Self, Infinity

Ricoeur’s idea of an ethical Self as an aim is an important new variant in the menagerie of nonequivalent concepts of self. Perhaps this one has been implicit for a while, but I had not clearly made this exact connection. I very much like Aristotelian ends and Brandom’s reading of Kantian unity of apperception as an ethical goal though, so it is a welcome addition. Now I suspect this is behind what Ricoeur later called ipse identity and narrative identity, which had been troubling me.

The same older work of Ricoeur’s also uses the term “infinite” for the relatively modest if still noteworthy kind of freedom that is indirectly apparent in ordinary language use and ordinary determination of concepts. I would probably still choose a different word to avoid other connotations, but have no objection to that meaning. Again though, a couple of later, less clear references to infinity that had troubled me could be explained by this.

Next in this series: “Transgression” as Ordinary?

Ricoeur on Recognition

Paul Ricoeur’s very last book The Course of Recognition (French ed. 2004) is a fascinating discussion of the history and variety of concepts of recognition in philosophy, from judgments of identification of things in general to Hegel’s ethical principle of mutual recognition. It is full of insightful remarks on the history of concepts of self, from Homer and Sophocles to Bergson and Husserl. I am myself especially interested in further progress that takes Hegel’s ethical principle as a starting point and is essentially unrelated to concerns of identification, but for its intended scope this is a fine study. Even recognition in the sense of identification turns out to be ramified in all sorts of interesting ways.

The introduction is devoted to a highly nuanced discussion of treatments of the word “recognition” in two large-scale French dictionaries that each included many literary citations, somewhat like the Oxford English Dictionary does. (Of course, as Ricoeur warned, lexicography does not directly translate into philosophy.) The 19th century Littré dictionary gave 23 distinct meanings for recognition, and attempted to show their interconnection in a “rule-based polysemy”. The 20th century Robert evinced a different theory of the interconnection of the different meanings. In both cases, a sort of lexicographical equivalent of the Thomistic doctrine of analogy seems to me to be at work, presenting the diverse meanings as unified after all, by means of a sort of ordered series.

The problem with such an emphasis on recovering unity through analogy is that it tends to reduce away the kind of non-univocity that Aristotle was so careful to point out. In the main body of the book, Ricoeur developed a similar ordered series from philosophical senses of recognition, attempting to connect the final ethical notion of mutual recognition back to purely cognitive or epistemic judgments of identity of things in general, using a discussion of what he calls self-recognition as a capable human being (via his notions of ipse identity and narrative identity of personal selves from Oneself as Another) as a sort of middle term to connect them. In the earlier book, narrative identity was itself supposed to be a sort of mean between the logical identity associated with sameness, on the one hand, and ethical notions of self-constancy and promise keeping that he developed there, on the other. (See also Solicitude.)

Although I think Ricoeur’s notions of self-constancy and promise-keeping are quite valuable and are indeed related to the ethical principle in mutual recognition, I would myself emphasize the difference between these concerns — which seem to pertain to the integrity of ethical beings — and concerns pertaining to the identification of individuals. One seems to address a kind of ethical substantiality associated with responsibility, whereas the other seems to address a kind of uniqueness. I don’t really see any mean between these, but rather an interweaving of strands that remain distinct. (But see Self, Infinity for a new insight on what Ricoeur was aiming at here.)

Nonetheless, the ramifications of the sense of “recognition” that starts from mere identification show how even a narrow concern with logical identity can be broadened in all sorts of unexpected ways. At the dictionary level, the ordered series progresses from recognition of sameness through various shadings of recognition of truth, then to various avowals and confessions, and finally to appreciation and gratitude.

The book’s main philosophical discussion moves from the technical role of an identity-related “synthesis of recognition” in Kant’s account of processes of synthesis, through the aforementioned discussion of notions of self, to an account of Hegelian mutual recognition as an alternative to Hobbes’ famous thesis of the state of nature as a war of all against all, and more positively in terms of Axel Honneth’s emphasis on an emergence of mutual recognition from an underlying “struggle” for recognition.

Ricoeur points out that even Descartes said judgments of identity are inseparable from judgments of difference. Augustine’s view of time as internal to the soul — in contrast to Aristotle, who associated time with a measure of externally perceptible change — is presented as a step toward modern forms of subjectivity, which Locke’s explicit association of personal identity with consciousness and continuity of memory is taken to successfully consummate, in spite of various paradoxes with which it is associated.

