Proclus’ Elements

The later neoplatonist Proclus (412-485 CE) was head of the Platonic Academy in Athens, at a time when the Athenian Academy was somewhat notorious as the intellectual center of resistance to the spread of Christianity in the Roman Empire. Nonetheless, his work had a profound influence on the Arabic, Byzantine, and Latin traditions. He is usually cited as the main philosophical influence on the early Christian theologian pseudo-Dionysius, who was taken very seriously by Albert the Great and Thomas Aquinas.

Proclus wrote extensive commentaries on Plato, as well as an influential commentary on book 1 of Euclid’s Elements of Geometry. Hegel called him the greatest dialectician of antiquity. Though I think Hegel by his own principles really should have given that title to Aristotle, Hegel was right to recognize Proclus as important.

Aquinas is credited with recognizing that the Latin Book of Causes — a translation of the Arabic Discourse on the Pure Good — was mostly derived from Proclus’ Elements of Theology. Aquinas treated Proclus himself with considerable respect. Dietrich of Freiberg made significant use of his work, and his student Berthold of Moosburg wrote a very long commentary interpreting the Elements of Theology in Christian terms. The Renaissance theologian Nicolas of Cusa and the maverick Giordano Bruno were much inspired by Proclus.

Along with Spinoza’s Ethics, Proclus’ Elements shares the peculiar distinction of being written in a style visibly influenced by Euclid’s Elements. Euclid’s work has often been cited as a sort of paradigm of demonstrative reasoning. Though Proclus, unlike Spinoza, did not work from explicit definitions and postulates and used a looser style of demonstration, his Elements consists of theorems and a sort of demonstrations.

Proclus defends the neoplatonic idea of a One that transcends being, but as Gwenaëlle Aubry and Laurent Lavaud point out in the introduction to the French collection Relire les Éléments de théologie de Proclus (2021), perhaps his most influential idea is that of a very strong continuity from the highest principles to the most mundane effects, which has been read as a strong assertion of immanence as well as transcendence. He is an important source for all the later theological traditions that want to argue for simultaneous immanence and transcendence.

Proclus very explicitly crystallizes what I have called the generalized “unmoved mover” model of causality in Plotinus. For Proclus, “higher” and “lower” causes cooperate in the constitution of worldly things, but the higher cause is always more of a cause than the lower cause. At the same time, he rejects Plotinus’ identification of matter with evil, while emphasizing all of Plotinus’ more positive affirmations of the goodness of manifestation and the beauty of the cosmos.

In a separate treatise On Providence, he develops a sort of epistemic analogue to the generalized unmoved mover theory. “Providence” (pronoia — literally, “forethought”) is a knowledge-like thing that is superior to knowledge in that it is supposed to be eternal and unextended, and to involve no separation of what we might call subject and object. Proclus develops a subtle and suggestive account of something metaphorically like implicit, unextended “seeds” of forms within the overflowing of the One that transcends all extended form. While the One does not “know” worldly things, it “pre-knows” their unextended “seeds”, within something like what Schelling later paradoxically called the identity of identity and nonidentity.

In the Elements, Proclus argues for an interdependence of being, life, and intellect. While one obvious reading of this would emphasize a foundational role of spiritual beings in Proclus’ metaphysics, I am intrigued that it can also be interpreted as a somewhat “deflationary” account of being, closer to Aristotle, and far removed from later notions of pure abstract existence. We can’t begin to have an account of being, without also having an account of life and intellect. With his endorsement of a One beyond “being”, Proclus had no need for a commitment to a notion of pure “being”.

Not Power and Action

My copy of Gwenaëlle Aubry’s Genèse du dieu souverain arrived today, and I’ve started to look at the front matter. She begins by explaining why Aristotelian potentiality and actuality are not reducible to concepts of power and action. In the Metaphysics, the most sophisticated sense of being and substance is associated with the pair en dunamei and energeia. Whereas the grammatical nominative form dunamis could connote an active power, she says the dative form en dunamei was used by Aristotle precisely to distinguish from this. The other essential distinguishing feature of Aristotle’s approach was to make the en dunamei dependent on an energeia (act, actuality, or at-work-ness), a term of Aristotle’s own invention. In French, Aubry translates en dunamei for potentiality as en-puissance, as distinct from the puissance that means power.

“[Potentiality] names, for a given being, the principle of a movement oriented by the act that is also its end and its proper good” (p. 10, my translation throughout). Actuality and potentiality, she says, thus provide an alternative model to that of efficient causality based on the relation between an active and a passive power.

“In the same way that potentiality is not power (active or passive), act is not action. Act does not act [L’act n’agit pas]. On the contrary, it names that for which we act or move: the telos or end, which is also the good” (ibid). Nor should the relation between potentiality and actuality be reduced to that between matter and form. She notes that Aristotle never referred to god as “pure form”.

