Is God infinite? First of all, we have to determine what the word "infinite" means when God is the referent of the term or in what sense He is infinite. (After all, we can describe the individual marks on a ruler as "infinite" but that's not the same as divine infinity.) If God is qualitatively infinite, then it means that He is unlimited with respect to His intrinsic perfections, not necessarily with respect to space-time. On the other hand, if God is infinite in the Thomistic sense of the word, it simply means that He is absolute or boundless perfection: God is not finite. Elsewhere (in the Summa Theologica), Thomas associates God's self-subsistent ESSE with His infinity. At any rate, it is difficult to see how qualitative infinitude implies being unlimited vis-a-vis space and time SIMPLICITER.
Aquinas also writes in Summa Contra Gentiles 1.43.1:
"Infinity cannot be attributed to God on the score of multitude, seeing there is but one God. Nor on the score of quantitative extension, seeing He is incorporeal. It remains to consider whether infinity belongs to Him in point of spiritual greatness. Spiritual greatness may be either in power or in goodness (or completeness) of nature. Of these two greatnesses the one follows upon the other: for by the fact of a thing being in actuality it is capable of action. According then to the completeness of its actuality is the measure of the greatness of its power."
From the same portion of SCG, Aquinas likewise explains:
"But in God infinity can be understood negatively only, inasmuch as there is no term or limit to His perfection. And so infinity ought to be attributed to God."
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