Saturday, February 24, 2007

Leo Sweeney, SJ, on Infinity

"Lawrence Gage" (the erstwhile Meta-Jester) has recently posted an excellent piece on the philosophical concept of infinity, and when I mentioned Leo Sweeney's work on the subject, Professor Gage asked me to say a bit more about what that theory was. Posting something about Sweeney is something that I have been meaning to do for a long time, and with the current incentive coming in the form of a reasonable request from a fellow-traveler in the Ivy League, I wouldn't be worth the name "Crimson Catholic" if I left this for later. So here is my attempt to fill out Professor Gage's post with some information from Leo Sweeney, SJ, Divine Infinity in Greek and Medieval Thought (NY: Peter Lang Publishing Co., 1998).

Sweeney summarizes the implications of Aristotle's concept of infinity as follows (p. 6):
"For Aristotle, then, infinity basically is associated with quantity and is synonymous with imperfection. This synonymity has two important consequences. The Greek philosopher cannot predicate it directly of God Himself (the First Mover and primal Separate Intelligence), but only of His power, and this through an extrinsic predication. [As one might guess, Fr. Sweeney uses this term to refer to descriptions of God as related to other entities rather than God's own being -- JP.] That is, His power is so perfect as to be the cause of an infinite effect, viz., the endlessly recurring circular motion of the heavenly bodies through an infinity of time; it is this motion alone to which infinity directly belongs and through which divine power receives the predication (Meta. 1073a6-10). Secondly, the material universe cannot be actually infinite in extent, nor is it merely one of an infinite number of universes, since such sort of actual infinites are contradictory and impossible. Moreover, it is finite in virtue of the fact that as "universe" it is whole, all-inclusive, complete, and perfect; and whatever is whole, complete, and perfect has an end, which is its limit and termination (Phys. 207a7-14)."

The next stage in development is the concept of Plotinus. Plotinus does not explicitly break the identification between infinity and imperfection so as to render "infinite" a proper predicate for God, but he does implicitly allow such predication in saying that God is "beyond being." Because of this status, infinity is not pejorative with respect to God because He is not the sort of entity in which the absence of limits is a deficiency. Sweeney (p. 7) explains the situation as follows:
"Infinity as Perfection. Unlike Aristotle, though, Plotinus developed a theory of infinity that is synonymous with perfection and that is applicable to God Himself. This theory rests on the insight that form and being are determining and terminating factors wherever found ([Enneads] If something is without form and being, it is without their determination and, this, is indeterminate or infinite. If it should possess them but does not, that status of indetermination is coterminous with imperfection. Thus, matter of itself is below form and entity and, accordingly, is indeterminate and simultaneously imperfect (;;;; On the other hand (and of this Aristotle shows no explicit awareness), God rises above the being and form proper only to the lower levels of reality, viz., the intelligible, psychical, and sensible universes, and thereby also transcends any formal determinations. By this transcendence He is infinite, and such infinity is aligned with absolute perfection and actual excellence.... (; see also;;;

Infinity and Nonbeing. In thus showing that inifinity can be coextensive with perfection and thereby predicable of the divine reality itself, Plotinus made a major contribution to the development of the concept of infinity. But one must remember that this predication is only implicit in Plotinus' text."

In Plotinus, we have at least an implicit metaphysical concept of a real infinity contrary to Aristotle. A similar explicit account based on the Neoplatonic concept of participation is articulated by Gregory of Nyssa; God is infinite in that he does not have His perfections by participation in any other entity (see p. xv and also Sweeney's "Augustine and Gregory of Nyssa: Is the Triune God Infinite in Being?" in Roland Teske et al. (eds.), Collectanea Augustiniana (vol. 2): Presbyter Factus Sum (NY/Bern: Peter Lang Publishing Co., 1992), 321-26). One might refer to this as the Neoplatonic concept of real infinity. It appears to be followed not only by Gregory Nyssen (who also employs what Sweeney calls a "homespun" anticipation of St. Thomas's later idea, but without the explicit concepts of act and potency) but also by Pseudo-Dionysius, John Damascene, and John Scotus Eriugena (p. 9). I would add St. Maximos Confessor per Eric D. Perl's 1992 dissertation at Yale: "Methexis: Creation, Incarnation, and Deification in St. Maximus"). The bottom line is that there was a metaphysical distinction (although not the same as St. Thomas's) introduced to avoid Aristotle's conclusion about infinity being predicated of a real entity.