She observes that book Lambda of the Metaphysics (1071a 4-5) singles out potentiality and actuality as applicable by analogy to all substances of all kinds. (Scholars debate whether “by analogy” adequately translates Aristotle’s pros hen or “toward one”, but that is a side issue.) “This assures at the same time the generality of the ontological discourse and the real primacy of the theological principle” (ibid). (I prefer to avoid the term “ontology”, but that is another side issue.)

“Determining [god] as pure act, [Aristotle’s view based on potentiality and actuality] poses [god] as at the same time identical with the good” (p. 11). She reads Aristotle’s statement of the project of the Metaphysics in book Alpha as “posing the good as a principle and identifying the causality proper to it” (p. 12). The Latin medieval tradition mostly followed Avicenna in treating the Metaphysics as what Duns Scotus called ontology, but the great commentator Averroes characterized the Metaphysics as a philosophical theology, and Aubry also calls it an axiology, or study of goodness and value.

Phenomenological Reduction?

This is a follow-up to my earlier article on Husserlian and existential phenomenology in light of the past year’s reading of Paul Ricoeur. In The Conflict of Interpretations (French ed. 1969), Ricoeur discusses the impact of his own view of hermeneutics as a “long detour” essential to understanding.

Ricoeur wrote that “It is in spite of itself that [Husserlian] phenomenology discovers, in place of an idealist subject locked within its system of meanings, a living being which from all time has, as the horizon of all its intentions, a world, the world. In this way, we find delimited a field of meanings anterior to the constitution of a mathematized nature, such as we have represented it since Galileo, a field of meanings anterior to objectivity for a knowing subject. Before objectivity, there is the horizon of the world; before the subject of the theory of knowledge, there is operative life” (p. 9). “Of course, Husserl would not have accepted the idea of meaning as irreducibly nonunivocal” (p. 15).

“In truth, we do not know beforehand, but only afterward, although our desire to understand ourselves has alone guided this appropriation. Why is this so? Why is the self that guides the interpretation able to recover itself only as a result of the interpretation? …the celebrated Cartesian cogito, which grasps itself directly in the experience of doubt, is a truth as vain as it is invincible…. Reflection is blind intuition if it is not mediated by what Dilthey called the expressions in which life objectifies itself. Or, to use the language of Jean Nabert, reflection is nothing other than the appropriation of our act of existing by means of a critique applied to the works and the acts which are the signs of this act of existing…. [R]eflection must be doubly indirect: first, because existence is evinced only in the documents of life, but also because consciousness is first of all false consciousness, and it is always necessary to rise by a corrective critique from misunderstanding to understanding” (pp. 17-18). This is a nice expression of what I take to be one of the greatest lessons of Aristotle and Hegel (see First Principles Come Last; Aristotelian Actualization; What We Really Want.)

For Ricoeur, Husserlian phenomenological reduction ceases to be a “fantastic operation” identified with a “direct passage”, “at once and in one step”. Rather, “we will take the long detour of signs” (p. 257).

Husserl’s “reductions” reduced away reference to putatively existing objects in favor of a sole focus on what would be the Fregean sense in meaning. Ricoeur wants to reintroduce reference, and in this way to distinguish a semantics that includes consideration of reference from a semiology addressing pure sense articulated by pure difference. Reference for Ricoeur is not a primitive unexplained explainer, but something that needs to be explained, and a big part of the explanation goes through accounts of sense. Ricoeur also wants to connect reference back to the earlier mentioned “self that guides the interpretation”, which again functions as an end rather than being posited as actual from the outset.

Similarly to his critique of phenomenological reduction “at once and in one step”, he criticizes Heidegger’s “short route” that in one step simply replaces a neo-Kantian or Husserlian “epistemology of interpretation” with an “ontology of understanding”. Ricoeur is a lot more deferential to Heidegger than I would be at this point, but for Ricoeur such an ontology is again only a guiding aim, and not a claimed achievement like it was for Heidegger. I think this makes Ricoeur’s “ontological” interest reconcilable with my own “anti-ontological” turn of recent years, because my objections have to do with claimed achievements. I broadly associate Ricoeur’s modest ontology-as-aim with my own acceptance of a kind of inquiry about beings that avoids strong ontological claims. Even Heidegger emphasized Being as a question.

Ricoeur of course rejects foundationalist epistemology (see also Kant and Foundationalism), but sees both an epistemology of interpretation and an ontology of understanding as aims guiding the long detour. He effectively contrasts the long path of investigation of meaning with the short path of appeals to consciousness (see also Meaning, Consciousness).

I actually like the idea he attributes to Husserl of reducing being to meaning or the sense(s) of being. If meaning is fundamentally nonunivocal as Ricoeur says rather than univocal as Husserl wanted, this would not be idealist in a bad sense.

Brandom’s simpler suggestion that reference is something real but that it should be ultimately explained in terms of sense seems to me a further improvement over Ricoeur’s apparent notion of reference as a kind of supplement to sense that nonetheless also needs to be explained in terms of sense, but without being reduced to it. I see the inherently overflowing, non-self-contained nature of real as compared to idealized being/meaning as making a supplement superfluous. (See also Reference, Representation; Meant Realities.)

