In this chapter, I look in some detail at the fine structure of Hegelian negation—and at its metaphysical consequences—when Hegel first introduces it, in the second chapter of the Phenomenology (presenting ideas corresponding to the transition from Sache to Dinge in the Science of Logic). These are only the first baby steps—soon to be aufgehoben—in his intricate story. But the structure revealed is both interesting in its own right and a cautionary tale for any readers tempted by univocal readings of such central Hegelian formulae as “the negation of the negation,” and “identity through difference.” I am particularly concerned to contrast Hegel’s order of explanation with the extensional semantics that defines the modern logistical tradition, which would not really begin for another 60 years, and which did not achieve equivalent expressive power until 160 years after Hegel wrote the passages I discuss. The considerations that drive this narrative of explicitation (transforming what is an sich into what is gesetzte) are, I think, individually all familiar. But the argumentative narrative that they jointly articulate, when suitably recruited and deployed, is a paradigm of Hegelian conceptual emergence. It is also a paradigm of analytic metaphysical argument pursued with Hegelian conceptual raw materials, so taking place in a setting substantially different from the Lewisian possible-worlds framework within which most such metaphysical argumentation and construction is pursued today. I think the metaconceptual contrast established by these two different orders of explanation is interesting and illuminating in its own right, quite apart from what it can teach us about Hegel’s ideas.

I. The Lessons of Sense Certainty

The way of understanding empirical consciousness that Hegel calls “sense certainty” (a form of self-consciousness—a way a consciousness can understand itself) seeks to secure the intelligibility of genuine knowledge by identifying these episodes of sensory awareness as themselves already amounting to knowledge, in a way taken to be independent of their relations to anything else. On this conception, error becomes possible when, but only when, the knowing consciousness actively does something with or to the passively acquired episodes of sensory awareness: compares or classifies them, or draws conclusions from them. The strategy of sense certainty is to discern an autonomous foundational layer of sensory knowledge that is incorrigible because it restricts itself to what is given in sensation. The thought is that where consciousness does not act, it cannot err. Hegel seeks to show that this notion of sensory givenness cannot survive the unpacking of its implicit presuppositions.

The main result of the arguments Hegel rehearses in Sense Certainty is that the token-credibility of unrepeatable episodes of immediate sensory awareness is not intelligible as freestanding and autonomous. This distinctive sort of epistemic authoritativeness is real and important, but it is intelligible as yielding a kind of knowledge only when it is understood as situated in a framework that includes two kinds of repeatability of the contents in which it is invested.

Diachronically, it must be possible for the subject to “hold on to” what has been experienced when not still experiencing it. One must be able to recollect and thereby secure what is known in acts of consciousness that are responsible to the original, authoritative sensory knowing. These dependent episodes are what the token-credible experiencing is authoritative over. What would be expressed linguistically by demonstratives can amount to knowledge only as part of a larger structure that includes what would be expressed linguistically by tokenings anaphorically dependent on the token-credible demonstrative episodes. Though as immediate in origin they are not themselves the conclusions of inferences, episodes of sensory awareness would be epistemically idle if they were not in principle available to serve as premises for inferences. An unrepeatable deictic tokening “that” (for instance, in “That is rain”) can count as expressing knowledge only if it can be picked up anaphorically and used to draw a conclusion (for instance, “It is wet”). Deixis presupposes anaphora.

The other sort of repeatability found to be implicit in the concept of the empirical epistemic authority of episodes of immediate sensory awareness, as part of the context within which alone it is intelligible, by contrast, is taken up as the central topic explored in the very next chapter, Perception. This is repeatability as universality.¹ To be understood as determinately contentful, even synchronically, experiences must be conceived as unrepeatable instances of repeatable kinds. More specifically, the Perception chapter investigates what is implicit in the idea of sense universals, as articulating the contents of what would be expressed linguistically by observation reports codifying perceptual judgments. The progression within the Consciousness chapters of the Phenomenology is from consideration of the presuppositions of the epistemic authority distinctive of sensory immediacy, to the presuppositions of the epistemic authority distinctive of universality (in the sense of sense universals, those that are noninferentially applicable), and finally to the presuppositions of the epistemic authority distinctive of pure mediation characteristic of theoretical concepts (those one can be authorized to apply only as the conclusions of inferences).

