Elements of Theology 15: Power and Complexity

[sdi]

Dodds calls the next section of the Elements of Theology, consisting of propositions LVI through LXV, "Of the Grades of Causality." I'm going to take it in a few parts, since ten propositions is a lot. In this first part, Proclus elaborates on the relationship of causes and effects, particularly with respect to how many effects a thing has, and how complex a thing is, given its relative position in the causal chain. Despite it taking me nearly a month, this section isn't terribly difficult: most of that time was spent just waiting for a day when my mind was sharp enough to work at it!

Power and Complexity: The higher up something is in the chain of being, the more productive power it has. The more causes something has, the more complex it is. These together mean that the middle of the chain of being tends to be more complex than the extremes.

LVI. Causes produce to a greater degree whatever their effects produce.

If a secondary thing is capable of production, it is clear that it gets this power from its cause, since all productive ability is communicated to it through the connection to the One mediated by its cause [XXV]. Since the thing is being lent its productive power by its cause, it's cause must contain this productive power inherently [XVIII]. Therefore it is evident that the secondary thing produces in the same manner as its cause, but that the cause possesses that productive power in a greater measure.

LVII. Causes themselves produce a greater number of effects than any of their effects do.

Causes produce to a greater degree what their effects produce [LVI]. But since the cause and the effect produce in the same manner, how shall we distinguish these except by number? So a greater cause produces a greater number of effects, and equal cause produces an equal number of effects, and a lesser cause produces a lesser number of effects. Therefore a cause will itself produce a greater number of effects than any of its effects do.

LVIII. The more causes a thing has, the more complex it is.

Every cause lends some quality to its effects [XVIII]; so if a thing has more causes, it has more qualities, and therefore it is more complex.

LIX. The chain of causation tends towards simplicity in its extremes and complexity in its center.

The more causes a thing has, the more complex it is [LVIII]. It is obvious that things near the top of the chain of causation have fewer causes than things in the middle, and so are simpler. [Indeed, we have already demonstrated the One as limit of this, being both totally simple [I] and the first cause [XII, XIII].] But it is also the case that things near the bottom of the chain of causation have fewer causes, because greater causes are capable of producing more things than lesser causes are [LVII], meaning ultimately that the last things must be produced by the greatest producer, which is the One itself. Therefore things in the middle of the chain of causation have more causes, and so are more complex.

I think LVII is incorrectly applied. While it's certainly true that higher principles are more powerful than lower ones and have more "children," I'm not certain VII and LVI place us on safe ground to assert whether those "children" are produced directly or indirectly: it seems to me at least plausible that more complex causes (see LVIII) can produce effects in a more complex manner, thus acting as a secondary constraint on the number of things they cause. Plotinus apparently thought so, too: he gives a concrete example in that the One is much more powerful than the Intellect, but the One's productions are all produced indirectly through the Intellect, hence the One only has a single direct effect but (infinitely?) many indirect effects.

LVIII seems a crucial principle. Proclus argues for it from the ground up, but (once again) part of why I like Plotinus' Neo-Pythagorean approach is that it's implicit in it: highly composite numbers simply have more prime factors, and that's just the way they work. Note that Proclus is not speaking strictly about vertical causation (e.g. any soul must depend on the Intellect and the One): he's talking about any causation (e.g. a soul will depend on some number of "higher" souls as well, thus lesser souls are more complex than greater souls). This is important to avoid an apparent contradiction with LIX.

I've mentioned Wolfram's A New Kind of Science before, and LIX is highly reminiscent of it: Wolfram says all the "interesting stuff" (e.g. things resembling what we recognize as "alive" and "intelligent," which is to say, the things resembling us) happens at the intersection of simplicity and complexity; because if something is too simple, it's too crystalline and repetitive to admit complex behavior, but if something is too complex, any behavior it could have dissolves into randomness. While Wolfram's argument isn't rigorous, and Proclus' is (IMHO) unsound, I think both are good at capturing the intuition that we, as rational beings (souls), exist somewhere in the middle of the chain of being rather than at either extremity.

Comments

[boccaderlupo]

To offer and even less rigorous observation, as is my wont: it is interesting that we seemingly witness a richer complexity here in the sublunar world, on Madre Terra, in the rich diversity of life, than as we get into interstellar space. But perhaps that just my impression...

Axé