Hegel and Scotus on the Infinite
According to Hegel, we abstract the notions of finitude and infinitude and tend to set these up as opposite notions. However, according to Hegel, if you analyze the notion of absolute infinity, the infinite must include the finite or else it is itself finite. A consequence of this reasoning results in Hegel’s claim that God must create.
Contrast this with Scotus’ definition of the infinite: “What I call ‘infinite’ is what excels any actual or possible finite being to a degree beyond any determinate measure you take or could take.”[1] Scotus recognizes that the notion of infinity as a perfection is not self-evident. For example, in Greek philosophy infinity was a sign of imperfection-of that which lacked form. That which was infinite lacked form and consequently was dominated by matter or potentiality. Interestingly, the transformation of this concept took place largely via Christians. Given the dominant Greek understanding of infinity, Scotus’ first move is to present the infinite as perfect rather than imperfect. Second, Scotus had to move beyond the notion of the infinite understood mathematically-i.e., in extensive terms where 10 is greater 9 and so on ad infinitum. This is to understand the infinite in a strictly quantitative sense. Third, Scotus develops an understanding of the infinite in an intensive sense.
If you consider a number sequence in which you can always add an additional number (the idea of 1, 2, 3., n+1…), this sequence is dominated by potentiality. Scotus then engages in a thought experiment in which this infinite sequence is understood in act. In other words, he asks us to imagine the sequence being finished. If we can think of the sequence as finished, we have an infinite quantity in actuality. If we grant Scotus’ thought experience, then we have an (actual) quantitative infinite.
Scotus then moves away from mathematical examples and speaks of entities. That is, he moves from quantity actualized to entity in terms of degrees of perfection. Here one has to accept that it is intelligible say that one being is more complete or better than another (a human e.g., is better than a dog). If we have the sequence A is less than B is less than C etc. and I = Infinite Being (God)-even if creatures were not created, God would persist in undiminished being and goodness. However, it does not follow from that that creatures are nothing, but it will appear that way if you approach the sequence (A, B, C=various creatures) as additive. In contrast, consider Aristotle’s god, who is the “best part” of the whole. For Aristotle, it would unintelligible to say that there is god and nothing else. Hence, the fact that this notion of the infinite applied to entity takes place in Christian philosophy is not accidental.
For Scotus, being is a perfection which is open to degrees of perfection; it is open to finite perfection which involves a large sequence of degrees, but with the infinite the difference is only one-and it is an infinite difference.*
*The reflections on Scotus are based largely on lectures given by Dr. W.A. Frank at the University of Dallas.
[1] Wolter and Frank. Duns Scotus Metaphysician, p. 59. [As found in Reportatio IA in the "reply to the third question"].
17 Responses so far
11:56 am
I would prefer Scotus above Aristotle, but he leaves severely unsatisfied. Not being a philospher, I struggle to clarify my non-satisfaction though. Maybe I should ask this: in Scotus’ universe, what is perfection? Note that the term “degrees of perfection” precede the concept of an infinte series of degrees of perfection leading up to God, so how does he define perfection, not refering to God?
8:04 pm
How one understands perfection depends upon what kind of being/entity one has in mind. E.g., an acorn (being the kind of thing that it is) reaches its perfection when it becomes an oak tree. Here I do not see Scotus departing from Aristotle much at all. When Scotus speaks of “degrees of perfection”, I do not think that that means that ultimately he doesn’t have God in mind as the Perfect Infinite Being. After all, for Scotus God and God alone “possesses” all the pure perfections (wisdom, being etc) infinitely–or better he is the pure perfections. The point that I was making in the post is simply that one would have to accept the idea that a human is a higher being than a dog given the fact that the latter does not possess rationality.
4:56 am
Starting from the fragmented point of view of the usual person it is really quite impossible to even begin to understand what “perfection” might look like or be.
10:09 am
But what what grounds do we have for claming rationality as a mark of greater perfection? Such a claim would certainly fit in with Hellinistic thought, though.
11:38 am
Such a claim would also fit in the medieval Christian world, as well as in contemporary Christian and non-Christian thought.
If you are asking for reasons why it is better to be a being with reason than a being without reason, it would seem that one could develop an argument by looking at the potentialities that are open to those with reason as opposed to those without reason (e.g., writing poems, composing symphonies, reflecting on one’s own self-awareness etc.). A Christian might also appeal to the idea that the will and intellect (keep in mind that Scotus argues that the will is a rational power) allow for the possibility of creature to freely choose to love and worship God and hence experience a more intimate union with God than non-rational beings.