The point of departure of the Perception chapter is this lesson we are to have learned by the end of Sense Certainty: sensuous immediacy, to be understood as determinately contentful, must be understood as involving an element of repeatability as universality. This conclusion emerges from the observation that playing a cognitive role as even potentially constituting a kind of knowledge entails that the deliverances of sense can be understood as immediate or noninferential in only one of the two senses that are run together by empirical consciousness understanding itself according to the structure of sense certainty. They can exhibit immediacy of origin, but not immediacy of content. That is, the cognitive deliverances of sense can be understood as exhibiting a distinctive kind of epistemic authority invested in unrepeatable mental events or acts in virtue of their etiology. This authority derives from their being exercises of responsive sensory consciousness, rather than of inferential capacities. The process from which they result (by which they are elicited) is not an inferential process. In that sense they are “immediate”: the process that issues in episodes of sensory awareness is not mediated by middle terms of the sort characteristic of a Schluss, an inferential move, construed syllogistically. However, the claim is, to be intelligible as cognitively contentful, the deliverances of noninferential sensings that are immediate in this procedural sense must in another sense be mediated immediacies. Specifically, they must consist in the application of sense universals: concepts that have observational uses in which their application is noninferentially elicited by the exercise of perceptual capacities.

II. Determinateness and Exclusive Negation

Understanding the basis for this claim depends on exploring a complex constellation of intricately interrelated philosophical (Hegel is happy to say “logical”) metaconcepts: mediation, universality, determinateness, and negation. The principal result of the investigation of the presuppositions under which purely sensory awareness could count as a kind of knowledge in the Sense Certainty chapter is that this constellation of concepts, articulating a notion of conceptual contentfulness, must be applicable to any sort of sentience that is intelligible as a kind of sapience. The Perception chapter argues that this requirement has surprising structural consequences. Whereas construing acts of sensory awareness according to the categories of sense certainty was compatible with understanding the contents of that awareness as what would be expressed in what Strawson calls a “feature-placing” vocabulary—“It is day,” “It is raining”—fuller consideration of those contents shows that sensings must present the richer structure of “objects with many properties,” which would be expressed linguistically in a vocabulary distinguishing and relating singular terms and predicates. That argument proceeds by teasing out the implications of Hegel’s nonpsychological conception of conceptual contentfulness, which is articulated by the aforementioned metaconcepts: determinateness, negation (or difference), mediation, and universality.

As I see the argumentative relations among these concepts that are in play early in the Perception chapter, our entry is provided by the concept of determinateness. When we investigate what determinateness requires, we find that it implicitly involves a complex notion of negation. In terms of that notion of negation, it then turns out to be possible to explain and show the applicability of both the concept of mediation and the concept of universality (see Figure 5.1). The linchpin of this structure is clearly the concept of negation. What is it, and how does it emerge from the consideration of determinateness?

The master idea here is the Spinozist scholastic principle Omnis determinatio est negatio; all determination is negation. The idea is that being determinate requires some limitation, contrast, or exclusion. The image is of something that has a limit or boundary, so that there is a contrast between it and what is not it. That is how negation comes into view (see Figure 5.2).

What is “Not It” is everything else, things that are outside of or different from “It.” Understanding the metaphor of limits or boundaries is a matter of understanding the sense of “not,” “else,” “outside,” or “different” that the metaphor appeals to. The observable contents expressible in a feature-placing vocabulary that were introduced in Sense Certainty offer a couple of alternatives. The day of “It is day” and the raining of “It is raining” are different. So are the day of “It is day” and the night of “It is night.” But they are different in different senses of “different.” In the language Hegel uses in Perception, day and raining are merely or compatibly [gleichgültig] different, while day and night are exclusively [ausschließend] different. For, though different, day and raining are compatible features (it can be both day and raining), while day and night are incompatible (it cannot be both day and night).

As I understand him, one of Hegel’s most basic thoughts is that determinateness must be understood in terms of exclusive difference. Mere difference is not enough. The contrast between It and Not It required for something to be determinate (for a feature to have definite boundaries) requires that nothing can be both It and not It. This modally robust exclusion is built into the geometric representational apparatus of Venn diagrams with literal boundaries, as in the preceding figure. For a point cannot be both inside and outside a closed plane figure. In this same modal sense, sets—for instance, those representing the extensions of properties—have exclusive “boundaries.” For it is impossible for something to be both an element of a set and not an element of that set. The “not” of Not It is an exclusive not. That is the point of the law of noncontradiction. It is not just that some regions or sets contingently do not both contain and not contain any points. That is a necessary feature of regions and sets. The negation that is defined model-theoretically as part of an extensional semantics for properties itself expresses a modally robust kind of exclusive difference, not mere difference. The modal force is just hidden in the metavocabulary that is the medium of expression of the semantics (whether set-theoretical or geometrical).

