Hegelian Genealogy

[The title above was conceived as an initial answer to the question posed below about the main ways Hegel extends Aristotle, but the article then wanders away from Hegelian genealogy in further pursuit of that question.]

Hegel was at the same time deeply Aristotelian, deeply Kantian, and highly original. Across numerous posts, I have been pointing out Hegel’s connections with Aristotle. This implicitly poses the question, how should we summarize the aspects of Hegel’s contributions that go beyond Aristotle?

What Brandom has called Hegel’s genealogy captures most of this at a high level. A Hegelian genealogy is a recollective making more explicit of our current best self-understanding in terms of a backward projection of part of that current understanding onto what we take to be its historic roots, in order to then trace a sequence of its development into our full current understanding. I would note that this sort of understanding involves the kind of interweaving of history and creative fiction that has been discussed at length by Paul Ricoeur.

Hegel is at one with Aristotle in recognizing that the end goal of a process is emergent rather than pre-established from the beginning, as someone like Leibniz or Plotinus might suggest. He does not mean to literally assert, e.g., that Socrates already explicitly thought in terms of German Idealist concepts like Subjectivity and Freedom. In part, he is deliberately using anachronistic terms as a sort of pedagogy for a contemporary audience. More significantly, he is making a historical claim based on current understanding that the roots of German Idealism go all the way back to Socrates.

On the other hand, while Aristotle and Hegel are both very concerned with development and take a retrospective perspective on it, Aristotle does not explicitly address the development of large cultural formations or development over long periods as Hegel does. Aristotle takes large formations in a mostly synchronic way.

On a small scale, while Aristotle makes heavy use of both material incompatibility and material consequence, he does not tightly combine these as Hegel does.

Aristotle recognizes that a concern for error and its rectification is integral to the pursuit of truth, but does not apply this to whole social formations or historical periods the way Hegel does. He does not have Hegel’s positive vision of the necessity of error for learning, and of a path to greater rationality that can only be achieved through the successive resolution of errors.

Aristotle treats mutual recognition as an important part of the description of the key ethical goal of friendship or love. Hegel further develops the idea of mutual recognition, makes it more primary, broadens its applicability, and also uses it to explain how normativity is socially and historically constituted.

Hegel also takes over Kant’s idea that normativity forms an outer frame around all other concerns. (See also Aristotle and Kant; Brandom and Kant; History of Philosophy; Edifying Semantics; Mutual Recognition.)

Hylomorphism

Hylomorphism refers to the fact that Aristotelian form and matter are found in a pair, are only analytically distinguishable, and have no separate existence. This is utterly different from a dualism such as the Augustinian one between a separately constituted soul and body, or the Cartesian one between mind and matter. Form and matter — an active way of being and its contingent situatedness — are so deeply interwoven that one cannot be empirically picked out from the other. I think something similar applies to substance and accident. At the end of the day, the distinction is only analytical. (See also Purpose, Contingency.)

Form

[This early skeletal note is preserved in its original form. For a somewhat more expansive treatment, see Form Revisited; Form as Value; Form, Substance; Form vs Action.]

The expressive metaconcept of form has multiple levels of meaning in Aristotle. A theme common to these various senses is that depending on the context, form is a way of being, or a way of being and doing.

A way of being and doing can be understood as constituted by a counterfactually robust effective orientation with respect to ends. The ends in question may belong either to whatever is considered as “having” the form, or to an intelligence that discerns the form, but in either case, the effective orientation that is form is attributed to the “thing” that “has” the form.

Thinking in terms of form is thinking in terms of a sort of primarily adverbial, richly modal, differential-consequential pragmatic determination rather than in terms of objects and extensional identity. That mouthful notwithstanding, it is often actually simpler than life in the kingdom of nouns.

The first sense is close to what Brandom would call a concept. (See also Conceptual, Representational.)

Then there is a hylomorphic biological one where psyche or “soul” is said to be the “form” or first actuality of the body, which seems to include its capacity for nutrition and self-movement and what we might call its elemental desire.

Things having to do with second nature or second actuality, such as character or intellect in a human, constitute a further level grounded in sociality and language.

Yet another is associated with the complete actualization of a thing, which includes not only actuality but its interweaving with material contingency and structured potentiality. It is at this level that we can speak of form as a counterfactually robust effective orientation in some delimited context, fusing potentiality and actuality together.