Historically this seems right, but to my surprise Ricoeur seems to have viewed it as progress toward a better understanding, whereas I see in early modernity an immense new confusion of subjectivity with selfhood that only began to be sorted out again with Kant and Hegel. “There is no doubt that we owe the decisive impulse in the direction of a what I propose calling hermeneutics of self to the Cartesian philosophy of the cogito and Locke’s theory of reflection” (p. 89; emphasis in original). I would agree as far as a decisive impulse in the direction of emphasis on self is concerned, but I think the confusion of subjectivity with selfhood has greatly impeded understanding of both. (See also Self, Subject.)

In this same context, Ricoeur speaks of Kant’s “effacement of ipseity in the treatment of moral autonomy” (p. 90). I would rather speak of his salutary separation of moral autonomy from notions of self. Moral autonomy is related to our integrity and substantiality as ethical beings — to what we really care about, specifically as made clear by how we show that care in our lives. Our ethical substance is actualized in the adverbial “how” of that care. Other biographical details that contribute to making us distinguishable from others are not really relevant to that.

I also think we love someone first of all in response to that “how” of their caring, and then because we love them for that, other details about them become dear to us.

Though broadly endorsing the ethical concept of mutual recognition, Ricoeur seems to have had a worry about its emphasis on reciprocity, related to his acceptance of Lévinas’ idea of an asymmetrical priority of the Other. I don’t understand this. Mutual recognition applies to relations between rational animals; it does not apply to the kind of relation to God that Lévinas often had in mind. It may well be appropriate to say that each participant should in various ways put consideration of the other before self, but in turn, the other should also do the same. An asymmetry in each direction is perfectly compatible with a symmetry between the directions.

Ricoeur did not live to see Brandom’s A Spirit of Trust, where the ethical concept of mutual recognition finally becomes a guiding criterion for judgment in general, and for the grounding of objectivity in general. I think he would have been highly intrigued by this landmark development. (See also Ricoeurian Ethics.)

Oneself as Another

Paul Ricoeur’s major ethical work Oneself as Another (1992; French ed. 1990) is a real treasure trove. At top level, it is devoted to distinguishing between separate notions of personal identity and ethical/epistemic transcendental subjectivity, then developing the dialectical relation between them, along with the central importance of relations with others. That could equally well characterize a major aspect of the work I have been pursuing here.

In the introduction, he speaks first of a “primacy of reflective meditation over the immediate positing of the subject, as this is expressed in the first person singular” (p. 1). I think this perspective is shared by Plato, Aristotle, Kant, Hegel, and Brandom. Second, he points out the equivocal nature of identity, distinguishing between Latin ipse (self) and idem (same). Selfhood in Ricoeur’s sense — identity in the sense of ipse — “implies no assertion concerning some unchanging core of the personality” (p. 2). Third, he draws attention to a dialectic of self and other. “[T]he selfhood of oneself implies otherness to such an intimate degree that one cannot be thought of without the other” (p. 3). As a result, “autonomy of the self will appear… to be tightly bound up with solicitude for one’s neighbor and with justice for each individual” (p. 18; emphasis in original).

Such a detour by way of analysis “challenges the hypothesis of reflective simplicity without thereby giving in to the vertigo of the disintegration of the self” (p. 19). A “faith that knows itself to be without guarantee” (p. 25) is supported by a “trust greater than any suspicion” (p. 23). This perspective is thus distinguished both from the foundationalist ambitions of “philosophies of the subject” like those of Descartes, Fichte, and Husserl, and from Nietzschean skepticism. Ricoeur also anticipates Alain de Libera’s connection of his work to Michel Foucault’s late “hermeneutics of the subject”, citing the “magnificent title” of Foucault’s book Care of the Self.

Next in this series: Persons, Identification

Foucault

Michel Foucault (1926-84) played a very great role in developing approaches to subjectivity as something that is constituted, rather than pre-existing or only one-sidedly constitutive. Despite some nontrivial issues with things he said at different times, this seems like a major contribution. In his later work, he also emphasized that people actively participate in the constitution of their own subjectivity. Foucault was not only a brilliant theorist, but often expressed his ideas in beautiful, sparkling prose.

