]. This is impossible in God. God, therefore, is not in a genus.
 Then, too, each thing is placed in a genus through the nature of its quiddity, for the genus is a predicate expressing what a thing is [Unumquodque collocatur in genere per rationem suae quidditatis: genus enim praedicatur in quid est]. But the quiddity of God is His very being. Accordingly, God is not located in a genus, because then being, which signifies the act of being, would be a genus. Therefore, God is not in a genus.
If being were a genus, we could presumably classify some things as belonging to the class of "existent beings" (i.e. in the genus of being) and others to the class of "nonexistent beings." But this is nonsense: a nonexistent being is not a being at all.
 Now, that being cannot be a genus is proved by the Philosopher in the following way [Metaphysics III, 3]. If being were a genus we should have to find a difference through which to contract it to a species. But no difference shares in the genus in such a way that the genus is included in the notion of the difference, for thus the genus would be included twice in the definition of the species. [The annotated edition remarks: "As if we took 'living' for a differentia attachable to the genus 'animal,' and so formed a species 'living animal.'"] Rather, the difference is outside what is understood in the nature of the genus. But there can be nothing that is outside that which is understood by being [Nihil autem potest esse quod sit praeter id quod intelligitur per ens], if being is included in the concept of the things of which it is predicated. Thus, being cannot be contracted by any difference. Being is, therefore, not a genus. From this we conclude necessarily that God is not in a genus.
For insofar as God is Being Itself, and as Being is not in a genus, God's essence cannot fall in the so-called genus of being. There is no genus of Being of which God partakes as one member of the class among others. Rather, His substance, and His alone, is to exist: all else partakes of Him in analogous modes of likeness and intrinsic perfection. As Thomas said in chapter 21, §4, "the divine essence exists through itself as a singular existent and individuated through itself."
The annotated edition has an interesting note: "There is always an ambiguity in this term of 'mere existence,' ipsum esse, auto to einai. Either it means ens abstractissimum, the thinnest and shallowest of concepts, denoting the barest removal from nothingness: or it is ens plenissimum, being that includes (virtually at least) all other being, as the Platonic auto to kalon virtually includes all beauty. In this latter sense the term is predicable of God alone. In God 'mere existence' means pure actuality."
And again: "God is mere and sheer existence, not existence modelled upon some quiddity…. In this study it should be borne in mind that 'essence' represents the ideal order: 'existence' the actual. God is the unity of essence and existence, of the ideal and the actual; the point at which the potential finally vanishes into the actual. In every existent being, under God, there is an admixture of potentiality. This is to be kept steadily in view in bringing St Thomas to bear upon Kant and Hegel."
 It is also clear that no demonstration is possible about God, except through an effect [Patet etiam quod non potest demonstratio de ipso fieri, nisi per effectum]; for the principle of demonstration is the definition of that of which the demonstration is made.
Sections 7 and 8 here are an astounding recollection of the argumentation in chapters 10 and 11, in which Thomas refuted Anselm's ontological argument, basically by saying that while God's self-evident existence is true intrinsically––given that "what God is" = "that God is"––, yet it is not self-evident to us in our current mode of existence. Thomas' point in these sections is that, since God is not a member of any genus, He cannot be defined by any number of predicates. A dog can be defined, roughly speaking, as a smallish, four-legged, carnivorous mammal. This definition can then be used in a demonstration of further claims about dogs. Something that cannot be defined, however, cannot be used in a demonstration of its existence. Since God cannot be defined, His "definition" cannot be used to prove His existence in the way St Anselm thinks. So the only way to demonstrate God's existence is by tracing effects of His power back to His being as cause of all things.
 Now it can seem to someone that, although the name substance cannot properly apply to God because God does not substand accidents [quia Deus non substat accidentibus; cf. chapter 23], yet the thing signified by the name is appropriate and thus God is in the genus of substance. For a substance is a being through itself [Nam substantia est ens per se]. Now, this is appropriate to God, since we have proved that He is not an accident.
 To this contention we must reply, in accord with what we have said, that being through itself is not included in the definition of substance [in definitione substantiae non est ens per se]. For, if something is called being, it cannot be a genus, since we have already proved that being does not have the nature of a genus. … A substance is a thing to which it belongs to be not in a subject [quod substantia sit res cui conveniat esse non in subiecto]. The name 'thing' takes its origin from the quiddity, just as the name 'being' comes from to be [nomen autem rei a quidditate imponitur, sicut nomen entis ab esse]. In this way, the definition of substance is understood as that which has a quiddity to which it belongs to be not in another [et sic in ratione substantiae intelligitur quod habeat quidditatem cui conveniat esse non in alio]. Now, this is not appropriate to God, for He has no quiddity save His being [Hoc autem Deo non convenit: nam non habet quidditatem nisi suum esse]. In no way, then, is God in the genus of substance. Thus, He is in no genus, since we have shown that He is not in the genus of accident.
The annotated edition has a closing note for this chapter: "Being means anything and everything that in any way is, and can at all be said to be removed from the merest nothing. There is being in thought, conceptual, or ideal being; and there is being of thing, -- actually existent being. Being in this latter sense of what actually exists cannot be a genus, because the whole apparatus of genus, species and differentia belongs to the business of definition; and definition does not lay down actual existence (esse), but ideal being (essentia. It is no part of the definition of a triangle to state that any such things as triangles do actually exist. Therefore we read in this chapter (n. 3): "The existence of each thing that exists in a genus is something over and above the quiddity of the genus." In other words, 'existence' lies outside every possible generic notion. Nor again can being in the sense of what is in thought be a genus, because such conceptual being penetrates and pervades the whole ideal order, to which genus, species and differentia belong: it is the fundamental notion of the order, and appears everywhere, and therefore cannot be screened off as a genus."