Ch. 18 - "The Infinity of God According to Essence" From the "Compendium of Theology" By St. Thomas Aquinas

Caput 18 Quod Deus est infinitus secundum essentiam

CHAPTER 18 THE INFINITY OF GOD ACCORDING TO ESSENCE

Hinc etiam considerari potest ipsum esse infinitum, non privative quidem secundum quod infinitum est passio quantitatis, prout scilicet infinitum dicitur quod est natum habere finem ratione sui generis, sed non habet; sed negative, prout infinitum dicitur quod nullo modo finitur. Nullus enim actus invenitur finiri nisi per potentiam, quae est vis receptiva: invenimus enim formas limitari secundum potentiam materiae. Si igitur primum movens est actus absque potentiae permixtione, quia non est forma alicuius corporis, nec virtus in corpore, necessarium est ipsum infinitum esse.

This leads to the question of God’s infinity. God is not infinite by way of privation, according to which infinity is a passion of quantity; in this sense whatever lacks limits, but is nevertheless capable of having limits by reason of its genus, is said to be infinite. Rather, God is infinite negatively, in the sense that a being that is unlimited in every way is infinite. No act is found to be limited except by a potency that is receptive of the act; thus we observe that forms are limited in accordance with the potency of matter. Hence, if the first mover is an act without any admixture of potency, as not being the form of any body or a force inhering in a body, it must be infinite.

Hoc etiam ipse ordo qui in rebus invenitur, demonstrat: nam quanto aliqua in entibus sunt sublimiora, tanto suo modo maiora inveniuntur. Inter elementa enim quae sunt superiora, maiora quantitative inveniuntur, sicut etiam in simplicitate; quod eorum generatio demonstrat, cum multiplicata proportione ignis ex aere generetur, aer ex aqua, aqua autem ex terra. Corpus autem caeleste manifeste apparet totam quantitatem elementorum excedere. Oportet igitur id quod inter omnia entia primum est, et eo non potest esse aliud prius, infinitae quantitatis suo modo existere.

The very order perceived in things is a proof of this. The higher the position occupied in the scale of being, the greater are things found to be in their own way. Among the elements, nobler things are found to be greater in quantity, as also in simplicity. Their generation demonstrates this: as the proportion of the respective elements is increased, fire is generated from air, air from water, and water from earth. And a heavenly body clearly exceeds the total quantity of the elements. Necessarily, therefore, that which is the first among beings and which has nothing above it, must in its own fashion be of infinite quantity.

Nec mirum, si id quod est simplex, et corporea quantitate caret, infinitum ponatur, et sua immensitate omnem corporis quantitatem excedere, cum intellectus noster, qui est incorporeus et simplex, omnium corporum quantitatem vi suae cognitionis excedat, et omnia circumplectatur. Multo igitur magis id quod est omnium primum, sua immensitate universa excedit, omnia complectens.

Nor is there anything to wonder at if what is simple and lacks corporeal quantity is said to be infinite and to exceed in its immensity all quantity of body. For our own intellect, which is incorporeal and simple, exceeds the quantity of all bodies in virtue of its knowledge, and embraces all things. Much more, then, that which is the very first of all exceeds the universe of beings in its immensity, and embraces them all.