Consider the following from A Resume of Metaphysics (1697, the same time period as the above quoted definitions of order): Distinct cogitability gives order to a thing and beauty to a thinker.
Leibniz frequently linked the concept of harmony to that which is "cogitable,"(18) or "contemplatible"--"the state where everything has the potential for observation," or a state which "extricates [the mind] from confusion."(19) Now given that order is itself characterized by Leibniz as imposed by distinct cogitability, and this, the above passage suggests, is to be contrasted with confusion, we can see that harmony and order are both associated with the concept of cogitability, or of what is thinkable or potentially observable.
In other words, only those collections which achieve the level of distinct cogitability are harmonious.
For right after defining harmony as "unity in variety," Leibniz continues: Harmony is the perfection of cogitability, insofar as there are cogitable things [quatenus cogitabilia sunt].
This passage has the virtue of bringing out the essential relational features of the concept of harmony.(21) We are told that harmony is "the perfection of cogitability"--terms strikingly similar to those used to describe the kind of order necessary for harmony.
Recall that for Leibniz, harmony, in addition to being "unity in multiplicity" (or "variety compensated by identity"), is also characterized as "perfect cogitability." In addition, Leibniz claims that that is a more perfect manner of thinking, where one act of thought extends to many things simultaneously: so there is more reality in that thought.
Leibniz tells us that "distinct cogitability gives [dat] order to a thing."(38) The point presumably is that if the relevant thing, or set of entities, is distinctly cogitable, it may be thought about in a way that permits one to distinguish one entity from another.
Some might seek help in Leibniz's calling order "nothing other than a distinctive relation of several things,"(39) and in his claim that distinct cogitability is what bestows order on a given thing.
In that same letter, Leibniz equated the harmony of things with "the state where everything has the potential for observation, that is, the state of agreement or identity in variety; you can even say that it is the degree of contemplatibility."(61) Years earlier, as we have seen above in the passage from the Elementa, Leibniz explicitly stated that "Harmony is the perfection of cogitability."(62) It seems reasonable to infer, accordingly, that in these passages, Leibniz's idea is that harmony results from considering a set of entities in such a way that one may deduce a range of properties from the set.
Thus, it is difficult to see how concept resolution is supposed to aid us here, for there is no thing, the concept of which is to be resolved such that we may see the level of distinct cogitability. (Similar remarks apply to the other harmonies noted at the beginning of this paper.) Perhaps the idea is that, nonetheless, once we grasp how these two kinds of causation work, we can come to infer certain intelligible properties about the whole system of causation, understood as involving a harmony between "realms," or "kingdoms."(66) In any event, this difficulty awaits further analysis.
(38) Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146.as "perfect cogitability." In addition, Leibniz claims that
(58) Russell Wahl pointed out to me that Leibniz's grounding the reality of relations, and thus the reality of harmony and distinct cogitability, in the divine mind seems to present a problem.