The connection between determinateness and modally robust exclusion—the ruling out of some alternatives—is codified in the technical concept of information. A signal is informative, contains or expresses information, just insofar as it rules out some alternatives. The measure of information, by which amounts of information are determined, compares the alternative situations or responses that are possible before receipt of the signal to those that remain after the signal has ruled out some of them as no longer possible (according to the signal). While information can distinguish merely different alternatives, it does so by ruling out some of them, excluding them as no longer possible. This same idea is expressed in possible-worlds semantics when a determinate proposition is identified with a set of possible worlds, a partition of all the possible worlds into those compatible with the proposition, and those incompatible with it or ruled out by it.

The thought with which Perception begins is that the determinateness of the content even of an immediately given sensory knowing, an act of sensory awareness, as conceived according to the metaconception Hegel calls “sense certainty,” must be understood in terms of what it excludes or rules out, what is exclusively different from it, not just what is merely or indifferently different from it. The metadifference between two kinds of differences shows up already in the contents of acts of sensory awareness that would be expressed in a feature-placing vocabulary. The determinateness of those contents cannot be made intelligible solely in terms of their mere difference. Exclusive difference must also be appealed to. If the contents of minimal sensory knowings stood to one another only in relations of compatible difference, none excluding or ruling out any other, then their occurrence would have no significance, would convey no information. They would be mere events, “that”s without “such”es, gears unconnected to any mechanism, their occurrence as devoid of cognitive significance as any other unrepeatable events. Their differences would be less determinate than “merely numerical” differences. For numbers are exclusively different from one another. Their differences would be less determinate than those of featureless Euclidean points, even apart from consideration of all the lines, circles, triangles, and so on, whose relations to those points might relate them to one another. For again, being one point precludes being another, whereas merely compatibly different contents can be instantiated together.

In fact contents that are merely or compatibly different are elements of different families of exclusively or incompatibly different contents. Shapes such as circular, triangular, and rectangular are exclusively different from one another. Exhibiting one rules out exhibiting any other (so long as we restrict ourselves to shapes exhibiting the same number of dimensions as the space they inhabit, because a three-dimensional pyramid with a rectangular base might be thought to exhibit both triangular and rectangular shapes). Colors also form a family of exclusively different contents (so long as we restrict ourselves to monochromatic regions). What can be compatibly different is pairs of contents drawn from different families of incompatibles: red and square, green and triangular, and so on. These merely or compatibly different contents are determinate only insofar as they also stand in relations of incompatibility or exclusion from contents drawn from the same family. It is as such that their occurrence conveys information, by excluding the occurrence of other members of the same family or incompatibles. Mere difference is intelligible in the context of such a structure exhibiting also exclusive differences. But by itself it is too weak to underwrite any notion of determinate content.

There are, then, fundamental conceptual reasons to understand the notion of determinate difference as implicitly involving the metadistinction between two kinds of differences: exclusive difference and compatible difference. I think Hegel also thinks that this metadifference is observable, that it is part of the phenomenology (in a more contemporary, vaguely Husserlian sense) of sense experience. That is, I think he thinks the compatibility of day with raining, and its incompatibility with night is part of what we are given when we have a sensory experience of the sort that might be expressed in a feature-placing language by “It is day.” In grasping that content, part of what we grasp is its place in a space of compatibilities and incompatibilities with other experienceable contents.

On this account, Hegel thinks that more is given in sense experience than empiricists such as Locke and Hume do. The experiences we label “red” and “green,” and those we label “rectangular” and “triangular,” are experienced as incompatible, as ruling each other out (as simultaneously located), while those labeled “red” and “triangular” and “green” and “rectangular” are experienced as different, but compatible. The different possibilities of combination, and so the arraying of features into compatible families of incompatibles is a ground-level structure of sensory awareness for Hegel, but not for traditional empiricists. Hegel sees the modal difference between the difference between red and triangular and the difference between red and green as something one knows simply by experiencing them.