Lévinas on the Other

Emmanuel Lévinas (1905-95) was an important religiously oriented philosopher within the existential-phenomenological tradition. He translated Husserl’s Cartesian Meditations to French. His most famous work Totality and Infinity (French edition 1961) — dedicated to Gabriel Marcel and Jean Wahl — argues at top level that philosophy has often been dominated by a drive for a vision of totality, and that we should abandon this in favor of the “infinity” of our experience of the Other, which for Lévinas leads from an ethical concern to a sort of eschatology. He puts ethics before ontology, which I like, but still takes a more metaphysical approach than Marcel, for instance.

I appreciate his stress on concern for others, but have trouble applying the notion of infinity in this context. I’m more comfortable talking about the essential incompleteness of our experience as finite beings. Lévinas is right that reaching for totality is overreaching, but I think Plato and Aristotle — and also Kant, and even especially Hegel (so different from the common stereotype) — already clearly recognized this. In my view, ordinary open-ended interpretation already implicitly poses a potentially infinite (i.e., indefinitely extensible, and therefore always incomplete) task that we cut short in order to act, but we never in experience encounter an actual or completed infinite. Ethical encounter with others highlights the incompleteness (i.e., non-totality, in Lévinas’ terms) of our understanding.

This incompleteness — and the thickness and “overflowing” character of meant realities or informal “being” that is its complement — already seems to me sufficient to support an ethical, hospitable relation to the other. I want to say that an overflowing beyond objectifying schemas is characteristic not just of absolute transcendence and infinity, but of ordinary being and ordinary meaning. Routinely in everyday life, there is meaningful intelligibility and there is overflow, in the very same context. Even in the most ordinary moments, with sufficient openness we can find poetic reverie and ethical awe that takes us outside of ourselves.

Lévinas speaks of the “absolutely other” as “truth” in the sense of a religious transcendence, to which ethics is the “royal road” (p. 29). Transcendence, Lévinas says, should not be confused with ecstasy or magical communion. He has in mind a more sober kind of religion. He cites Marcel and Martin Buber on the irreducibility of the relationship to the Other to objective knowledge, and associates the driving of practice by theory with a failure to recognize this primacy of the other. With Kant, Hegel, and Brandom, I think we should recognize that theoretical reason actually depends on a practical reason that renounces Mastery; that theoretical reason is more of a tool, whereas practical reason is more of an agency; and that practical reason begins with recognition of the other.

I like when he speaks of a “generosity nourished by the Desired” (p. 34). He goes on to talk about a metaphysical Desire for the absolutely Other, “non-adequate to the idea” (ibid). Less metaphysically, I see forms overflowing their boundaries without thereby ceasing to be forms, and locate meaning in a foundationless but relatively stable difference in a relation of reciprocal co-grounding with moral commitment and practical judgment.

He talks about the reduction of the Other to the Same, and seems to think most philosophy does that. I have a more optimistic or charitable view that I think is also more historiographically valid. Aristotle and Hegel especially (contrary to common stereotypes) are very careful to avoid claiming overly strong Identity, so it is really not fair to say they reduce the Other to the Same.

Directly contrary to my view, he says that “The calling into question of things in a dialectic is not a modifying of the perception of them; it coincides with their objectification” (p. 69; emphasis in original). Disappointingly, he seems to prefer an authoritative teacher whom he calls an absolute Stranger. “The absolutely foreign alone can instruct us” (p. 73). It’s starting to sound like Kierkegaard here. I feel that hyperbolic expressions like this begin to denigrate ordinary life, and ultimately lead to a sort of absolute inflation. Lévinas’ Other is supposed to be a source of gentleness rather than arbitrariness, but to me what is gentle — much as it may exceed any objectification — cannot be absolutely foreign. I prefer to emphasize goodness rather than power, and I want to say that goodness speaks to us, so it cannot be absolutely foreign. (See also Immanence, Transcendence.)

Marcel on Being

I’ve been looking at Marcel’s The Mystery of Being (1950). “[I]t is not possible to treat all experience as coming down in the end to a self’s experience of its own states…. we shall see… how difficult it is to succeed in getting a direct glimpse of whatever it is that we mean by self.” (Vol. 1, p. 63-64; emphasis in original). “I appear to myself both as a somebody and not a somebody, a particular individual and not a particular individual” (p. 106). “This self to which I have to be true is perhaps merely the cry that comes out to me from my own depths — the appeal to me to become that which, literally and apparently, I now am not” (p. 176). Properly speaking, we should not say that our self exists, as this would make it a thing among other things.

Marcel says Truth should not be reduced to what is the case; it is an illumination. He distinguishes between primary reflection, which is objectifying, and secondary reflection, in which we ourselves are part of the reflection. In secondary reflection, we are participants rather than spectators. For example, “my” body is not some thing that I have, but rather something in which I am involved. More problematically from this writer’s point of view, he adds that my body is to me a sort of “non-mediatizable immediate” (p. 135).