The complex functional role of form in Aristotle has a relatively close analogue in the role of mediation in Hegel. (See also

Substance; Mutation of Meaning; Concept, Form, Species; Aristotelian Dialectic; Structure, Potentiality; Meant Realities; Difference; More Difference, Less Conflict.)

Structure, Potentiality

I now want to say, structure — which statically captures a determinate field of potential inferences — is isomorphic to Aristotelian potentiality. These concepts are mutually illuminating.

This helps clarify how Aristotelian potentiality differs from the Platonic power referenced by the same Greek word, as well shedding light on the association I have made between potentiality and counterfactual inference.

From the other direction, the thing to notice is that for Aristotle, potentiality exists only in a pair with actuality or at-work-ness. Similarly, synchronic structure exists only in a pair with diachronic process. I always read the conspicuous lack of definition of the synchronic/diachronic interface as reflecting something like Aristotle’s principled use of underdetermination in order to focus on what is most essential and clearly justifiable.

A lot of people seem to have been very confused about this latter point during the drama over 1960s French structuralism. What passed for dialogue was often a complete disconnect. “Look at how much can be explained synchronically!” “Oh no, you’re abolishing history, free will, personality, and identity!” If the new viewpoint was forgivably one-sided in its enthusiasm, some of the reaction verged on hysteria. (See also The Dreaded Humanist Debate.)

Another source of confusion seems to be that many people apparently thought of structural causality in terms of a monolithic, complete determination. I think instead that structural causality comes in many separate blocks, in an overall context of less-than-complete determination. (See also Structural Causality, Choice; Values, Causality; The Importance of Potentiality.)

Structuralism

As a very youthful person in the 1970s, I was delighted to discover support for “my” thesis that relations are prior to things (and much else of interest) in the French writers associated with so-called structuralism. (The Anglophone comparative literature people had not yet invented “poststructuralism”.) There have been many structuralisms and attributions thereof over the years. I tend to be sympathetic to a lot of them — mathematical, linguistic, and historiographical.

From my current perspective, the unifying theme is that structure — of whatever sort —statically captures a field of potential inferences. Fields of potential inference are the basis on which diverse things such as mathematical theories, proprieties of linguistic usage, practices and practical attitudes of individuals, and large cultural formations are all constituted as determinate. I actually use a variant of the notion of static capture in my day job, at the mundane level of capturing potential inferences in a software or data model. (See also Difference; Althusser’s Hegel; Foucault; Empirical-Transcendental Doublet; Archaeology of Knowledge; 1968; Imaginary, Symbolic, Real; Immediacy, Presence; Ricoeur on Structuralism; Genealogy.)

In Aristotelian terms, in addition to structure’s connection with potentiality, what has been called structural causality is actually a good interpretation of efficient causation, and also turns out to look like the operation of an unmoved mover. (See also Structure, Potentiality; Efficient Cause, Again; Potentiality, Actuality; Values, Causality.)

Leibniz

Leibniz was one of the greatest minds ever — deeply original, vastly prolific, encyclopedic like Aristotle, but working in the ferment of early modernity. He formulated many differently detailed systems, in an exploratory and tentative way. What he published during his lifetime was only a tiny fraction of his output, and not fully representative of his thought. The critical edition of his collected works will not be completed for many decades yet to come.

Leibniz favored an ethical and political ideal of what he called wise charity. An ethical being is one who does more for others than is required to satisfy rights and responsibilities or social contract, and demands less of others than would be justified, while taking care to act in ways that are sustainable and not self-destructive. I like this very much.

An avowed Lutheran who cultivated extensive dialogue with Catholic scholars and religious leaders, Leibniz was deeply disturbed by Europe’s terrible religious wars. He sought to promote tolerance, diplomacy, and understanding.

As a Platonist in theology who stressed the importance of Plato’s Euthyphro, Leibniz said that God is first and foremost supposed to be good and reasonable, not just obeyed. His God would never say “…because I said so!” Leibniz was highly sensitive to the dangers of subordinating Reason and the Good to any kind of arbitrary Will, be it divine or political. To those who objected that this limited God’s power, he replied that attributing an arbitrary will to God would degrade God to a mere tyrant and despot rather than a good and wise ruler (see Leibniz on Justice vs Power).

Leibniz partly anticipated Einstein in saying that space and time are relations.

He held that mathematical physics of the sort he helped develop was fundamentally compatible with — and complementary to — what I have referred to as Aristotle’s semantic physics.

He argued for what I take to be the Aristotelian position that identity is just discernibility.