Is this difference of opinion about what is given in sensory experience an empirical disagreement? Can it in principle be settled by introspection? Has traditional empiricism suffered from restricting itself to too narrow a conception of the basic knowledge delivered by sense experience? Hegel’s analysis of what is implicit in the idea that basic sensory knowledge has a content that is determinate provides an argument for the claim that knowledge of which experiential features are exclusively different from which, and which merely different, must be part of what one knows in having experiences with those features. (This is not to say that a subject need be incorrigible on such matters.)

One important way in which the enriched empiricism Hegel is considering differs from traditional empiricism (including its twentieth-century variants) lies in its rejection of the latter’s atomism about the contents of immediate sensory experience. If their exclusive differences from one another are an essential part of what is given in experience, then each has the content it does only as a member of and in virtue of the role it plays in a constellation of interrelated contents. An experienced red triangle must locate the experiencing of it in the mere (compatible) difference of members of two different families of incompatibles: colors and shapes. (It is interesting to note in this connection that the intrinsic incompatibilities of color properties were a principal consideration leading Wittgenstein away from the logical atomism of the Tractarian idea of elementary states of affairs as independent of one another.) The result is a kind of holism about what is immediately given in sensory experience. The atomism characteristic of the conception of sensory consciousness understood according to the categories of sense certainty is seen to be incompatible with understanding such consciousness as determinately contentful.

Equally important, and equally radical, is the fact that Hegel’s principal metaphysical primitive, determinate negation, is intrinsically and essentially a modal notion. The material incompatibility of red with green and circular with triangular is a matter of what can and cannot be combined, what is and is not possible. Modality is built into the metaphysical bedrock of his system. Possibility is conceptually more basic than actuality, in the sense that an immediately given actual experience is intelligible as having the determinate content it does only insofar as it is situated in a space of possibilities structured by relations of compatible and incompatible differences. The empiricism Hegel is considering is a specifically modally enriched empiricism. And we shall see that, by contrast to Kant, for Hegel the essentially modal articulation of what is determinate is not restricted to subjective thoughts or experiencings. It also characterizes objective determinate states of affairs, whether possible objects of sensory experience or not.

III. Formal Negation and Two Orders of Explanation

If the contents that can be given in sensory experience, some of which actually are (contents that might be expressed linguistically in a feature-placing vocabulary), are determinate in that they stand to one another in relations of determinate negation in the sense of modally exclusive difference or material incompatibility, then they also stand to one another in relations of material inferential consequence. In Hegel’s idiom, this is to say that although they may be given immediately, the contents of sensory experience are themselves “thoroughly mediated.” For some feature A (such as “It is raining”) has another feature B (such as “It is precipitating”) as a material inferential consequence just in case everything materially incompatible with B (such as “It is fine”) is also materially incompatible with A. In this sense scarlet entails red and square entails rectangular.

In much the same way, even if the features in virtue of which sensory experiences are determinately contentful were construed as unrepeatable, their relations of exclusive difference from one another would ensure that they also fall under repeatables, i.e., that they exhibit a kind of universality. For many colors are alike in that they are exclusively different from red, and all shapes are alike in that they are not exclusively different, but merely compatibly different from red. These repeatable commonalities ramify into arbitrary Boolean complexity. For instance, two otherwise dissimilar features might share not being exclusively different from A or B, but being exclusively different from both C and D. More natural sense universals are constructable using entailments defined by exclusions. Thus all the features that entail red—for instance, shades of red such as scarlet and crimson—can be grouped together. Similarly, all the features entailed by rectangular form a kind. As Wilfrid Sellars observes, the primitives appealed to by classical empiricists are determinate sense repeatables. They were concerned with how merely determinable sense repeatables might be understood in terms of these, not with how unrepeatables might give rise to determinate repeatables.

It is in virtue of these facts that I take determinate negation to be for Hegel a more metaphysically fundamental concept than mediation and universality, as pictured in the first figure in Section II. The concept of negation that plays the axial role in the metaphysics Hegel introduces in Perception is a rich and complex one. As I have indicated, it is introduced as one element of a dyad. This is the metadifference between two kinds of differences: mere or compatible difference and exclusive or incompatible difference. We have seen that these two kinds of differences articulate determinate repeatable features into compatible families of incompatible features, as in the paradigm of colors and shapes.

