Multiple Explanations

One of the great strengths of Aristotle’s approach to things is the way it makes use of multiple, complementary kinds of explanation. The paired modalities of actuality and potentiality and the four “causes” (ends and means, form and materiality) all interweave together to create rich tapestries of understanding. Aristotle famously said that to know is to be able to explain, and his notion of explanation is clearly hermeneutic and expansive, rather than reductive. (See also Interpretation; What and Why.; Difference; Classification; Definition.)

Ricoeur on Foucault

I still vividly recall the moment over 40 years ago when the sharp questioning of unities of all kinds in the preface and first chapter of Michel Foucault’s 1969 work The Archaeology of Knowledge very suddenly awoke me from erstwhile slumber in neoplatonic dreams about the One. Today I would say Foucault like many others was terribly wrong in his reading of Hegel, but I still look on that text as a sort of manifesto of historical method. As Aristotle too might remind us, distinctions are essential to intelligibility and understanding.

Just this year, the work of Paul Ricoeur has become very significant to me. Ricoeur expressed admiration for Foucault’s late work The Care of the Self, but in both volume 3 of Time and Narrative and his late work Memory, History, Forgetting, he criticized The Archaeology of Knowledge rather severely.

Ricoeur did not object to Foucault’s emphasis on discontinuities in (the field Foucault did not want to call) the history of ideas, but rather to Foucault’s closely related polemic against the subordination of such discontinuities to an encompassing continuity of historical “consciousness”, and to his further association of the idea of an encompassing continuity of consciousness with the would-be mastery of meaning by a putatively purely constitutive Subject. Ricoeur as much as Foucault objected to such notions of Mastery, but he still wanted to articulate a kind of narrative continuity of what he still wanted to call consciousness.

Ricoeur scholar Johann Michel in his book Ricoeur and the Post-Structuralists agrees that “the subject” for Ricoeur is far from purely constitutive, and “in reality, is not a subject in the substantialist sense” (p. 107). Rather, it is mediate, and only understandable via a long detour through cultural objectifications. As Ricoeur says, consciousness is “affected by the efficacity of history” (Time and Narrative vol. 3, p. 217). “We are only the agents of history insofar as we also suffer it” (ibid, p. 216). Ricoeur’s suffering-as-well-as-acting “subject” gives very different meaning to this highly ambiguous term from the kind of voluntaristic agency attributed to the Cogito by Descartes, and Ricoeur’s “consciousness” is very far from the notion of immediate “consciousness” classically formulated by Locke. I prefer to avoid confusion by using different vocabulary, but agree that the notions Ricoeur wanted to defend are quite different from those Foucault wanted to criticize.

This leaves the question of the relative priority of continuity and discontinuity. Foucault in his Archaeology phase advocated a method grounded in the conceptual priority of discontinuities of meaning, while Ricoeur wanted to give discontinuity an important subordinate role in an approach dedicated to recovering a continuity of consciousness. In my own current Aristotelian phase, I want to emphasize a view that is reconciling like Ricoeur’s, but still puts the accent on discontinuity like Foucault’s. My historiographical notes both tell stories and offer explanations somewhat in the way that Ricoeur advocated, and emphasize the differences and discontinuities favored by Foucault.

Ricoeur also seems to have been troubled by Foucault’s disinterest in what Ricoeur calls the “first-order entities” (p. 218) of history — actual communities, nations, civilizations, etc. (I would note that he is not using “first order” in the logical sense, which is a purely syntactic criterion; he just wants to suggest that these kinds of things are more methodologically primitive for historical inquiry.) I actually think apprehension of something like form comes before apprehension of any substantialized “things”, so my sympathy is more with Foucault on this point. Undoubtedly Ricoeur would say these have a narrative identity rather than a substantial one, which seems fine in itself, but I think any narrative identity must be a tentative result and not a methodological primitive.

Ultimately, I think Ricoeur was motivated by an ethical desire to put people first — a concern Foucault did not make clear he actually shared until The Care of the Self. Ricoeur would also agree, though, that historiography is not simply reducible to ethics, but has largely independent concerns of its own. He seems to have wanted to say that the history of ideas is fundamentally a history of people. I’m a pluralist, so I have no objection to this sort of account as one alternative, but I think people’s commitments tell us who they are more than who holds a commitment tells us about the commitment. I also think higher-order things come before first-order things, and that people are better thought of as singular higher-order trajectories of ways of being throughout a life than as first-order entities. Ricoeur, I believe, was reaching for something like this with his notion of narrative (as opposed to substantial) identity, which I would rather call something other than identity.