Leibniz defended the principle of sufficient reason (cleverly phrased by the scholastics as “nothing comes from nothing”). At the same time, he held that all necessity is of the hypothetical (if-then) variety, which means that nothing is unconditionally necessary, either.

The famous monads apply his pioneering work on infinite series to an inspiration from his friend Leeuwenhoek’s discovery of microscopic organisms. On the one hand, each monad is supposed to be a self-contained microcosm of the entire universe; on the other hand, each monad contains many others that each contain many others that are also such microcosms (each with its own unique point of view on the whole), and so on to infinity. (See also Unity of Apperception.) Leibniz also had a fascinating theory of unconscious microperceptions.

Monads are said not to causally interact, but instead to mutually reflect one another in a purely synchronic way. For Leibniz, it is as though in reality everything has always already happened. It all comes down to one eternal act of God selecting the best of all possible already completely formed worlds. His thesis of the unreality of interaction seems bizarre and was never widely accepted, but the idea of synchronic mutual reflection is fascinating. (This is quite different from the pattern of determination in Hegelian mutual recognition, which has a substantial synchronic dimension but is based on interaction and has an irreducible diachronic component.) (See also Things In Themselves; Redding on Morals and Modality.)

I think Leibniz’s preformationism may be intended as a kind of edifying Platonic myth, but that is a side issue. Its practical consequence is a vision of determination and explanation by synchronic structure rather than sequential causality. Like most people, I think we also need a diachronic, interactive dimension. However, the possibilities of synchronic structural explanation are huge.

Leibniz controversially argued that we live in the best of all possible worlds. Whether or not we adopt such a view, it is important to understand that it was not nearly as naive as Voltaire’s famous satire made it out to be. For Leibniz, the criteria for a possible world are rather rigorous. A possible world is certainly not just any world we might idly imagine. All its details and all their realistic consequences must be able to coherently coexist.

Brandom has characterized Leibniz as an early inferentialist. In English, recent secondary literature is far better than most older accounts. In French, I was impressed by Yvon Belaval’s Leibniz, critique de Descartes (1960) and his student Michel Serres’ dissertation Le Système de Leibniz et ses modèles mathémathiques (1968).

Categorical “Evil”

If we are aiming at any kind of true unity of apperception, then in any given logical moment we should aim to reason in ways that are invariant under isomorphism. Over time our practical and theoretical reasoning may and will iteratively change, but synchronically we should aim to ensure that reasoning about equivalent things will be invariant within the scope of each iteration.

In higher mathematics, difficulties arise when one structure is represented by or in another structure that has a different associated notion of equivalence. This requires maintaining a careful distinction of levels. The expected consequence relation for the represented notion may not work well with the representation. Such failures of reasoning to be invariant under isomorphism are informally, half-jokingly referred to by practitioners of higher category theory as “evil”. This is a mathematical idea with a clear normative aspect and a very high relevance to philosophy.

The serious slogan implied by the half-joke is that evil should be avoided. More positively, a principle of equivalence-invariance has been articulated for this purpose. One version states that all grammatically correct properties of objects in a fixed category should be invariant under isomorphism. Another states that isomorphic structures should have the same structural properties. On the additional assumption that the only properties of objects we are concerned with are structural properties, this is said to be equivalent to the first.

There are numerous examples of such “evil”, usually associated with uncareful use of equality (identity) between things of different sorts. A significant foundational one is that material set theories such as ZFC allow arbitrary sets to be putatively compared for equality, without providing any means to effect the comparison. Comparison of completely arbitrary things is of course is not computable, so it cannot be implemented in any programming language. It is also said to violate equivalence invariance, which means that material set theories allow evil. The root of this evil is that such theories inappropriately privilege pre-given, arbitrary elements over definable structural properties. (This issue is another reason I think definition needs to be dialectically preserved or uplifted in our more sophisticated reflections, rather than relegated to the dustbin in favor of a sole emphasis on recollective genealogy. A concern to define structures and structural properties of things appears in this context as the determinate negation of the effective privileging of putatively pre-given elements over any and all rational considerations.) ZFC set theory offers a nice illustration of the more general evil of Cartesian-style bottom-up foundationalism.

The evil-generating supposition that utterly arbitrary things can be compared (and that we don’t need to care that we can’t even say how this would be accomplished) implicitly presupposes that all things whatsoever have a pre-given “Identity” that is independent of their structural properties, but mysteriously nonetheless somehow contentful and somehow magically immediately epistemically available as such. This is a mathematical version of the overly strong but still common notion of Identity that I and many others have been concerned to reject. Such bad notions of Identity are deeply involved with the ills of Mastery diagnosed by Hegel and Brandom.