To be is to be in a situation, understood in the participatory rather than the objectifying sense. We navigate situations by active processes of recognition and reconnoitring. “[A] being that can say, ‘My situation’… is not… self-contained; on the contrary, such a being is open and exposed” (p. 178; emphasis in original). “My life infinitely transcends my possible conscious grasp of my life… fundamentally and essentially it refuses to tally with itself” (p. 206). We should not represent a life as a series of movie stills.

Being is also being with, or togetherness with others. “[I]ntersubjectivity plays its part also within the life of the subject, even at moments when the latter’s only intercourse is with itself” (p. 224).

We should distinguish between an object and a presence. A presence lies beyond the grasp of any possible prehension, and can only be invoked or evoked. A rose in a poem is present to us in a way that a rose in a seed catalog is not. A mystery for Marcel is something that transcends the realm of technical solutions, in that we cannot hold it at arm’s length and objectify it, because it involves our own very being. Every Marcelian “presence” is mysterious in this way. “A felt quality… is not a mental object” (p. 231). Truth is not a thing, but a spirit. It is in this sort of way, he says, that essence should be understood.

In approaching the question of what Being is, “I have to think not only for myself, but for us… for everyone who may have contact with the thought which is mine” (Vol. 2, p. 6). We must exorcize the ego-centric spirit. “A complete and concrete knowledge of oneself… must be hetero-centric” (p. 9). He contrasts “we are” with “I think”. “[T]he intelligible milieu… is only the projection on an ideal plane of what existentially speaking presents itself to us as the intersubjective nexus” (p. 12). “[I]t is literally true to say that the more exclusively it is I who exist, the less do I exist” (p. 38; emphasis in original). He equates a transcendental ego with solipsism, but says that Being is not reducible to intersubjectivity, either.

Ontology for Marcel is concerned with acts of judgment associated with the “is” of predication, rather than with objects. He contrasts the “fullness” of truth with “the hollowness of a functionalized world” (p. 47). Fullness is not to be confused with totality, and being cannot be reduced to totality. Any fullness of truth involves secondary reflection, from which we cannot separate ourselves as participants. Being cannot be indifferent to value. Faith must be distinguished from opinion; it is a matter of believing in, not believing that. Real prayer, he says, is possible only where intersubjectivity is operative.

A free act is one that “I come to think of, after the event, as having helped to make me what I am” (p. 131). “[W]e are concerned here with a certainty which I am rather than with a certainty which I have… I am a living testimony” (p. 144). Just as there is creative fidelity, there is creative testimony, but the creativity in question involves an active receptivity, not a simple production.

Marcel’s invocations of “being” and “existence”, as well as of “presence” and of “ontology” all seem rather different from the standard, representationally oriented usages of these terms, to which I have expressed various objections. He also did not engage in anything like Heidegger’s dubious historiography of a “forgetting of Being”.

Early in the book, he seemed to reject “what is” questions as inherently objectifying. I think that questions of what and why are most naturally treated as matters of open-ended interpretation, and that ontology, epistemology, and all manner of specific technical disciplines can be subsumed under hermeneutics, which is in turn subsumed under ethics. From my perspective, what Marcel would have regarded as objectifying perspectives can thus be subsumed in a way that undoes their objectifying character.

Although Marcel’s style of exposition and vocabulary are very different from Aristotle’s, the broad spirit of his perspective seems very close in important respects. To a greater extent than most other philosophers, Aristotle and Marcel each in their own way brought to the fore an emphasis on concreteness and the way we encounter things in life. (Marcel’s pessimistic view of “what is” questions is perhaps the most significant difference. Aristotle also did not have explicit analogues of Marcel’s “presence” and “mystery”.)

While I am uncomfortable with Marcel’s top-level characterization of my relation to my body as an un-mediatizable immediacy because I think it involves the mediation of something like the unconscious level of Kantian processes of synthesis, I very much like the ethical contrast of being and having that informs the details of his account of this. Marcel doesn’t explicitly say as I do that “being” is primarily an ethical concept, but his account seems open to such an interpolation. (See also Ricoeur on Embodiment; Platonic Truth; Meant Realities; Being, Consciousness.)

Ricoeurian Ethics

In the final chapters of Oneself as Another, Ricoeur develops a meta-level discourse about ethics, and concludes with a few “ontological” suggestions. Universalizing Kantian morality and the obligation it entails are said to provide a valuable extension to Aristotelian ethics, but ultimately to require supplementation by a return to Aristotelian practical judgment. This seems just about exactly right.

On the Kantian side, norms are said to concretize Aristotelian aims. The most important and general Kantian norm, according to Ricoeur, is reciprocity. He argues for the importance of the golden rule, citing Rabbi Hillel and the Gospels of Luke and Matthew. The distinction between “power over” and “power to” is discussed. The notion of persons as ends in themselves is emphasized. Procedural justice is seen to complement Aristotelian distributive justice. John Rawls’ summary of justice as fairness is endorsed. Although it is ultimately necessary to return to the openness of practical judgment, the passage through universalizing morality is equally necessary, as a safeguard against arbitrariness. Universality and contextuality go hand in hand, much as I have been arguing.

