Theoremata Scoti, Pars II

The second part of the Theoremata is concerned with showing the priority of quality over quantity. I note that, if we accept this, there are some interesting implications for the sciences. Mathematical physics, our paradigm modern science, is primarily concerned with what can be quantified, but for Scotus quantity and the quantifiable are not primary substantial traits.

The editors of the new edition number four main conclusions. Why these propositions are called conclusions in Part II and propositions in Part I is unclear to me. In any case:

I. Quality is naturally prior to quantity.

"Because [quality] is found in every substance, but quantity only in corporeal substances." Quantity can be attributed to separated souls, angels, and so forth, only insofar as they are numerable, i.e. insofar as we can mentally collect them into multitudes. In himself an angel has no dimensive quantity, since he has no dimensions.

"Quality is in substance by reason of form, quantity by reason of matter." Form is primary over matter, ergo, etc. Note that this would not be accepted by earlier Franciscans who would admit matter in the angels, but not dimensive quantity, which they would attribute to corporeitas.

"Again, quality is the principle of acting, quantity [is] not. Quality is that by which an agent alters [something]. But alteration precedes augment[ation]. It is impossible for quantity to be induced except through the action of quality, [but] not conversely."

II. Qualities are attributed to God as perfections, not so quantities.

That is, some quality can be seen as a pure perfection, and when existing in an infinite mode can be identified with God himself. For any quantity, however, this is simply nonsense. There cannot be an actually infinite quantity.

III. Qualities have many species in both spiritual and corporeal [things], as light, etc., by which entities attain their ends, as man [attains] beatitude through grace and charity, etc. But continuous quantity has only three species and no being attains its end through it.

This is losing the pithy aphoristic edge a bit, but is there a shorter way to say it? Since quality pertains to the form more than quantity, one can see how it helps to attain a thing's end. No thing attains its end, however, merely or primarily by being a certain size, mass, etc., even if a certain quantity is a sine qua non of its natural perfection. Quantity is of the same sort for everything; it's general, not specific. In other words:

"[Quantity] accompanies any species according to its actuality, not so quantity. According to it is the order of the universe and natural place and motion and rest. According to them as objects are distinguished the powers of the soul."

IV. A being has more perfect [quality] the more perfect it is. Not so with quantity. Neither an angel nor a man has as much quantity as the earth does.

A more perfect tree has more perfect flourishing. A more perfect man has more perfect intelligence. But if my quantity were to increase much I would get less perfect, not more!

This covers about the first third of Part II. The rest is devoted to what I called in my last post one of Scotus' frequent rabbit-trails. Not because they're pointless, but because they lead you down into a hole. Like the rabbit-hole in Alice in Wonderland, Scotus' digressions can sometimes wander into a wonderland of argumentation, in which everything is brilliant and stuffed to the rafters with things to consider, but you never know quite where you are, who's talking, how things got so tangled up, or what's at stake. So here. After the discussion of quality and quantity Scotus starts thinking about accidental inherence in general and asks, "What can be the subject of an accident?" Not God, since he is completely perfect and so not in potentiality to receive new forms. Only things with some perfection--i.e. per se actual existence--and some imperfection can be the subject of accidents. He then considers arguments that 1) substantial form, 2) accidental form, 3) matter, and 4) angels don't meet these criteria, before opposing them.