In the West, this distinction was more or less unknown, and St. Augustine's teaching on the subject was not detailed or rigorous (summarized well in Sweeney's article in Presbyter Factus Sum, to which I will refer the interested reader in the interest of keeping this post more focused on its topic). Acccordingly, the predicate "infinite" was frequently treated according to the example of Aristotle of Boethius as being only improperly predicated of divinity and properly only of the infinite motion God produces (Sweeney cites numerous examples on p. 9). It wasn't until Bonaventure and Aquinas that the philosophical problem was studied in detail, and this was the point at which St. Thomas's famous notion of God as unmixed with either matter or potency (subsistent being) was used to resolve the problem. Sweeney says the following of Aquinas and Bonaventure (p. 16):
"[T]hey broke with Aristotle by predicating infinity of God Himself, as Plotinus also had. Yet their positions significantly differ from the Neoplatonist's because especially Aquinas' rests upon an obviously different metaphysics (see below, ch. 19).

For example, Aquinas agreed with Plotinus that forms and, in general, every sort of act are determining factors for whatever receives them. Accordingly, a recipient such as matter is indeterminate and infinite (and also imperfect) when considered in itself and as lacking form. But in contrast to Plotinus, Thomas taught also that matter and all other types of potencies are not mere negations, privations, or mental constructs, but are genuinely real and actually existing components within existents and cause their own sort of determination. Accordingly, a subsistent form or act is without the limiting determination of matter or of potency and, thus, is infinite and infinitely perfect."

Given the novel concept of potency that St. Thomas introduces, which recognizes the difference between existence and essence, I think Zellini has erred in his understanding of St. Thomas's infinity "on the part of matter." St. Thomas would certainly say the limiting determination of matter and potency is an imperfection in an entity's act of being (perhaps "mode of existence" would be a helpful synonym), but at the same time, it is a true part of that act. This is not the same as Aristotle's view (or Boethius's), which neglects the distinction between essence and existence based on the same confusion between form and matter that Prof. Gage identified. Viewed in this way, I do not think that Descartes has departed from the Schoolmen in anything other than terms, as Fr. Sweeney points out (p. 11): "R. Descartes thought that only God should be called 'infinite,' whereas quantitative itsems should be termed 'indefinite' (see Reply to Obj. 1, 2:17; Principles of Philosophy, 1.14, 26, 27)." As further evidence that the doctrine of potency is at the heart of what St. Thomas's means by infinity "on the part of matter," I would note that the controversy with Duns Scotus on this topic (Sweeney, p.553-558) seems to clearly turn on Scotus's confusion about St. Thomas's doctrine of potency.

As I said, I think that Prof. Gage has actually identified the conceptual problem in Aristotle correctly, but I don't believe that Zellini has taken the full implications of that distinction into account in concluding that Descartes was an innovator. It seems to me that the metaphysical roots of Descartes's idea were well in place in St. Thomas. While one can't really deny that "Where previously it was assumed that the essence of mathematical infinity lay in quantity and variability, now the concepts of order and multiplicity are basic" (Sweeney, p. 12), the general direction away from Aristotle appears to have been the work of St. Thomas, perhaps taking some conceptual inspiration from the work of Richard Fishacre (though likely not much earlier than that for the explicit concept; see Francis Catania, "Albert the Great on Divine Infinity: A Reply to Francis Kovach" in Greek & Medieval Studies in Honor of Leo Sweeney, S.J., William J. Carroll & John J. Furlong, eds. (NY: Peter Lang Publishing, Inc., 1994)). I'm always wary of giving the Enlightenment and modernity credit for "innovations" that really owed their concepts to Scholastic thought (as is often done with empiriological science), and this seems to be another example where the Schoolmen beat the Enlightenment to the punch.


At 2:00 PM, Blogger Apolonio said...