We should not allow evil in foundations, so many leading mathematicians interested in foundations are now looking for an alternative to the 20th century default of ZFC. Some combination of dependent type theory for syntax with higher category theory for semantics seems most promising as an alternative. The recent development of homotopy type theory (HoTT) is perhaps the most vigorous candidate.

Another way to broadly characterize this mathematical “evil” is that it results from treating representation as prior to inference in the order of explanation, as Brandom might say, which means treating correspondence to something merely assumed as given as taking precedence over coherence of reasoning. This is a variant of what Sellars famously called the Myth of the Given. It is a philosophical evil as well as a mathematical one. Besides their intrinsic importance, these mathematical issues make more explicit some of the logical damage done by the Myth of the Given.

Another broad characterization has to do with mainstream 20th century privileging of classical logic over constructive logic, of first-order logic over higher-order logic, and of model theory over proof theory. Prior to the late 19th century, nearly all mathematics was constructive. Cantor’s development of transfinite mathematics was the main motivation for mathematicians to begin working in a nonconstructive style. Gödel’s proof that first-order logic was the richest logic for which all propositions that are true in all models are also true was thought to make it better for foundational use. Logical completeness and even soundness are standardly defined in ways that privilege model theory, which is the formal theory of representation.

It is now known, however, that there are several ways of embedding and representing classical logic — with no loss of fidelity — on a constructive foundation, so the old claim that constructive logic was less powerful has been refuted. Going in the other direction, however, classical logic has no way of recovering the computability that is built into constructive logic once it has been violated, so it is increasingly recognized that a constructive logic provides the more flexible and comprehensive starting point. (Also, transfinite mathematics can reportedly now be given a constructive foundation under HoTT.)

Since the mid-20th century there has been an immense development of higher-order concepts in formal domains, including mathematical foundations; the theory of programming languages; and the implementation of theorem-proving software. Higher-order formalisms offer a huge improvement in expressive power. (As a hand-waving analogy, imagine how hard it would be to do physics with only first-order equations.)

Type theory, proof theory, and the theory of programming languages are kinds of formalism that put inference before pre-given representations. Category theory seems to take an even-handed approach.

Although I noted some interest in Brandom on the part of people working in a higher-order constructive context, Brandom himself seems much more interested in things that would be described by paraconsistent logics, such as processes of belief revision or of the evolution of case law or common law, or of normativity writ large. (In the past, he engaged significantly with Michael Dummett’s work, while to my knowledge remaining silent on Dummet’s arguments in favor of the philosophical value of constructive logic.)

Paraconsistency is a property of some consequence relations, such that in absence of an explicit assumption that from a contradiction anything follows, not everything can in fact be proven to follow from a given contradiction, so the consequence relation does not “explode” (collapse into triviality).

In view of the vast proliferation of alternative formalisms of all sorts since the mid-20th century, it may very well be inappropriate to presume that we will ever get back to one formalism to rule them all. I do expect that homotopy type theory or something like it will eventually come to dominate work on mathematical foundations and related aspects of computer science (and everything else that falls under Hegelian Understanding, taken as a positive moment in the larger process); but as hugely important as I think these are, I am also sympathetic to Brandom’s Kantian/Hegelian idea that considerations of normativity form an outer frame around everything else, as well as to the Aristotelian view that considerations of normativity tend to resist formalization.

On the formal side, it seems it is not possible to synchronically reconcile HoTT with paraconsistency, which would seem to be a problem. (At the opposite, simple end of the scale, my other favorite logical mechanism — Aristotelian syllogism interpreted as function composition — apparently can be shown to have a paraconsistency property, since it syntactically constrains conclusions to be semantically relevant to the premises.)

Diachronically, though, perhaps we could paraconsistently evolve from one synchronically non-evil, HoTT-expressible view of the world to a dialectically better one, while the synchronic/diachronic distinction could save us from a conflict of requirements between the respective logics.

I think the same logical structure needed to wrap a paraconsistent recollective genealogy around a formal development would also account for iterative development of HoTT-expressible formal specifications, where each iteration would be internally consistent, but assumptions or requirements may change between iterations.