Writing at a time when French anti-Hegelianism was still quite influential and before the rise of new interest in Hegel, Ricoeur did not think Hegelian Geist — which he mistakenly saw as turning the state into an “agency capable of thinking itself by itself” (p. 255) — fit well with the notion of self Ricoeur wanted to advance. He did not want to follow what he saw as Hegel’s path in returning to an ethics of Sittlichkeit or mores embedded in concrete culture, but saw great potential value in a Sittlichkeit separated from the “ontology of Geist” (ibid) and the “thesis of the objective mind” (p. 256), especially if Sittlichkeit were “bent” in the direction of the openness of Aristotelian practical judgment. (A reading of Geist free of such ontology has more recently been argued by Brandom and others to be a better reading of Hegel himself.) “Our final word in this ‘little ethics’… will be to suggest that the practical wisdom we are seeking aims at reconciling Aristotle’s phronesis, by way of Kant’s Moralität, with Hegel’s Sittlichkeit” (p. 290).

On other matters such as the broad thrust of Hegel’s critique of atomistic individualism in the Philosophy of Right and the general value of dialectic, Ricoeur defended Hegel. The Hegelian concept of Right, he says, “surpasses the concept of justice on every side” (p. 253). The “problematic of realization, of the actualization of freedom, is ours as well in this study” (ibid). Reflection, he says, needs the mediation of analysis.

He says that institutionalized conflict is an essential feature of democracy. We should be accepting of conflict, but draw the line at violence. The idea of Rawls that argumentation is “the critical agency operating at the heart of convictions” (p. 288; emphasis in original), raising convictions to the level of considered convictions and resulting in a “reflective equilibrium”, is cited with approval. Ricoeur speaks of a “reflective equilibrium between the ethics of argumentation and considered convictions” (p. 289).

Respect for persons should take priority over respect for the law. The importance of keeping promises extends beyond its role with respect to personal identity to the space of reciprocity and the golden rule. Gabriel Marcel is quoted as saying all commitment is a response to an other. A notion of imputability is introduced as an ascription of action “under the condition of ethical and moral predicates” (p. 292). To this is added a notion of responsibility. Finally, he endorses Hegel’s concept of mutual recognition.

Unlike Brandom, Ricoeur construed the philosophy of language as analytically separate from ethics. He thus saw a need to go beyond its boundaries, and characterized that as an “ontological” moment. This seems to have two main ingredients.

First, the key to understanding the notion of self he wants to advance lies in Aristotelian potentiality and actuality. He also wants to understand actuality and self in connection with Heideggerian being-in-the-world. “[S]elf and being-in-the-world are basic correlates” (p. 313). Actuality should not be thought in terms of presence. Self should not be confused with “man”, and is not a foundation. Spinoza’s conatus or the general effort of beings to persevere finds its highest expression in Aristotelian energeia or actuality, and thus overflows its deterministic origins. The distinction between actuality and potentiality is associated with that between selfhood and sameness. (See also The Importance of Potentiality.)

Second, a discussion of Husserl’s distinction between the body (viewed externally) and “flesh” in which we live leads eventually to the conclusion that a dialectic of the Same and the Other cannot be constructed “in a unilateral manner” (p. 331). A final discussion of Nietzsche, Heidegger, and Lévinas leads to an “ultimate equivocalness with respect to the Other in the phenomenon of conscience” (p. 353). We need an alternative to “constitution in and through the ego” (p. 334), and he thinks an adaptation of Husserl’s notion of flesh provides this. Unfortunately, he speaks in passing of an “originary, immediate givenness of the flesh to itself” (p. 333). I think the notion of flesh is supposed to suggest something that softens the kind of rigid boundaries between self and other that we associate with an ego, and that is all good. But the other big issue with constitution of meaning through the ego is precisely that the ego was supposed to be a locus of originary, immediate givenness. It seems to me that one of the great values of a hermeneutic perspective is that it does not need to assume anything like that.

With the exception of this brief reference and his apparent attribution in passing of a reflexive “self” to Aristotle, the degree of convergence with what I have been developing here is impressive indeed.

(I think the kind of reflexivity Ricoeur had in mind in the latter case was only intended to be related to action, so his intent was to capture the fact that we can and do act on ourselves. This, I think, is a true and important observation. My quibble there is with attributing a notion of self as a simple unity to Aristotle.)

Heidegger

Martin Heidegger (1889–1976) was a tremendously original, highly influential, and troublesome philosopher. What makes his work troublesome is not only conceptual difficulty and a deliberate practice of translating the familiar into the unfamiliar, but also his never clearly repudiated attempt to influence the Nazi movement in Germany. He seems to have been a cultural and linguistic chauvinist who rejected pseudo-biological racism, but nonetheless put hopes in an “inner truth and greatness” of National Socialism as an alternative to American and Soviet materialism. This identification puts a dark cloud over the interpretation of his writing, which was, however, generally very far removed from politics. The question is, how much it is possible to detach his work from a stance that seems worse than one of mere bad judgment.