I see his focus on the constitution of subjectivity itself as an invaluable and necessary complement to the notion of a constituting subjectivity, as exemplified by, e.g., Kantian synthesis.

Much of Foucault’s work tended to fit the common trope of a “hermeneutics of suspicion” — pointing out how liberal reforms actually implemented more efficient strategies of social control, and so on. Unlike most of the people who use this phrase, I think this sort of “suspicion” of usual assumptions can play an invaluable critical role. However, I agree it can also be taken too far.

For example, received truths may turn out to be mere prejudice, and the notion of truth itself may turn out to have been naively hypostasized in many instances. But it is going too far to say — as Foucault did on several occasions — that truth and knowledge as such are inevitably caught up in strategies of domination, or — as Nietzsche and Foucault both did — that there really is no Platonic truth. In matters like this, we need an Aristotelian mean that avoids both naivete and cynicism.

I always preferred to pay more attention to Foucault’s practical multiplication of articulable differences, distinctions, and discontinuities in his historiography than to his negative rhetoric about truth and knowledge in general. During his earlier “archaeological” period, which greatly impressed me in my youth, this multiplication of articulable differences was the positive side of his questioning of too-easy unities, identities, and continuities in history.

In his later work, he developed a distinctive theory of power in society, treating it as distributed everywhere at a micro level, rather than emanating from a central authority. On a practical level, this seems to me to contain valuable lessons, although it also seems to play on an ambiguity between power as capability and power as domination. (It is easy to see that power as capability is ubiquitous, and illuminating to think of how what are really modes of control may be actualized at a micro level. But capabilities and modes of control, while they are both distributed, are two different things that cannot be just identified or assumed to have the same distribution.)

He also pointed out how control can be effectuated through the very formation and self-formation of people and things, without the overt involvement of any sort of repression or repressive apparatus. This seems like another important insight.

Foucault was much influenced by the philosopher of science Georges Canguilhem’s investigations of the concept of normality in biology and medicine, which highlighted the importance of pathology for an understanding of normality. (It also appears that within the French context, the term “normativity” has strong connotations of mere empirical “normality” and conformity, in sharp contrast to its value-oriented significance in analytic philosophy and my own usage.) Foucault himself had a sort of fascination with what sociologists call deviance, and a bit of a morbid streak that I never liked.

The discursive regularities he analyzed in his earlier work represent a kind of empirical “normality” rather than an ethical normativity. Again, these are two entirely different concepts.

In Aristotelian terms, discursive regularities fall under the domain of “art” or technique, rather than that of ethos. Technique is the canonical example of an Aristotelian means or efficient cause (not to be confused with later notions of impulse, or a scholastic act of creation). As efficient causes, Foucaultian discursive regularities operate under the mode of actuality. (Ethical normativity, by contrast, involves derived ends considered under the mode of potentiality.)

Foucault’s “archaeological” method can be seen as a specialized historiographical application of what I have been calling Aristotelian semantics, concerned with fine distinctions in the ways things actually said might be meant, as well as of Aristotelian dialectic, concerned with making the practical consequences of those distinctions explicit. (See also Empirical-Transcendental Doublet; Archaeology of Knowledge; Ricoeur on Foucault; Genealogy; Immediacy, Presence.)

Contradiction

Contradiction is a kind of logical judgment of error in things said. It applies when things said are either syntactically or semantically incompatible with one another. To be incompatible is to be incapable of “properly” coexisting in a single context or unity of apperception. Aristotle strongly emphasized this normative aspect of the principle of noncontradiction.

In the syntactic case, the concern is with purely formal rules for the well-formedness of expressions. A syntactic contradiction would be something like “A, and also not-A”, where either A and not-A have both been explicitly said, or both are implied by things that have been said. In this case, we need know nothing at all about the meaning of “A”. We are only concerned with generic rules for the application of logical operators like “and” and “not”.

In the semantic case, contradiction involves the specific meanings of concrete expressions, applied together to some one meant reality. Unlike the syntactic case, background knowledge is essential to judging whether or not meanings can compatibly coexist. We may also think we know the whole story when we don’t. New facts or understandings may change our generalizations and schemas of classification. (See also Interpretation; Error.)

Nothing follows from the principle of noncontradiction alone. Given some inputs, we can judge whether or not they are contradictory — by rigorous analysis in the syntactic case, and up to some level of practical confidence in the semantic case.