The next step in understanding exclusive difference is to consider it in relation to another kind of negation. Determinate negation also contrasts with formal or abstract negation. The latter is logical negation, in a non-Hegelian sense of “logical.” Two features stand in the relation of determinate negation if they are materially incompatible. I am helping myself here to Sellars’s terminology, itself not wholly uninfluenced by Hegel. The idea is that items determinately negate one another in virtue of their nonlogical content. Such items stand in the relation of formal or abstract negation if they are logically incompatible: incompatible in virtue of their abstract logical form.

This distinction is as old as logic. It is the distinction between Aristotelian contraries and Aristotelian contradictories. Red and green, circular and triangular, are contraries, while red and not-red, and circular and not-circular are contradictories. Both of these are kinds of exclusive differences. So this is a further metadifference, between two species of exclusive differences. The first metadifference, between compatible and incompatible differences, is a structure of coordination. Neither sort of difference is definable in terms of the other; both are required for determinateness. Together they yield compatible families of incompatible feature kinds. By contrast, contrariety and contradictoriness are interdefinable There are accordingly two orders of explanation one might pursue in relating them, depending on which one takes as primitive. One can define contraries in terms of contradictories, and so determinate negation in terms of formal negation: for Q to be a contrary of P is for Q to imply P’s contradictory, not-P. Green is a contrary of red and triangular of circular just insofar as green implies not-red and triangular implies not-circular. Or one can define contradictories in terms of contraries, so formal negation in terms of determinate negation: for something to be the contradictory of P, not-P, is just for it to be the minimal contrary of P, in the sense of being implied by every contrary Q of P. Not-red is implied by all of red’s contraries: green, blue, yellow, and so on, and not-circular is implied by all of circular’s contraries: triangular, square, pentagonal, and so on (see Figure 5.3).

Hegel takes determinate negation to be prior in the order of explanation to formal or abstract negation. He accordingly has the second picture in mind, understanding contradictories in terms of contraries. The tradition of extensional logic and semantics, extending from Boole through Russell to Tarski and Quine, adopts the other order of explanation, understanding material incompatibility as contrariety in terms of formal incompatibility as contradictoriness or inconsistency. Each approach has its characteristic advantages. It is worth noting at this point that the interdefinability of contraries and contradictories (hence of determinate and abstract formal negation) depends on the availability of a notion of implication or consequence. The Hegelian order of explanation has a native candidate. For, as already pointed out, material incompatibility underwrites a notion of entailment: Q is a consequence of P just in case everything materially incompatible with Q is materially incompatible with P. What I call the Tarskian extensionalist tradition also has available a notion of implication. But it is not directly definable in terms of formal logical negation. It becomes available only if one widens the focus of the Tarskian explanatory strategy. Doing so will illuminate the metaphysical project Hegel pursues in the Perception chapter. In particular, it makes manifest the difference between building modality in at the metaphysical ground floor, as Hegel does, and adding it as a late-coming, perhaps optional afterthought (think of Quine), as the extensionalist tradition does.

The widening of focus I have in mind is to the structure of singular terms and predicates presenting objects and properties that Hegel argues is implicit already in the idea of determinate features presented by a feature-placing vocabulary. I am going to call a conception of the objective world as consisting of particular objects that exhibit repeatable properties (universals) as having an “aristotelian” structure (with a lowercase a). I do so because I take it that it is such a commonsense conception, suggested by the way our languages work, that Aristotle aims to explain using his proprietary metaphysical apparatus of individual substances and their essences. I am after the Aristotelian explanandum rather than the explanans. I take it that it is also the common explanatory target of the Perception chapter and of the extensionalist semantic tradition that culminates in Tarskian model theory. (Russell pitched the shift from traditional logics of properties to modern logics of relations as transformative, and along one important dimension, it was. But that difference is not of the first significance for the contrast I am concerned to draw here.) Unlike Aristotle himself, neither Hegel in this chapter (though he does in the Logic) nor the extensionalist tradition in general makes anything of the distinction between sortal predicates expressing kinds such as “fox” (which come with criteria of identity and individuation), and mere characterizing predicates expressing properties such as “red” (which do not individuate)—which is part of what Aristotle’s essentialism is a theory of.

There are two broad explanatory strategies available to explicate the aristotelian structure of objects-and-properties. Hegel wants to explain it in terms of determinate negation, relating property-like features. I want to illuminate that metaphysical approach by contrasting it with the extensionalist Tarskian tradition, which starts with objects understood as merely different. The two orders of explanation exploiting the relations between contraries and contradictories (hence determinate and formal, abstract negation) are embedded in more encompassing converse explanatory strategies for articulating the aristotelian object / property categorial structure, rooted in the metadifference between incompatible and compatible differences.

