Friday, September 28, 2007

Scotus’ first move is to present the infinite as perfect rather than imperfect

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”].

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