12:20 pm
Good answer. But as a nominalist-leaning fellow, I’d like to ask if there are other criteria beyond rationality.
7:32 pm
It is not clear to me what you mean by your last statement. Would you unpack it?
8:39 pm
Thank you for a very lucid post.
I appreciate Scotus’ notion of perfection. I feel more at home with it than with the more “maximal” notion of perfection that I tend to associate with Hellenistic thinking. To say that perfection is that which lies outside the boundaries of our imagination (much less our ability to attain) is to respect God’s beyond-ness without presuming to impose a precise criterion on him. At the very least, this would avoid the silly questions about really heavy rocks that God can’t lift, etc.
Would the “degrees of perfection” notion leave room for a proposal akin to Moltmann’s? Could this validate the suggestion that God isn’t perfectly at home until his Sabbath is realized in creation–insofar as Revelation 21-22 are the “seventh day of Genesis 2?
At any rate, thank you for a compelling post.
Go well,
Eric
5:10 am
“Note that the term “degrees of perfection” precede the concept of an infinte series of degrees of perfection leading up to God, so how does he define perfection, not refering to God?”
Might I say that it seems to me that perhaps Scotus could appeal to the priority that the univocal concept of being has with respect to God and creatures. He could then apply his understanding of disjunctive transcendentals in coming to terms with perfection. Just a thought.
Good luck on your presentation, Cynthia. I’ve sent a few prayers your way.
All the best,
Victor
6:45 am
Hi Victor,
Thanks for your helpful comment. Would you say that the key disjunctive pair then is infinite/finite (where the actual or intensive infinite applies only to God and hence between God and creatures there is an un-measurable so to speak gap)?
Best wishes,
Cynthia
p.s. Thank you so much for your prayers!
9:39 pm
I’m a little confused…there aren’t an actual infinitude of degrees of creatures leading up to God, are there?
12:58 pm
Lee,
I take Scotus’ position to be something along the lines of the following: Unlike a situation in which you have beings/entities that are “measurable” by some finite measure, when you get to the actual infinite (viz. God) you have that which exceeds them all by a non-finite degree. Hence, the idea that being is a perfection which is open to (finite) degrees of perfection, but between the (speaking more theologically) Uncreated and the created the difference is infinite. Is this correct or would you explicate/nuance it differently?
Cynthia
2:35 pm
Cynthia,
I think you have it right. some of the comments were making it look as if there were God (infinite) and an infinite series of creatures leading up to him (so, the universitas entium as a second infinite being). But obviously Scotus doesn’ think that.
One might qualify the ‘infinite’ gap, as being bridged by a conceptual univocity (but I realize that’s not the point of the post or comments). Otherwise I think you’re spot on.
8:04 pm
In response to “The Scylding”’s first comment (regarding the problem of knowing what degrees of perfection means):
When I make the claim during a lecture that some people are better than others, my students invariably look at me with shock (as well they should, given the evil uses to which those words have been put). I then present Mother Theresa and Hitler to them, and the looks of shock turn to looks of comprehension.
I have to start from such an example to explain Plato, Aristotle, and Augustine’s view of the universe. It’s the most effective way I know of beginning to convince them that talk of “degrees of perfection in being” might actually make sense. In other words, I think they buy the claim that since Mother Theresa was a better person than Hitler, she was “more of a person,” more of what a person should be.
12:02 pm
Micah,
Your illustration on seems to expand an undeniable ethical claim into the ontological realm. Our ability to see a great ethical difference between two humans is taken as a sign of an underlying ontological divide.
Isn’t that just the mistake that is made in “evil uses” like Hitler’s?
In other words, Mother Theresa was certainly more of a person than was Hitler, and as such, she had a more perfect being, but can we really say that her being was more real? The conflation of the ontological and the ethical (at least in terms of human judgment) scares me.
But, I may just be reflecting a “look of shock”!
I’d rather apply the “degrees of perfection” notion (in the ontological sense) at the level of species rather than individuals.
1:05 pm
Sorry – little internety access over the weekend.
I’m a bit(!) out of my depth here, but I simply do not venerate rationality. I like the image that Lewis used in “The Pilgrim’s Regress”, where Reason, a mounted and armed lady on a horse, spoke to the traveller, and upon him questioning her, told him that she cannot tell him anything other but what is already in his mind.
Or as Pascal put it – the very height of reason is that there is a limit to reason.
So, given these insights, I would say that completeness is reached when reason lives within its limits. Attempts at transending of these limits yields error.
So maybe my statement was badly worded – my apologies. I was more moaning at the common assumption (not yours) that rationality is the acumen of humanity. In this it would appear that Scotus is a help.
1:11 pm
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