The notion of compatible difference that applies to the objects with which metaphysical extensionalism begins does not appeal to modal notions of possibility or necessity. The mere difference that characterizes elements of the domain of objects of the Tarskian scheme is a primitive material relation, in that it—like the contrariety with which Hegel’s converse explanatory strategy begins—is not defined in terms of formal logical concepts. Properties are represented in Tarskian structures as sets of objects: the extensions of the properties. The indiscernibility of identicals—that is, that if objects a and b are identical, they have the same properties—will follow set-theoretically from this definition. The other direction of Leibniz’s Law, the identity of indiscernibles, will not, unless one insists that every different set of objects determines or constitutes a property.

On this basis, contradictoriness, and so formal negation, can be introduced. Contradictory properties are definable as properties with complementary extensions within the domain of objects. Not-P, the contradictory of P, is the property whose extension consists of all and only the objects in the domain that are not in the extension of P. The relation of contrariety is not really represented in such extensional structures. What are intuitively contraries, such as square and circular, will have disjoint extensions. But not every pair of disjoint extensions corresponds to proper contraries. If the domain does not happen to include a mountain made of gold, being made of gold and being a mountain will be disjoint properties, without being contraries. The failure of Tarskian structures to represent contrariety is the result of the modal character of that notion. Contradictoriness of properties is represented, because negation is given the same reading in all models: contradictory properties are those pairs whose extensions exhaustively and exclusively partition the domain of objects. In order to represent contrariety of properties, we could in this object-based framework impose a nonlogical, material constraint on the Tarskian interpretation function, to ensure that the extensions of contrary properties P and Q are disjoint in every model.

That, in effect, is what the possible-worlds development of Tarskian model theory does. The modal element can be thought of as added by treating contrariety of properties the way logical negation is treated: as a constraint on all interpretations. The account moves up to intensions of properties by looking at functions from indices to extensions. The indices can be models—that is, relational structures. Or they can be possible worlds. We have come to see that the differences between these are great. One important one is that models have domains of objects. Possible worlds do not. Another is that some logically possible worlds (i.e., combinatorially possible constellations of objects and properties) do not count as really (metaphysically or physically) possible. Whereas any relational structure with the right adicities can be a model. This is the point where modality gets incorporated—that is, at the end. It then trickles down, via the intensions of properties, to the properties. But it should be emphasized that this constraint is, from the point of view of the underlying raw materials, arbitrary and extraneous. One simply stipulates that the disjointness of domains of certain predicates, square and circular, is de jure, while that of others, gold and mountain, is not. Such stipulations come in at the very end of the process of semantic construction, not at the beginning. So possible-worlds semantics in the end also takes the distinction between incompatible and compatible difference (exclusive and mere difference) for granted. It just builds it in at a different level, as something late coming.

A particularly extreme version of the extensionalist order of explanation is that of the Tractatus. Not only does it not build modality into its primitives; it offers only the most attenuated version of modality, constructed at the very end as something to be understood in terms of logical contradictoriness and (so) formal negation. The Tractarian scheme starts with mere difference of objects, and mere difference of relations among them. Properties are understood as just relations to different objects. All elementary objects can stand in all relations to all other objects. At the ground level, there are no combinatory restrictions at all, except those that follow from the adicity of the relations. What is syntactically-combinatorially categorically possible (“logically possible”) is possible tout court. Elementary objects put no constraints on the Sachverhalte they can enter into, and so no restrictions on the properties they can simultaneously exhibit. At this level, properties do not stand to one another in relations of exclusive difference—e.g., where being A’s mother implies one cannot be B’s father. (Indeed, it is a good question whether and how monadic properties can even be merely distinguished.) More complex facts can be incompatible, but this is intelligible only where one truth-functionally includes the logical negation of an elementary fact included in the other. As I mention earlier, dissatisfaction with this treatment of contrariety of colors seems to have played an important role in moving Wittgenstein away from the Tractarian way of thinking about things.