A serious and innovative reader of Aristotle who also developed thought-provoking readings of Plato, Kant, Hegel, and Nietzsche, Heidegger combined a sympathetic but critical take on Husserl’s phenomenology with an interest in the hermeneutics of Wilhem Dilthey. Widely read as an “existentialist”, he sharply repudiated Sartre’s appropriation of his work. In his later works, he approached philosophy as a kind of poetic meditation.

His most famous thesis was that Western thought largely lost its way from Plato onward, neglecting the question of the meaning of Being in favor of preoccupation with things. While he made good points about the preconceptions involved in our ordinary encounters with things, I think he too sharply rejected “ontic” engagement with empirical, factual concerns in favor of a purified ontology. He also promoted a valorization of what I would call the pre-philosophical thought of the pre-Socratics Heraclitus and Parmenides. I think Plato and especially Aristotle represented a gigantic leap forward from this.

Some of Heidegger’s very early work was on the medieval theologian Duns Scotus, who seems to have originated the standard notion of ontology later promoted by Wolff and others. In sharp contrast to the tradition stemming from Scotus, Heidegger argued that Being is not the most generic concept, and wanted to emphasize a “Being of beings” in contrast to their factual, empirical presentation. He did not follow the path of Aquinas in identifying pure Being with God, either, and Aquinas probably would have rejected his talk of the Being of beings.

I think his most important contribution was an emphasis on what he called “being-in-the-world” as a way of overcoming the dichotomy of subject and object. His associated critique of Cartesian subjectivity has been highly influential. In later works, he also recommended putting difference before identity, and relations before things. Although the way he expounded these notions was quite original, I prefer to emphasize their roots in Aristotle, Kant, and Hegel. (See also Being, Existence; Being, Consciousness; Beings; Phenomenological Reduction?; Memory, History, Forgetfulness — Conclusion.)

Form as a Unique Thing

Ever since Plato talked about Forms, philosophers have debated the status of so-called abstract entities. To my mind, referring to them as “entities” is already prejudicial. I like to read Plato himself in a way that minimizes existence claims, and instead focuses on what I think of as claims about importance. Importance as a criterion is practical in a Kantian sense — i.e., ultimately concerned with what we should do. As Aristotle might remind us, what really matters is getting the specific content of our abstractions right for each case, not the generic ontological status of those abstractions.

One of Plato’s main messages, still very relevant today, is that what he called Form is important. A big part of what makes Form important is that it is good to think with, and a key aspect of what makes Plato’s version good to think with is what logically follows from its characterization as something unique in a given case. (Aristotle’s version of form has different, more mixed strengths, including both a place for uniqueness and a place for polyvocality or multiple perspectives, making it simultaneously more supple and more difficult to formalize.) In principle, such uniqueness of things that nonetheless also have generality makes it possible to reason to conditionally necessary outcomes in a constructive way, i.e., without extra assumptions, as a geometer might. Necessity here just means that in the context of some given construction, only one result of a given type is possible. (This is actually already stronger than the sense Aristotle gave to “necessity”. Aristotle pragmatically allowed for defeasible empirical judgments that something “necessarily” follows from something else, whenever there is no known counter-example.)

In the early 20th century, Bertrand Russell developed a very influential theory of definite descriptions, which sparked another century-long debate. Among other things (here embracing an old principle of interpretation common in Latin scholastic logic), he analyzed definite descriptions as always implying existence claims.

British philosopher David Corfield argues for a new approach to formalizing definite descriptions that does not require existence claims or other assumptions, but only a kind of logical uniqueness of the types of the identity criteria of things. His book Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy, to which I recently devoted a very preliminary article, has significant new things to say about this sort of issue. Corfield argues inter alia that many and perhaps even all perceived limits of formalization are actually due to limits of the particular formalisms of first-order classical logic and set theory, which dominated in the 20th century. He thinks homotopy type theory (HoTT) has much to offer for a more adequate formal analysis of natural language, as well as in many other areas. Corfield also notes that most linguists already use some variant of lambda calculus (closer to HoTT), rather than first-order logic.

Using first-order logic to formalize natural language requires adding many explicit assumptions — including assumptions that various things “exist”. Corfield notes that ordinary language philosophers have questioned whether it is reasonable to suppose that so many extra assumptions are routinely involved in natural language use, and from there reached pessimistic conclusions about formalization. The vastly more expressive HoTT, on the other hand, allows formal representations to be built without additional assumptions in the representation. All context relevant to an inference can be expressed in terms of types. (This does not mean no assumptions are involved in the use of a representation, but rather only that the formal representation does not contain any explicit assumptions, as by contrast it necessarily would with first-order logic.)

