I. To the Question

5. I reply to the question, and first I prove the divine simplicity through certain particular middle terms, and second from common middle terms, namely infinity and necessity of existence.

A. Proof of the Simplicity of God through Particular Middle Terms

6. Proceeding in the first way, I show that [divine] simplicity is opposed to composition from essential parts, second that it is opposed to composition from quantitative parts, and third opposed to composition from subject and accident.

7. [God is not from essential parts] - The first thus: the causality of matter and form is not simply first, but necessarily presupposes a prior efficient causality, - therefore if the First thing were composed of matter and form it would presuppose the causality of an efficient cause; but not the causality of this First thing, because it does not, by joining its matter with a form, cause itself -     therefore of a different efficient cause, a prior one; therefore God would not be the first efficient cause, the opposite of which was proved in distinction 2 question 1 [I d.2 nn.43-59]. Proof of the first proposition: the causality of matter and form involves imperfection, but the causality of the efficient and the final cause do not involve imperfection but perfection; every imperfect thing is reduced to a perfect one as to what is essentially prior to it; therefore etc     .

8. I prove the same thus: matter is of itself in potency to form, and this in a potency that is passive and open to contradictories, as far as concerns itself, - therefore it is not under a form of itself but through some other cause, reducing the matter to the act of the form; but this cause reducing it cannot be called form only as it is form, because thus it does not reduce matter save by formally actualizing the matter itself; therefore one must posit something effectively reducing the matter to that actuality. Therefore if the First thing were composed of matter and form, there would be some efficient cause through whose effecting act its matter would be under the form, and so it would not be the first efficient cause, as before [n.7].

9. Third in this way: every single caused entity has some one cause from which comes its unity, because there cannot be unity in the caused without unity in the cause. The unity therefore of a composite, since it is caused, requires some one cause from which comes this caused entity. The causality in question is not of matter or form, because each of these is a diminished entity in respect of the composite entity; therefore besides these two causalities, namely of matter and form, some other one must be posited - it will be the efficient cause, and so the same result returns as before [n.8].

10. [God is not from quantitative parts] - The second, namely the lack of quantitative composition, seems to be proved by the Philosopher in Physics 8.10.226a24-b6 and Metaphysics 12.7.1073a3-11, because the First thing is of infinite power; but infinite power cannot exist in a magnitude; and the proof of this is that in a greater magnitude there is a greater power, and so an infinite power cannot exist in a finite magnitude; but no magnitude is infinite; therefore neither does any infinite power exist in a magnitude.

11. But this argument seems deficient, because one who would posit that an infinite power exists in a finite magnitude would say that the power is of the same nature in a part of the magnitude as in the whole magnitude, and so of the same nature in a greater as in a lesser magnitude; just as the intellective soul is whole in the whole of the body and whole in any part of it, and is not greater in a greater body, nor greater in the whole body than in a part; and if an infinite power of understanding were consequent on this soul, this infinite power would exist in a finite magnitude, and in a part just as in the whole and in a little part just as in a big one. So should it be said in the proposed case, because an infinite power in a magnitude would be of the same nature in the whole as in the part.

12. Making clear, then, the reasoning of Aristotle [n.10], I say that his conclusion is this, that an infinite power, extended per accidens to the extension of the magnitude, ‘does not exist in a finite magnitude’. His reasoning proves this in the following way: any power that is extended per accidens is, ceteris paribus, greater - that is more efficacious - in a greater magnitude, and it is not greater as follows, namely that it is more intense formally, because a small fire can have more heat than a big one if the big one is very diffuse and the small one concentrated (and therefore one must add the ‘ceteris paribus’ clause in the major); the example too is about heat in the same fire, which although it is of equal intensity in the part as in the whole, yet a greater fire is ‘of a greater power’, that is, more efficacious.

13. And from this it follows that every such power ‘extended per accidens’, as long as it exists in a finite magnitude, can be understood to grow in efficacy by increase of magnitude - but as long as it is understood to be able to grow in efficacy it is not infinite in efficacy; and from this it follows that every such power ‘extended per accidens’, as long as it exists in a finite magnitude, is finite, because an intensive infinity cannot exist without infinity in efficacy; and from this it follows that a power infinite in efficacy cannot exist in a finite magnitude, - nor therefore can a power infinite in intensity so exist; and then further: since there is no infinite magnitude, it is plain that there is no such infinite power in a magnitude.

