John Duns Scotus defines infinite being as "a measure of intrinsic excellence that is not finite." For the Subtle Doctor, God is qualitatively infinite or exemplifies all of His divine qualities without limit. The Most High is therefore infinite power, infinite wisdom and infinite goodness. Infinity, for Scotus, is an intrinsic (non-relational) property.
Thomas Aquinas also considers divine infinity to be a negative property: it describes what God is not. He writes in Summa Contra Gentiles 1.43.1:
"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."
In the same part of SCG, Aquinas supplies this data about infinity:
"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."
Many years later, Louis Berkof similarly construes God's infinity in a qualitative (intensive) sense. He argues that infinity (as a descriptive term for God's perfection) "should not be understood in a quantitative, but in a qualitative sense; it qualifies all the communicable attributes of God. Infinite power is not an absolute quantum, but an exhaustless potency of power; and infinite holiness is not a boundless quantum of holiness, but a holiness which is, qualitatively free from all limitation or defect. The same may be said of infinite knowledge and wisdom, and of infinite love and righteousness" (Systematic Theology, p. 60).