Hegel sometimes used the word “contradiction” in an idiosyncratic, highly metonymical or metaphorical way, straining language to the breaking point as part of a larger effort to draw out the complexities and subtleties involved in applying logic to concrete meanings and the real world, when no vocabulary existed for many of the subtleties involved. (See also Three Logical Moments.)

Some people, mainly Marxists, have talked about real-world conflict and social injustice as “contradictions” objectively existing in the world. Conflict and injustice are very real, but it is a misunderstanding of Hegelian dialectic and an inappropriate mixing of levels to associate them directly with contradiction. (See also Contradiction vs Polarity.)

Especially since the mid-20th century, many authors have pointed out common errors and issues associated with too-easy assumptions about identity. (See also Aristotelian Identity.) The Žižekian school has developed a sophisticated variant of the old talk about objective contradictions, by explaining it largely in terms of the issues with identity. If this were just a new metonymical or metaphorical usage in the style of Hegel, we could simply note that “contradiction” is being said in a nonstandard way, and move on. But unfortunately, the Žižekians have gone further, and also claimed that the logical principle of noncontradiction ultimately fails to hold, even though this logical (or illogical) claim is not necessary to address the social concerns that according to them need to be addressed, or to explain the things that according to them need to be explained. (See Split Subject, Contradiction.) We have to be very careful in moving back and forth between very different levels of analysis like this.

Just as on an interpersonal level we can reduce conflict by omitting those too-easy assumptions about identity, omitting those assumptions with respect to things said — and thus making more distinctions — also greatly reduces the potential for logical contradiction.

It is a category mistake to talk about contradiction driving events. Actual change does not result in contradiction either. Different things are true at different times, and the explanation for that is not “contradiction” but change.

Why is this important? The simple answer is that denial of the principle of noncontradiction allows someone to argue absolutely anything, including nonsensical and false things, and to sophistically respond to any refutation by simply introducing more inconsistency. This rejection of responsibility effectively ends the possibility of dialogue.

There ought to be no conflict between social criticism and the possibility of dialogue. Social criticism should be based on shareable, rational analysis. It may be unreasonable to suppose that all social issues can be resolved through dialogue (see Stubborn Refusal), but I do think all those concerned with doing something about those issues ought to be able to resolve their differences through dialogue.

I think Brandom has made an epic contribution in this area by finding a new way to simultaneously affirm — as Aristotle implicitly anticipated long ago — both the world’s recalcitrance to mastery and identity and its fundamentally rational, intelligible character. (See also Self-Evidence?)

Acts in Brandom and Žižek

Both Brandom and Žižek recognize what Brandom has called the “world’s stubborn recalcitrance to mastery and agency”, and yet hold out for the possibility of transformative action.

Brandom ingeniously secures the practical reality of choice through the indirect route of an Enlightenment idea that we can only be bound by values to which we have at least implicitly committed ourselves. The recalcitrance of the Real prevents this from becoming a subjectivism, specifically by virtue of his complementary thesis that the meaning of our commitments is not up to us. But actively taking responsibility for things beyond our power turns out to indirectly have a kind of efficacy. Retrospectively, this may change meant reality.

A lengthy article by Fabio Vighi and Heiko Feldner discusses agency in Žižek from various angles. This account at least is happily free of the Badiouian narrowing of consideration to a few inflationarily conceived “exceptional” acts that afflicts some of the Žižekians (see “Hard” Kantianism?). The concern is with acts in general, and subjectivity in general. Here I can find a good deal more common ground.

For Žižek, our desires are not our own, but the split in the subject that makes us never fully ourselves also connects us with the social. A subject is contrasted with subjectivation. Although passive, alienating subjectivation is inescapable, it also can never be complete. A subject is positively constituted by its own nonidentity or “impossibility” (i.e., impossibility of complete identity with itself). According to Vighi and Feldner, “this decentred kernel of otherness embodies my self-consciousness, the only place where I have a chance to locate the truth about myself”. The conscious activity of individuals is said to be not free, but we can nonetheless accomplish a free act through identifying with the destabilizing effect of what is “in us more than ourselves”. They argue that Žižek does not hypostatize an abstract negativity in the way that I think Sartre did.