14. But how does this result, that every such power would not exist in a magnitude, relate to the intended proposition [nn.5-6],?

I reply. By joining with this result the conclusion proved earlier by the Philosopher [Metaphysics 12.6.1071b19-22], - that such a ‘potent thing’ is without matter - the intended proposition follows. For, because it is by extension that a thing is extended, or, if extension were to be per se existent, there would be something that was the form informing the extension, and the form would be extended per accidens, -therefore if the infinite power were to be posited in a magnitude, I ask what thing is this extension of magnitude? Not the infinite power itself, as was proved [n.13], - nor does the infinite power perfect the magnitude as form does matter, because the power is not in matter, from the conclusion shown before [sc. by the Philosopher ibid.]; therefore one would have to posit that the matter is what is extended with this magnitude, which matter would be perfected by infinite power, just as our matter or our body is extended in magnitude and is perfected by a non-extended intellective soul; but there is no matter in a possessor of such [infinite] power, from the conclusion shown before by the Philosopher [ibid.]. From this immateriality then - shown before by the Philosopher and just shown in this conclusion [n.13] - the reasoning in question [that God is not a quantity, n.10] gets its efficacy.

15. [God is not from subject and accident] - The third conclusion is proved specifically from these [first two conclusions, nn.7, 10]: for because God is not material or a quantity,     therefore he is not capable of any material accident fitting a material thing in the way a quality fits a material thing; therefore he is only capable of those accidents that fit spirits - to wit intellection and will and the corresponding habits - but such things cannot be accidents of such a nature, as was proved in distinction 2 [I d.2 nn.89-110], because its understanding and its willing, and its habit and power etc     ., are its substance.

B. Proof of the Simplicity of God through Common Middle Terms

16. Second I prove the intended proposition [n.5] generally.

[From necessary existence] - First from the idea of necessary existence, - because if the First thing is composite, let the components be a and b; I ask about a, whether it is of itself formally necessary existence, or is not but is possible existence (one of these two must be given in each thing, or in the whole nature, from which something is composed).

But if it is of itself possible existence, then necessary existence of itself is composed of possible existence, and so it will not be necessary existence; if a is of itself necessary existence, then it is of itself in ultimate actuality, and so with nothing can it make itself to be per se one thing. Likewise, if the composite is of itself necessary existence, it will be necessary existence through a, and by parity of reasoning it will be necessary existence through b, and so it will be twice necessary existence; it will also be a composite necessary existence through something which, when taken away, will leave it to be no less necessary existenceI.e., if it is necessary existence through a and through b, then, if b is taken away, it will still be necessary existence through a; therefore it will not really be necessary existence through b, and so it will not be a necessary existence composed of a and b. ⁴¹, which is impossible.

17. [From infinity] - Second I show the intended proposition from the idea of infinity, - and first that God is not combinable; for this reason, that everything combinable can be part of some composite whole which is combinable from itself and from something else; but every part can be exceeded; but to be able to be exceeded is contrary to the idea of infinity;     therefore etc     .

18. And there is a confirmation of the reason, and it is almost the same, - because everything combinable lacks the perfection of that with which it is combined, such that the combinable does not have in itself complete identity, and identity in every way, with that with which it is combined, because then it could not be combined with it; nothing infinite lacks that with which it can in some way be the same, nay everything such has all that in itself according to perfect identity; because otherwise it could be understood to be more perfect, for example if it had all that in itself as a ‘composite’ has it and if the

‘infinite’ does not have it;Sc. suppose the infinite combined with something, then by itself, or uncombined, it does not have it; therefore, when combined with it, it is more perfect. ⁴² but it is contrary to the idea of infinity simply that it could be understood to be more perfect, or that something could be understood to be more perfect than it.

19. From this follows further that it is altogether incomposite, - because if it is composite, then composed either of finite things or of infinite things; if of infinite things, nothing such is combinable, from what has been proved [nn.17-18]; if of finite things, then it will not be infinite, because finite things do not render anything infinite in the perfection that we are now speaking of.