Actuality

Aristotelian energeia — traditionally translated as actuality — captures the status of being active or effectively operative in a process. I have somewhat awkwardly rendered it as “at-work-ness”. “Being-at-work” sounds like better English, but might wrongly be taken to refer to a kind of Being in the intransitive sense qualified by a predicate of at-work-ness. (I think Aristotle was in fact very little interested in Being in an intransitive sense. He devotes much more attention to several transitive senses.) There is no “being” at all in the Greek. Energeia is most literally “in-work-ness”, but I and others have preferred to substitute “at” for “in”, as better conveying the intended connotation in English.

Contrary to Plato’s doubts about the possibility of understanding becoming, Aristotle is committed to eliciting its intelligibility. Rather than looking for generative powers behind things as Plato had obscurely suggested might be our best hope, part of Aristotle’s strategy is to draw our attention to what is immanently at work in a process as a kind of methodological starting point. The discernment of what it was to have been such and such a thing begins from the indistinct apprehension of something we merely take to have been effectively operative. (That something would be a mediated immediacy in Hegelian terms.) It is eventually constituted with greater precision and a degree of universality through inferential elaboration of the counterfactual potentiality of what we initially took to have been effectively operative, as well as through the implicit correction over time of errors that become apparent in the course of this elaboration.

Worlds away from the dry stereotype of “essentialism”, Aristotle is if anything more of a process thinker or pragmatist. He directs our attention to the concrete actualization of things, which “essentially” involves the interweaving of effectively operative actuality with both counterfactual potentiality and material contingency. Hegel makes large use of this Aristotelian concept. Brandom associates Hegelian actualization with expression and making explicit.

There is a very interesting distinction suggested by Aristotle and developed by later writers between a “first” and “second” actuality. Whereas the first actuality of an organic body is not too far from the later Stoic conatus as an internal source of primitive desiring activity, second actuality applies to things associated with evolved practice like habit, character, and intellect.

Aristotle also speaks about the “First” cause as pure at-work-ness, with no admixture of potentiality. I take this to mean that the “First” cause — just as the higher-order goal at which everything indirectly aims — is effectively operative in things, but unlike other effectively operative things, it has no counterfactual aspect (because it has no factual aspect, because it exactly is a pure aim rather than something having an aim). It functions as an ideal of normativity that we can retroactively see to have been at work, as a sort of virtual, uplifting attractor of purely natural desire, and also more speculatively as a posited virtual attractor for the directionality in material tendencies. (See also Aristotelian Actualization; Moved, Unmoved.)

Identity, Isomorphism

Many strands of Western thought — from Augustinian theology to Cartesianism to set theory — have suffered from overly strong notions of what amounts to a privileged, originary, self-evident, contentful Identity of things. (There are also many significant exceptions. With their emphasis on distinctions of form, Plato and Aristotle only needed a weak identity. Spinoza’s emphasis on relations; Leibniz’s identity of indiscernibles; Hume’s dispersive empiricism; and Kant’s critical perspective are all closer to Plato and Aristotle in this regard. Hegel makes identity derivative from a Difference associated with Aristotelian contrariety or Brandomian material incompatibility. Nietzsche, Wittgenstein, and many 20th century continentals explicitly criticized the overly strong concept.)

21st century mathematics has seen tremendously exciting new work on foundations that bears on this question. Homotopy type theory very strongly suggests among other things that the identity needed to develop all of mathematics is no stronger than isomorphism. This provides a formal justification of the common practical attitude of mathematicians that isomorphic structures can be substituted for one another in a proof by an acceptable “abuse of notation”.

More generally, type theory and category theory provide an independent basis in contemporary mathematics for reaffirming the priority of form as difference over identity. I am tempted to say that they exemplify a kind of inferentialism in mathematics. (To those who say mathematics holds no lessons for philosophy, I would say that generalization disregards the specific character of these developments. nLab, the website for higher category theory, even has a page on Hegel’s logic as a modal type theory that explicitly refers to Brandom’s interpretation of Hegel!)

Matter, Potentiality

I’ve suggested nonstandard readings of both Aristotelian matter and Aristotelian potentiality. While traditionally there is thought to be a loose analogy such that matter is to form as potentiality is to actuality, the two concepts as I am reading them are sharply distinct. Matter captures the accumulation of contingent fact. Potentiality captures counterfactually robust inference. Matter particularizes, while potentiality universalizes.

Potentiality seems to me to be a kind of form. This is a bit tricky, because an important classical sense of Aristotelian matter that I have not been emphasizing is associated with a disposition to respond in certain ways when acted upon. This, however, sounds like counterfactual potentiality to me.