Žižek himself wrote that “To ‘pass to the act’ means to assume the risk that what I am about to do will be inscribed into a framework whose contours elude my grasp” (Tarrying with the Negative, p. 31). This connects agency with the Lacanian Real. He also wrote that freedom corresponds to “my ability to choose/determine which causes will determine me. ‘Ethics’, at its most elementary, stands for the courage to accept this responsibility” (The Parallax View, p. 203).

So, despite huge differences in approach and terminology and Žižek’s negative comments about Brandom, on this question at this level of abstraction, there is a similar practical import.

Split Subject, Contradiction

The Žižekians, referencing Lacan, like to talk about a “split subject” that is noncoincident with itself. In broad terms, I think this is useful. What we call subjectivity is divided, and lacking in strong unity. (See also Pure Negativity?; Acts in Brandom and Žižek.) But it seems to me that if we try to speak carefully about this, we should not then go on using singular articles like “the” or “a”.

I tend to think subjectivity is not just fractured or un-whole, but also actually consists of a complex overlay of different things that we tend to blur together. In particular, it seems clear to me that a common-sense, biographical “self” whose relative unity over time is trackable by relation to the “same” physical body — or by Lockean continuity of memory — is not the same as what we might in a given moment view from a distance as an individualized ethos, or up close as a unity of apperception. This is, I believe, the same distinction that Brandom discusses in terms of sentience and sapience.

Ethos and unity of apperception, and their constituent values and conceptions — the very things that most properly say “I”, and play the functional role of an ethical “subject”, or of a subject of knowledge — are profoundly involved with language, social relations, and what Lacan in his earlier work called the Symbolic and the “Other”. These instances of sapience are pure forms whose identity can only be expressed in terms of sameness of form — nonempirical, but inseparable from a larger ethical world — and simultaneously intimate to us, but by no means strictly “ours”. (See also Self, Subject.)

Where I am still a bit torn is that I also feel that emotions — which I’ve been locating on the former, “self” side — are fundamental to subjectivity as a whole, but I have theoretically separated them from the main locus of transcendental ethical and epistemic subjectivity, even though they play an essential role in making it possible. One logical solution would be to say this just means subjectivity as a whole is more than just ethical and epistemic. Another would be to say that there is a separate kind of emotional subjectivity. I’m not entirely satisfied yet, because I think feeling combines these, but the noncoincidence of our factual selves with our ethical and epistemic being seems very important in understanding how we overcome empirical limitations.

The Žižekians will perhaps remind us that they were not talking about a split between self and subject, but about a split within the subject. I think we habitually overstate the degree of unity and identity we attribute to selves, subjects, and things in general, so I’m fine with that, too. They also want to expand this into a general “ontological” point, which I see as a semantic point.

Perhaps the Žižekians are more comfortable talking about “a” or “the” subject in part due to their doctrine of the ubiquity of contradiction. Todd McGowan in Emancipation After Hegel (2019) nicely distinguishes the Žižekian notion from the old confusion between contradiction and conflict or polarity — and from immediate self-contradiction — but still wants to maintain that the standard logical law of noncontradiction ultimately “refutes itself”, and that Hegel thought this as well. This argument combines a laudable awareness of some of the practical issues with identity, with a logically invalid use of the distinction between explicit and implicit self-contradiction.

Hegel meditated profoundly on the difficulties of applying logic to meaningful content and to real life. He strained language to the breaking point trying to express his conclusions.

On the frontiers of mathematical logic today, the so-called law of identity has been replaced by a requirement to specify identity criteria for each formally defined type, and identity in general has been weakened to isomorphism. (See also Form as a Unique Thing.)

Real-world applications of strong identity typically involve loose “extensional” reference to things assumed to be the same, and a lot of forgetting. The linchpin of old “identity thinking” was inattention to difficulties of formalization from ordinary language — basically an illegitimate moving back and forth between formal and informal domains, resulting in lots of homogenizing confusion of things that ought to be distinct. Weaker, “intensional” assertions about identity as specifiable sameness of form make it the exception rather than the rule. What come first conceptually are distinctions within the manifold, not pre-synthesized things already possessed of identity. Where things are not the same to begin with, contradiction — far from being omnipresent — is not even potentially at issue. (See also Self-Evidence?)

Meanwhile, Sellars and Brandom have revived material inference about meant realities in contrast to formal logic, which deals with purely syntactic relations between presumed extensional “things” with presumed identity. Things Kant and Hegel said about Understanding and Reason can be nicely understood in terms of the relation between syntactic inference about symbolic terms standing for formless extensional “things” and substantive, material inference about the actual form of meant realities. Especially in the reading of Hegel, not having the resource of this distinction available now seems positively crippling.