A main reason for the major difference between first-order logic and HoTT with respect to assumptions is that first-order logic applies universal quantifications unconditionally (i.e., for all x, with x free or completely undefined), and then has to explicitly add assumptions to recover specificity and context. By contrast, type theories like HoTT apply quantifications only to delimited types, and thus build in specificity and context from the ground up. Using HoTT requires closer attention to criteria for identities of things and kinds of things.

Frege already had the idea that logical predicates are a kind of mathematical function. Mathematical functions are distinguished by invariantly returning a unique value for each given input. The truth functions used in classical logic are also a kind of mathematical function, but provide only minimal distinction into “true” and “false”. From a purely truth-functional point of view, all true propositions are equivalent, because we are only concerned with reference, and their only reference (as distinguished from Fregean sense) is to “true” as distinct from “false”. By contrast, contemporary type theories are grounded in inference rules, which are kinds of primitive function-like things that preserve many more distinctions.

In one section, Corfield discusses an HoTT-based inference rule for introduction of the definite article “the” in ordinary language, based on a property of many types called “contractibility” in HoTT. A contractible type is one that can be optionally taken as referring to a formally unique object that can be constructed in HoTT, and whose existence therefore does not need to be assumed. This should also apply at least to Platonic Forms, since for Plato one should always try to pick out the Form of something.

In HoTT, every variable has a type, and every type carries with it definite identity criteria, but the identity criteria for a given type may themselves have a type from anywhere in the HoTT hierarchy of type levels. In a given case, the type of the identity criteria for another type may be above the level of truth-functional propositions, like a set, groupoid, or higher groupoid; or below it, i.e., contractible to a unique object. This sort of contractibility into a single object might be taken as a contemporary formal criterion for a specification to behave like a Platonic Form, which seems to be an especially simple, bottom-level case, even simpler than a truth-valued “mere” proposition.

The HoTT hierarchy of type levels is synthetic and top-down rather than analytic and bottom-up, so everything that can be expressed on a lower level is also expressible on a higher level, but not necessarily vice versa. The lower levels represent technically “degenerate” — i.e., less general — cases, to which one cannot “compile down” in some instances. This might also be taken to anachronistically explain why Aristotle and others were ultimately not satisfied with Platonic Forms as a general basis for explanation. Importantly, this bottom, “object identity” level does seem to be adequate to account for the identity criteria of mathematical objects as instances of mathematical structures, but not everything is explainable in terms of object identities, which are even less expressive than mere truth values.

Traditionally, mathematicians have used the definite article “the” to refer to things that have multiple characterizations that are invariantly equivalent, such as “the” structure of something, when the structure can be equivalently characterized in different ways. From a first-order point of view, this has been traditionally apologized for as an “abuse of language” that is not formally justified. HoTT provides formal justification for the implicit mathematical intuition underpinning this generally accepted practice, by providing the capability to construct a unique object that is the contractible type of the equivalent characterizations.

With this in hand, it seems we won’t need to make any claims about the existence of structures, because from this point of view — unlike, e.g., that of set theory — mathematical talk is always already about structures.

This has important consequences for talk about structuralism, at least in the mathematical case, and perhaps by analogy beyond that. Corfield argues that anything that has contractible identity criteria (including all mathematical objects) just is some structure. He quotes major HoTT contributor Steve Awodey as concluding “mathematical objects simply are structures. Could there be a stronger formulation of structuralism?”

Thus no ontology or theory of being in the traditional (historically Scotist and Wolffian) sense is required in order to support talk about structures (or, I would argue, Forms in Plato’s sense). (In computer science, “ontology” has been redefined as an articulation of some world or domain into particular kinds, sorts, or types, where what is important is the particular classification scheme practically employed, rather than theoretical claims of real existence that go beyond experience. At least at a very high level, this actually comes closer than traditional “metaphysical” ontology did to Aristotle’s original practice of higher-order interpretation of experience.)

Corfield does not discuss Brandom at length, but his book’s index has more references to Brandom than to any other named individual, including the leaders in the HoTT field. All references in the text are positive. Corfield strongly identifies with the inferentialist aspect of Brandom’s thought. He expresses optimism about HoTT representation of Brandomian material inferences, and about the richness of Brandom’s work for type-theoretic development.

Corfield is manifestly more formally oriented than Brandom, and his work thus takes a different direction that does not include Brandom’s strong emphasis on normativity, or on the fundamental role of what I would call reasonable value judgments within material inference. From what I take to be an Aristotelian point of view, I greatly value both the inferentialist part of Brandom that Corfield wants to build on, and the normative pragmatic part that he passes by. I think Brandom’s idea about the priority of normative pragmatics is extremely important; but with that proviso, I still find Corfield’s work on the formal side very exciting.

In a footnote, Corfield also directs attention to Paul Redding’s recommendation that analytic readers of Hegel take seriously Hegel’s use of Aristotelian “term logic”. This is not incompatible with a Kantian and Brandomian emphasis on the priority of integral judgments. As I have pointed out before, the individual terms combined or separated in canonical Aristotelian propositions are themselves interpretable as judgments.