Here is an interesting article on infinity

I'm not sure about the argument presented on your post. Does "infinite" simply mean maximal? humans can do infinitely many things. Language has the ability to express infinitely many things. It doesn't mean we are infinite.

At 12:27 PM, Blogger CrimsonCatholic said...

I'd say "free from limits in perfection," which can be applied with respect to a particular power or to powers in general.

At 9:54 PM, Blogger Apolonio said...


But isn't that was maximal simply means? In a philosophy of religion conference here in rutgers, someone actually gave an argument saying that we should be careful in saying that God is infinite, or at least, we should try to understand what we really mean by that. He gave an analogy to zeno's paradox but I can't remember the argument.

Your working definition might work. I have to think about it more. Intuitively, I think one might see problems with it.

At 7:55 AM, Blogger Lawrence Gage said...

Great post! It's interesting that Plotinus began the line of thinking that Aquinas perected. I wonder how Augustine fits into the picture--he being the most quoted source in the Summa (next to the Bible?), as I understand, and in many ways equivalent to Plotinus.

As far as the formal (divine)concept of infinity, it's perhaps not far of the mark to say that it is equivalent to saying "infinitely definite or articulated," where defintion is understood as a perfection.

The mistake to avoid with regard to divine infinity is that it's not some amorphous blah (the material infinite), but quite the contrary. That misconception is of course the trap that New Agers fall into.


At 11:25 AM, Blogger CrimsonCatholic said...

But isn't that was maximal simply means?

I'd be reluctant to admit that, because I have trouble seeing how it doesn't confuse existence and essence. "Maximal," as it is ordinarily used, would seem to pertain to the latter and not the former. To some extent, the question with Aristotle is whether infinity can exist, not just whether it is "real" in any sense (given that Aristotle himself didn't distinguish the two).

Thanks to Prof. Gage for the kind comments. If you can get ahold of that volume of Collectanea Augustiniana with Fr. Sweeney's article contrasting Augustine and Gregory of Nyssa, it covers Augustine pretty well. I'd say the best description would be "inchoate," in that he doesn't focus on the issue explicitly. Much like divine simplicity, you can see some patterns of what his thinking is, but it's generally lurking behind the discussion of some other topic.

At 7:39 PM, Anonymous lee faber said...

"...Scotus's confusion about St. Thomas's doctrine of potency."

at the risk of coming across as being of a one track mind (I do have many interests beyond scotus, believe it or not), I think this is the sort of attitude that one gets reading scholars whose field of research is thomas or ancient philosophy or whatever. they think that because scotus says something different that he must be disagreeing with thomas or have thomas in mind. But scotus just doesn't care most of the time. he might not even have known the doctrine of thomas in question in any great detail, as thomas was forbidden to be read in the franciscan studium without the corrections of walter de la mare. Thomist academic scholars inparticular tend to project aquinas 19th century stature into the medieval period as if there was some moment when the university of paris bowed low before thomistic doctrine. which simply was not the case. in the post 1277 climate, henry of ghent was the dominating figure at the universit of paris, for over 20 years. to be sure, there was the correctorium controversies, though thomists seem to dislike those early defendors of thomas for getting him all wrong (but then, they were facing direct criticism of thomistic positions not conceived of by thomas himself, so it is understandable if they would differ somewhat.). anyhoo, my point is, in the discussions of infinity and univocity in scotus' writings, henry of ghent's views are the springboard. they are the views summarized then criticized.

At 7:41 PM, Anonymous lee faber said...

since i'm here, your earlier request regarding sources:

is all contained in the first 3 questions of distinction 3 part 1 of the ordinatio [vatican ed. III pp.1-ca. 150]

some bits have been translated in wolter's "duns scotus philosophical writings" and there is a bit in the Hyman and walsh anthology

At 2:44 PM, Blogger CrimsonCatholic said...

Thanks for both the correction and the citations, Lee. I'm definitely vulnerable to the temptation in intellectual history to set everything up as a retroactive battle between "teams" on the side of one idea or another, as if Scotus and Aquinas were on the historical equivalent of the Yankees and the Red Sox. I definitely need to do more reading to be entirely fair to Scotus, although it sounds like I'm going to have to work on my Latin to do so.


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