IV. Properties and Objects

Grafting on at the end substantive modal constraints on admissible models in the way of possible-worlds semantics does not alter the basic Tarskian extensionalist order of explanation. The order of explanation Hegel pursues in Perception is the converse of it. It is of the essence of extensional approaches to appeal only to mere or compatible difference of objects. Hegel starts with features rather than objects, and in addition to compatible differences of features, Hegel also acknowledges incompatible or exclusive differences. We have seen that these come in two Aristotelian species: formal contradictories and material contraries. Hegel focuses on the material (nonlogical) incompatibility of such contraries. On the basis of this nonlogical modal primitive, he then elaborates the full aristotelian structure of objects-with-properties (particulars characterized by universals).

There are three distinct moves in the process by which the metaphysical structure of objects-with-properties is found to be implicit already in what would be expressed by a purely feature-placing vocabulary, once the features deployed in that vocabulary are understood to stand to one another in relations both of compatible and of incompatible differences. Each one involves adding to the picture a further kind of difference, and so a further articulation of the complex notion of determinate negation. The first move puts in place the intercategorial difference between properties and objects, or universals and particulars. The second move puts in place an intracategorial difference between two roles that particular objects must play with respect to properties, reflecting the intracategorial difference between merely different and exclusively different properties. The third move registers a fundamental intercategorial metaphysical difference between objects and properties with respect to mere and exclusive differences.

The first move in this argument finds the aristotelian structure of objects-and-properties, or particulars-and-universals, to be implicit already in the observation that the features articulating the contents of sense experience stand to one another in relations of material incompatibility or exclusive difference. This argument can be thought of as beginning with the role that what in Sense Certainty Hegel calls “the Now” plays in the distinction between the two basic kinds of differences, compatible and incompatible. What would be expressed by “Now₁ is night,” is not incompatible with what would be expressed by “Now₂ is day.” It is incompatible with “Now₁ is day.” The incompatibility applies only to the same “Now.” We could say that the “Now” is playing the role of a unit of account for incompatibilities.

What this role is becomes clearer when we think of it in connection with the second dimension of repeatability that emerged from the consideration of the form of self-consciousness that is sensory consciousness understanding itself as sense certainty—namely, recollective repeatability. For what would be expressed by “Now₁ is night” is also incompatible with what would be expressed by “Then₁ was day” if “then₁” expresses a recollection, a holding on to, of what is expressed by “now₁.” The unit of account for incompatibilities is the “holding on to” that is expressed by the whole anaphoric chain of recollections of the initial demonstrative “now.”

Further, “here” expresses a similar unit of account for incompatibilities. What would be expressed by “Here₁ is a tree” is not incompatible with what would be expressed by “Here₂ is a house.” But it is incompatible with what is expressed by “Here₁ is a house.” And it is incompatible with what would be expressed by “There₁ is a house” if what would be expressed by “there₁” stands to what would be expressed by “here₁” as a recollection, as what would be expressed by “then₁” stands to what would be expressed by “now₁”—that is, as an anaphoric repeatable “holding on to” the spatial demonstrative “here₁.” Indeed, the temporal and spatial indexicals can be combined into the spatiotemporal indexical “here-and-now.” What such indexicals express are still units of account for incompatibilities. So are the anaphoric repeatables formed from them, what would be expressed by “there_i-and-then_j”s that are holdings-on-to what would be expressed by any “here_i-and-now_j.” And what holds for these indexical experiencings holds also for demonstrative ones. That what would be expressed by “This₁ is triangular” does not exclude what would be expressed by “This₂ is circular.” But it does exclude what would be expressed by “That₁ is circular” if the “that₁” functions as an anaphoric dependent recollecting the original tokening “this₁.”

In all these cases the same anaphorically extended structure relating unrepeatable indexical or demonstrative experiencings plays the role of a unit of account that excludes possession of materially incompatible sensible features. At this point we can see that the notion of incompatible difference, determinate negation, or material incompatibility (which I have been claiming are three ways of talking about the same thing) among features implicitly involves a contrast with a different kind of thing—something that is not in the same sense a feature—that is an essential part of the same structure. For incompatibilities among features require units of account. What is impossible is not that two incompatible features should be exhibited at all. After all, sometimes it is raining, and sometimes it is fine. What is impossible is that they should be exhibited by the same unit of account—what we get our first grip on as what would be expressed by a tokening of “now” or “here-and-now” or “this” and the anaphoric repeatability structures they initiate.

