Scotus on Intensive and Extensive Infinity

Embedded in a lengthy question on the "action" of the created and uncreated agents with respect to the Eucharist, Scotus examines an interesting objection based on the divine attributes.  Basically, the claim is that if the divine will is formally infinite, then it must include very other perfection intrinsic to God, because there can be no addition to infinity, and thus the will, rather than the divine essence, is the infinite sea of substance that John Damascene spoke of and the scholastics so love to cite.  Scotus' answer is to distinguish between two kinds of infinity, intensive and extensive.  The passage is long enough and probably well enough generally known that I give only a translation.

Duns Scotus, Ordinatio IV d. 13 q. 1 nn. 122-24 (Vat. XII 472-3):

Therefore briefly, it is clear, because God is unqualifiedly blessed in the operations of his intellect and will; for he is not unqualifiedly blessed in his essence as it is infinite, unless he comprehends it; and just as the intellect comprehends by seeing, so the will ... comprehends by loving, for this that it is perfectly blessed. And consequently, each power and each act of each power around the divine essence -- as it perfectly makes itself blessed -- will be infinite.

As proof of that minor [premise] I say that there can be understood in the divine a quasi extensive infinite, as if there would be understood a quasi infinite number of perfections; in another way, an intensive infinite of some unqualified perfection, so that that perfection, according to its own definition [ratio], is without limit and term. And in this second way something can have not only formal infinity, but also fundamental, -- something, however, can have formal intensive [infinity], although not fundamental [infinity].

I say therefore that nothing of one formal definition [ratio] is infinite in the first way, indeed neither perhaps is there such an infinity absolutely in God: for perhaps just as the persons are finite, speaking about that finitude, so also the unqualified perfections are finite in number or in their multitude, and the relations and notions, and this and that are joined together; but formal intensive infinity and fundamental [infinity] are together there in the divine essence as it is essence, and for this reason it is called by the Damascene a 'sea'. Formal [infinity] only, however, not fundamental, is in every other perfection [than the will] unqualifiedly; for each one has its own formal perfection from the infinity of the essence just as from a root and foundation. Neither formal nor fundamental infinity, however, is in the relations, as was shown in Book I distinction 13, because it is better for the Father not to have filiation; 'an unqualified perfection is that which it is better for something to have than not to have'. [cf. Anselm, Mon. c. 15]

The response is then clear, that although the will is formally infinite, nevertheless it does not formally include in itself all intrinsic perfections, because neither the essence nor something other includes them in that way; but neither does it fundamentally include all perfections, but so only the essence [does include them], which is a 'sea'; it includes by identity both whatever unqualified perfection and whatever relation.