Ontology

Ontology as a supposed science of being acquired its basic shape in the middle ages, as a sort of reification of Aristotelian semantics. Duns Scotus was very proud of his ontological “improvement” of Aristotle. Aristotle himself preferred to shift clumsy, sterile discussions of sheer being onto more subtle and fruitful registers of form and meaning at the earliest opportunity.

Kant pointed out that existence is not a property, and Hegel pointed out the equivalence of Being to Nothing. When Hegel talks about “logic” as the form of future metaphysics, this means a return to the original meaning of “metaphysics” as Aristotelian dialectical semantics, not an ontologization of dialectic. Broadly Aristotelian dialectical semantics give us all the “ontology” we will ever need.

For the historical back story of how Scotus invented ontology as we know it today, if you read French, see Olivier Boulnois, Être et représentation: Une généalogie de la métaphysique moderne à l’époque de Duns Scot (XIIIe–XIVe siècle). As suggested by the title, this work also has extremely important things to say about the premodern history of strongly representationalist views. The famous univocal “being” invented by Scotus was defined in terms of representability. (See also Being, Existence; Aristotelian Dialectic; Objectivity of Objects; Form; Repraesentatio.)

Johnston’s Pippin

Adrian Johnston’s A New German Idealism just arrived, and I’m taking a quick look. It is mainly concerned with Slavoj Žižek’s work. But for now, I’m just concerned with chapter 2 — where Johnston launches a broadside against “deflationary” readings of Hegel, particularly the one he attributes to Robert Pippin — and the preface.

Johnston can be forgiven for not addressing Pippin’s 2018 work on the Logic, but I do not understand why he ignores my favorite book by Pippin, Hegel’s Practical Philosophy (2008).

There, Pippin dwells extensively on Hegel’s Aristotelian side. Much of interest could be said on what it means to be Aristotelian in a post-Kantian context. Many received views will be challenged by such an examination. (For a beginning, see Aristotle and Kant.) As I have said, I read Hegel as both Kantian and Aristotelian (as well as original).

In any case, Johnston seems to think Pippin in Hegel’s Idealism (1989) was intent on reducing Hegel to Kant. That book was indeed concerned to show a strong Kantian element in Hegel. But I did not think of it as reductive. If anything, I read Pippin’s book as a salutary response to those who want to reduce Hegel to a pre-Kantian, and to read Hegel as rolling back from Kant rather than moving forward from Kant. Because he assumes a bad old subjectivist reading of Kant, Johnston seems to think Pippin’s reading of Hegel necessarily rules out the possibility of seeing a realist side to Hegel.

The whole challenge of Hegel is to understand how it it is possible in his terms to be both Critical and realist, without engaging in logical nonsense. (But see Realism, Idealism.) This sort of thing typically requires significant semantic labor, but the achievement of such semantic elaboration is the whole point. Here I worry where Johnston intends to go with his defense of “undialectical” distinctions in the preface. It is one thing to recognize that Hegel does not intend to just do away with Understanding and its distinctions, and quite another to treat those distinctions as final. (See also Univocity.)

Johnston’s lengthy discussion of the positive value of Understanding in the preface does not address how it relates to dialectical transitions. He mainly wants to defend Žižek’s tactic of presenting forced binary choices at particular moments. In particular cases and circumstances this conceivably can be good pedagogy, but it is the details that matter, and Johnston offers no advice on how we are to distinguish a pedagogically good forced choice from a bad one.

(I suspect Žižek’s tactic may be related to his friend Badiou’s defense of the Maoist “One divides into Two” line, which always seemed like blustering nonsense to me. There have been some very rational strands within Marxism; I do not comprehend why someone as intelligent as Badiou would prefer to apologize for the coarsest and most anti-intellectual, but to a lesser extent Althusser did as well. See also Democracy and Social Justice.)

(Worlds away from this, Brandom has a wonderfully clear account of the nonfinality of Understanding’s particular conclusions, illustrated precisely by its very important positive role in the recognition and resolution of error, in which the operations of the Understanding on its own terms give rise to dialectical transitions at the level of Reason, understood in terms of the revision of commitments and possibly of concepts.)

Johnston also seems to assume there is something necessarily reductive about a non-ontological (or not primarily ontological) reading of Hegel. Again, I don’t see why.

I think Aristotle’s metaphysics was basically a semantic investigation, just like his physics. It is the historic forcing of this inquiry back from the wide universe of meaning onto narrow registers of being and existence that I see as reductive.

Based on the work of Olivier Boulnois on the role of the medieval theologian Duns Scotus in the reinterpretation of metaphysics as ontology, I have come to think that in general, modern emphasis on ontology tends to reflect what I take to be historically a medieval Scotist mystification of things Aristotle approached in clearer terms we should recognize today as mainly semantic. (For what it’s worth, the homonymous use of “ontology” in computer science is also mainly semantic.)

Metaphysics or “first philosophy” or “wisdom” was supposed to help us with higher-order understanding, not to be a place where strange existence claims are made.