Constituted Intentionality

It seems to me that Brandom effectively says intentionality — the basis of meaning — as such not only is not a mental act, but not an act at all or in any way reducible to an act, even though intending is certainly a doing. Further, unlike Husserl’s version, Brandom’s intentionality seems to be something constituted by something else. That something else would be processes of mutual recognition both actual and ideal, which I think also normatively but not causally ground judgment and objectivity, knowledge and logic, while in addition incorporating considerations of reasonableness grounded in feeling, associated with the respect in recognition. I think intentionality is a kind of form having to do with linguistic meaning and potentialities for material inference, and that this form is normatively constituted through mutual recognition.

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.

Substance Also Subject

Hegel’s many references to Aristotle should help to clarify the Hegelian claim that “Substance is also Subject”. In particular, Aristotle’s own thesis of the identity of thought with the thing thought is relevant, as is his dialectical development of the different senses of ousia (“substance”) in the Metaphysics.

A thought for Aristotle is identical with its content. It just is a discursively articulable meaning, not a psychological event. What we care about in thought is shareable reasoning. Moreover, this shareable reasoning has a fundamentally ethical character.

Thought in this sense is essentially self-standing, and unlike the mental-act sense not dependent in the determination of its meaning on a “thinker” (who optionally instantiates it, and if so is responsible for the occurrence of a related event). This gives a nice double meaning to the autonomy of reason. (What such thoughts do depend on is other such thoughts with which they are inferentially connected.)

The primary locus of Aristotelian intellect is directly in shareable thoughts of this sort and their interconnection, rather than in a sentience that “has” them. Hegel adopts all of this.

Concepts in a unity of apperception are forms to be approached discursively, not mental representations or intentional acts. They are more like custom rules for material inference. The redoubling implied in apperception, like that of the Aristotelian “said of” relation, hints at the recursive structure of inferential articulation. The Hegelian Absolute, or “the” Concept, just nominalizes such an inferential coherence of concepts.

Thus, “Substance is also Subject” has nothing to do with attributing some kind of sentience to objects, or to the world. Rather, it is the claim that Substance properly understood (in the Aristotelian conceptual sense of “what it was to have been” a thing, rather than in the naive sense of a real-world object, or of a substrate of a real-world object, that Aristotle starts with but then discards) is already the right sort of thing to be able to play the functional role of a transcendental subject. A “Subject” for Hegel just is a concept or commitment, or a constellation of concepts and commitments.

Consistent with this general approach, I consider the direct locus of the subject-function to be in things like Brandomian commitments and Kantian syntheses. The subject-function is also indirectly attributable to “self-conscious individuals” by metonymy or inheritance, and to empirical persons by a further metonymy or inheritance. (See also Subject; Substance; Aristotelian Dialectic; Brandom and Kant; Rational/Talking Animal; Second Nature.)

Matter, Mind

I don’t think any kind of stuff could come first, be it matter or some sort of mind-stuff. What comes first in the sense of principle would be something like form or structure or mediation. (“First” in the general sense of principle is said in several ways, but I’m inclined to re-collapse some of them. These days, I consider ontology to be mostly either redundant with semantic and epistemological methodological senses, or else just a mistake. This leaves a long view of methodology as the best candidate for a principle.) The air of paradox associated with saying something like mediation comes first is dispelled if we recall that apparent immediacy is mediated immediacy. This just reflects the fact that methodologically, we are never at a completely pure beginning, and always start in medias res.

Mind especially seems to me not best approached as a kind of stuff at all. It is first and foremost a way of doing. (See also Mind Without Mentalism.) Then, too, what is loosely called the “matter” that we care about in concrete cases often comes down to potentiality, or dispositions to respond in certain ways when acted upon (which is distinct from Aristotelian matter, as I understand it). Both of these are adverbial characterizations, though things of this sort can always be nominalized for convenient reference.

Aristotle suggests that what is first “for us” (the short view of methodology) is some sort of activity that we tentatively pick out within appearance. We then move forward by developing the adverbial characterization of that activity in terms of form or structure or mediation. (See also Objectivity of Objects; First Principles Come Last; Owl; Passive Synthesis, Active Sense; Radical Empiricism?; Realism, Idealism; Johnston’s Pippin.)

Form

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

Concept, Form, Species

Where Kant and later writers talk about concepts, Plato and Aristotle and medieval writers talked about forms in somewhat analogous ways. Neither concepts nor forms have the immediate unproblematic accessibility that is claimed for Cartesian mental representations or Lockean ideas or medieval species. Where concepts or forms are to the fore, we are generally in discursive territory.

Leen Spruit has documented that the middle ages also saw a huge variety of doctrines of so-called “species”, both perceptible and intelligible, which in one aspect were mental representations, some resembling phantasmata in Stoicism, some seeming rather like Cartesian mental representations or Lockean ideas. These were generally considered to be contents immediately accessible to the mind. I tend to think a lot of these were probably associated with what Brandom calls two-stage models of representation, where representings are considered to have an immediate intelligibility that representeds lack.