It occurred to me recently that one complication in the dispute over the Filioque that is often overlooked is that the Latins think of the matter chiefly in terms of spiration. One might expound the view as follows. When you take the notion of spiration seriously, it becomes difficult to see how you can avoid saying that both the Father and the Son spirate, or that the Holy Spirit is spirated by both Father and Son alike. For we know that the Holy Spirit is not merely the Spirit of the Father, nor merely the Spirit of the Son; He is the Spirit of the Father and the Son both, and, moreover, He is the Spirit of the Son precisely because He is the Spirit of the Father. If we were to deny that the Holy Spirit is spirated by the Son, we would have effectively denied that He is really the Spirit of the Son; if we were to hold that He is spirated only by the Father, we would have effectively affirmed that He is really the Spirit only of the Father.
In this light we can make sense of virtually all Latin claims about the procession of the Spirit. First, that the Spirit proceeds from the Father and the Son: for He is spirated by Father and Son alike. Second, that the Spirit proceeds from the Father principally: for He is the Spirit of the Son because He is the Spirit of the Father, not vice versa. Third, that the Spirit proceeds from the Father and the Son as from one principle: for He is the Spirit of both wholly in virtue of the fact that He is breathed forth by the Father. Fourth, that the Spirit proceeds from the Father through the Son: for He is immediately the Spirit of the Father and also the Spirit of the Father by being the Spirit of the Son. Bonaventure, in fact, has lots of arguments very similar to these; and his sharpest criticism of the Greeks on this issue (to whom he generally tends to be sympathetic) is that they have an inadequate understanding of spiration.
So the Latin understanding of procession is dominated by this notion of spiration. And, indeed, the scholastic way of discussing the Filioque, although not common today, suggests this very strongly. For, if we might summarize it a little oversimply it is this: essentially, i.e., insofar as He subsists in the divine nature, He is God in His own right; personally, i.e., insofar as He receives the divine nature from the Father as Principle of the Godhead, He is from the Father alone; notionally, i.e., insofar as He is not the Son but the Spirit of both the Father and the Son, He is from the Father and the Son. The Father and the Son are one notional principle of the Spirit inasmuch as the Spirit must be marked by an idea that makes Him the Spirit of the Father and of the Son alike, and that not incidentally; thus He is spirated from both, but by a single spiration; which is why the Father and the Son are said to breath forth the Spirit inasmuch as they are the same God, for the Son has it from the Father that the Spirit is the Spirit of the Son.
This does not, I think, resolve the dispute; rather, it shows more clearly just how difficult the dispute is to pin down; thus, for instance, the argument never occurs in terms of spiration, although the Latin notion of spiration is clearly a significant reason why the Latins think the Filioque not only to be plausible but essential to the faith.