Finally, Aristotle, who originated the law of noncontradiction as a kind of ethical imperative, and stands in the background to all of Hegel’s discussions of logic, was himself rather cautious and tentative about applying identity to real things, and in his logic was also mainly concerned with (composition of) material inferences, which have more to do with the actual form of things .

Hegel never violated Aristotle’s imperative not to say opposite things about the same thing said in the same way. What he did was to constantly point out the gap between reality and traditional semi-formal logic applied to ordinary language — not to encourage us to reject logic, but rather to refine and sublimate it. (See also Aristotelian and Hegelian Dialectic.)

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.

Interpretation

It seems to me that the main thing human reason does in real life is to interpret the significance of things. When we think of something, many implicit judgments about it are brought into scope. In a way, Kant already suggested this with his accounts of synthesis.

In real-world human reasoning, the actually operative identity of the things we reason about is not the trivial formal identity of their names or symbols, but rather a complex one constituted by the implications of all the judgments implicitly associated with the things in question. (See also Identity, Isomorphism; Aristotelian Identity.)

This is why people sometimes seem to talk past one another. The same words commonly imply different judgments for different people, so it is to be expected that this leads to different reasoning. That is why Plato recommended dialogue, and why Aristotle devoted so much attention to sorting out different ways in which things are “said”. (See also Aristotelian Semantics.)

I think human reason uses complex material inference (reasoning based on intermediate meaning content rather than syntax) to evaluate meanings and situations in an implicit way that usually ends up looking like simple summary judgment at a conscious level, but is actually far more involved. A great deal goes on, very rapidly and below the level of our awareness. Every surface-level judgment or assertion implicitly depends on many interpretations.

Ever since Aristotle took the first steps toward formalization of logic, people have tended to think of real-world human reasoning in terms modeled straightforwardly on formal or semi-formal logical operations, with meanings of terms either abstracted away or taken for granted. (Aristotle himself did not make this mistake, as noted above.) This fails to take into account the vast amount of implicit interpretive work that gets encapsulated into ordinary terms, by means of their classification into what are effectively types, capturing everything that implicitly may be relevantly said about the things in question in the context of our current unity of apperception.

A logical type for a thing works as shorthand for many judgments about the thing. Conversely, classification and consequent effective identity of the thing depend on those judgments.

As a result of active deliberation, we often refine our preconscious interpretations of things, and sometimes replace them altogether. Deliberation and dialectic are the testing ground of interpretations.

In general, interpretation is an open-ended task. It seems to me that it also involves something like what Kant called free play. (See also Hermeneutics; Theory and Practice; Philosophy; Ethical Reason; The Autonomy of Reason; Foundations?; Aristotelian Demonstration; Brandom on Truth.)

Aristotelian Identity

Aristotle’s notion of identity is initially relational or structural, and ultimately processual. I read his emphasis on concrete entities in the Categories as pragmatic rather than ontological, and as of a piece with his general methodological recommendations about starting from what is close to us. Aristotelian starting points normally end up being substantially revised or discarded in the actual carrying out of an inquiry; they are intended just to begin a discussion in an accessible way. In the Metaphysics and the biological works, a nuanced and multi-leveled notion of form is developed that also represents Aristotle’s best thought on what we call identity.

For Aristotle, the identity of a thing at a given moment is almost reducible to what is true of it at that moment, i.e., to its articulable properties. There is no ineffable but contentful remainder underpinning individuality, like a Scotist haeccitas would seem to be.

I say almost reducible because the relational or structural criteria for identity of “this” continuing thing may change substantially over time, either straightforwardly because the thing itself changed, or more subtly because something else changed in the context of evaluation. Aristotle shares Hume’s scruples about applying identity in the first case, and Hegel’s about applying it in the second. Like Hegel but unlike Hume, he is also concerned to articulate and progressively improve criteria for higher-order stability of conceptual articulation in the face of first-order flux. This in a sense re-vindicates most of what is behind the common-sense notion of persisting “things”, provided we avoid overly rigid notions of the identity of those things. (See also Substance; Things Said; Aristotelian Dialectic; Being, Existence; Equivocal Determination.)