Force and Understanding

After Perception, Hegel discusses what is basically the attitude of mathematical physics. Harris in his commentary notes that Hegel is much more sympathetic to natural science than some of his supporters have seemed to recognize. Hegel accepts mathematical physics as an authoritative account of the physical world, and is impressed by the concept of mathematical natural law.

More generally, this is where Hegel introduces what he calls Understanding, which seeks to give a fully univocal (thus also formalizable) account of things. Understanding will have permanent value in securing definiteness and discipline of thought. Hegel often makes sharp remarks about its limitations, so it is important to recognize that he also respected its strengths.

Perception already took a relational approach to the properties of things, but still held fast to the idea that its objects were independent things. Newton’s concept of force as characterized by mathematical law effectively takes a relational approach to determination in the physical world as a whole. Mechanics treats force subject to mathematical laws as the objective reality underlying the world of Perception and “things”, which it treats as Appearance rather than an immanent truth.

Force for Hegel is a supersensible rational construct. For the Newtonian physicist, it is a supersensible reality. Hegel approves of the physicist’s recognition that sensible reality is not all there is, and applauds what he sees as the physicist’s thoroughgoing relational approach. His main caveat is just that what the physicist sees as an independent physical necessity that is only described by mathematics, Hegel see entirely in terms of the formal necessity of the mathematics and logic used in the physicist’s theory.

This concludes the “Consciousness” section of the Phenomenology, where “consciousness” for Hegel is the attitude that treats objects and objectivity in a “pre-Kantian” way, as just being out there. The physicist’s thoroughly relational approach to the external world takes this to its highest sophistication. What remains is to examine the ways in which there is actually continuity and reciprocity between “us” and the world we inhabit, and the role that we play in its development.

The Importance of Potentiality

I think modern philosophy generally is handicapped in its thinking about the empirical world by its lack of a notion like Aristotelian potentiality. To build context, I need to first say a bit more about the role of actuality.

The modern concept of a factual, existing world is relatively close to Aristotelian actuality, but the first big difference is that it is not paired with anything. The modern concept of a factual world is something that is supposed to be complete in itself, whereas for Aristotle, actuality in the world is always complemented by some correlative potentiality. Aristotle did not consider actuality alone to be sufficient to account for the world as we experience it.

Actuality also does not exactly correspond to a state of things, but rather expresses what is effectively operative. This is semantically a bit deeper than a notion of state. At the same time, it does not have state’s strong implications of complete determination. It also does not have the monolithic unity of a state. Actuality in the world consists of many coexisting things. Further, it is not intended by itself to provide all the resources needed to account for change and what happens next. This is related to the fact that for Aristotle, the operative determination of things is not entirely univocal. (See also Equivocal Determination.)

Enter potentiality. Potentiality is exactly what is not univocal in the actual determination of things. It corresponds to multiple alternative concrete possibilities of realization already implicit in current reality. This is a far more specific notion than mere logical possibility. Potentiality is closely tied to and informed by the current actuality, in that it exactly occupies the real gaps or holes in the actuality’s incompletely univocal determination. For each aspect of things where there is not univocal determination, there are instead multiple potential alternatives. This correlates with the fact that, for Aristotle — in contrast to Poincaré’s classic formulation of modern determinism — the present does not completely determine the future.

Poincaré famously claimed that from the state of the universe at any arbitrary point in time, its entire future is completely determined. This resembles the Stoic notion of fate, transferred to a modern event-based model of causality. For both the Stoics and Poincaré, the world is completely univocally determined. Like Aristotle, they emphasized the intelligibility of the world and of change in the world, but they made the very strong assumption of complete univocal determination. Aristotle did not.

Aristotle’s notion of intelligibility was broadly semantic, whereas Poincaré’s was mathematical. With semantic interpretation, there is always a question of how far we develop the account, which in principle could be extended indefinitely. It thus naturally lends itself to an account of incomplete determination, corresponding to some stopping point. Aristotle does not claim any more determination than he can show. Poincaré’s approach, by contrast, requires that we assume there is a complete univocal determination of the world by mathematical laws, even though we can never even come close to knowing enough to show it. This assumption leaves no room for anything like potentiality. Potentiality, it seems to me, could only have a place in a semantic approach to intelligibility.

The modern factual world is usually considered as something that just is, without modal qualification, but I have increasingly begun to doubt whether for Aristotle there is any non-modal account of the world. I read actuality and potentiality both as modal concepts, and everything in the Aristotelian world as parsable into actuality and potentiality.

What’s important about this is that potentiality is not just some mysterious “metaphysical” concept that we could maybe do without. It is a distinct logical/semantic modality supporting multiple virtual alternatives for the same thing. It allows us to intelligibly account for the incomplete determination we really experience, rather than treating real-world incompleteness and ambiguity as if it were a kind of flaw. (See also Structural Causality, Choice; Values, Causality; Structure, Potentiality.)

Aristotelian Causes

I’ve explained each of the four classic Aristotelian “causes” as playing what Brandom would call an expressive role, helping to explain other meaning, and pointed out how different this is from standard modern notions of what I’ve been calling univocal causality. An Aristotelian cause (aitia) is much more like a nonexclusive reason than it is like anything expressed by mechanical metaphors.

There is another very important modern way of thinking about these matters, inspired by Hume’s critique of realism about causes in the modern sense. Hume pointed out that modern-style talk about cause and effect involves a kind of inferential extrapolation from observed regular patterns of succession. Implicitly influenced by this, much work in the sciences relies directly on statistical correlations observed in data from controlled experiments. What particular causes are said to be at work then becomes a matter of optional statistical inference, subject to possible debate.

Then, too, from the side of subject matter, in fields concerned with complex dynamical systems that can only be modeled in a very tentative way — like ecology, economics, and medicine — it has come to be widely recognized that many causes combine to produce the results we see.

Both the statistical approach and what I’m gesturing at as a “complex systems” approach to causality avoid reliance on mechanical metaphors. Neither of these perspectives rules out underdetermination or overdetermination, or the simultaneous presence of both.

Aristotelian “causality” is simultaneously underdetermining and overdetermining. That is to say, in advance it leaves room for varying outcomes, but in hindsight it provides multiple rationales for a given outcome. Its purpose is to provide not certain prediction, but intelligibility and reasonableness.

In principle, nothing would stop us from combining this with statistical or complex-systems views, but these are still very different approaches. The statistical approach is quantitative and relies on counting minimally interpreted facts, where the Aristotelian approach is qualitative and puts the whole emphasis on rational interpretation. The complex-systems view relativizes causes in the modern event-based sense, without making them like any of the Aristotelian ones, none of which corresponds to an event. It is also not interpretive in the sense developed here.

One might consider mathematical-physical law as a kind of formal cause. Statistics and things like dynamic models could be taken as modern, quantitatively oriented descriptions of what I have called material tendencies. (See also Secondary Causes; Form; Aristotelian Matter; Efficient Cause; Ends; Natural Ends; Aristotelian Identity; Aristotelian Demonstration.)