So from the fact that what would be expressed by different “now”s can exhibit incompatible features it follows that the structure of sense contents that includes features that can differ either incompatibly or compatibly also essentially includes items that are not features, but that play a different role. These units of account are of a different ontological category from the features for which they are units of account. Besides the intracategorial difference (concerning relations of features) between two kinds of differences (incompatible and compatible) of features in sensory experience that would be expressed by sentences in a feature-placing language, sensory experience also implicitly involves the intercategorial difference between features and units of account for incompatibilities of features.

That is to say that that what I have called the “aristotelian” structure of objects-and-properties, or particulars-and-universals, is now seen to have been all along implicit in sense experience, even as originally conceived according to the categories of sense certainty. Making this implicit structure explicit yields the form of sensory self-consciousness Hegel calls “perception.”

A decisive line has been crossed. The content-repeatables exhibited by unrepeatable sense experiencings are no longer to be construed as features, but as properties. What enforces the transition is the association of those sense repeatables not with what is expressed by the indiscriminate “it” of “It is raining,” or the undifferentiated merely existential “there is” of “There is red,” but with different, competing units of account. Looking over the shoulder of the phenomenal self-consciousness that is developing from the categories of sense certainty to those of perception, we see that this differentiation of what exhibits the sense repeatables was implicit already in the different “now”s acknowledged by sense certainty from the beginning. No longer are the contents of basic sensory knowings construed as what would be expressed in feature-placing vocabularies. Now they are articulated as what requires expression in vocabularies exhibiting the further structure of subjects and predicates. What is experienced is now understood not just as features, but as objects with properties, particulars exhibiting universals.

V. Two Metaphysical Roles of Objects

Understanding functional units of account for incompatible sense repeatables more specifically as objects or particulars involves further unfolding of what is implicit in distinguishing compatible or merely different sense repeatables from incompatible or exclusively different ones. Hegel says of the features that “these determinatenesses … are really only properties by virtue of the addition of a determination yet to come”—namely, thinghood. [PG 113] He elaborates that notion of thinghood along two dimensions: the thing as exclusive and the thing as inclusive. In talking about these two different roles essential to being a “thing of many properties,” he describes it as on the one hand “a ‘one,’ an excluding unity,” and on the other hand as an “ ‘also,’ an indifferent unity.” The unity of the units of account essentially involves this distinction and the relation between being a “one” and being an “also.” [PG 114] These correspond to the roles played by objects with respect to incompatible properties, which they exclude, and their role with respect to compatible properties, which they include. So the intracategorial metadifference between two kinds of differences between what now show up as properties is reflected by the intracategorial difference between two complementary roles objects play with respect to those properties, as repelling incompatible properties and as a medium unifying a set of compatible properties.

As to the first, he says:

[I]f the many determinate properties were strictly indifferent [gleichgültig] to one another, if they were simply and solely self-related, they would not be determinate; for they are only determinate in so far as they differentiate themselves from one another [sie sich unterscheiden], and relate themselves to others as to their opposites [als entgegengesetzte].

This is the by now familiar point that determinateness requires exclusive, incompatible difference, not just mere or indifferent, compatible difference.

Yet; as thus opposed [Entgegensetzung] to one another they cannot be together in the simple unity of their medium, which is just as essential to them as negation; the differentiation [Unterscheidung] of the properties, insofar as it is … exclusive [ausschließende], each property negating the others, thus falls outside of this simple medium.

The “medium” here is thinghood, the objects that exhibit the properties:

The One is the moment of negation … it excludes another; and it is that by which “thinghood” is determined as a Thing. [PG 114]

If A and B are different things, then one can be circular and the other triangular, one red and one green. But one and the same thing cannot have those incompatible properties. A’s being circular and red excludes its being triangular or green. Objects are individuated by such exclusions.

On the other hand,

[t]his abstract universal medium, which can be called simply thinghood … is nothing else than what Here and Now have proved themselves to be, viz. a simple togetherness of a plurality; but the many are, in their determinateness, simple universals themselves. This salt is a simple Here, and at the same time manifold: it is white and also tart, also cubical.… All these many properties are in a single simple “Here,” in which, therefore, they interpenetrate.… And at the same time, without being separated by different Heres, they do not affect each other in this interpenetration. The whiteness does not affect the cubical shape … each … leaves the others alone, and is connected with them only by the indifferent Also. This Also is thus the pure universal itself, or the medium, the “thinghood,” which holds them together in this way. [PG 113]

The thing as the medium in which compatible properties can coexist is the thing as “also.” It is the thing of many (compatible) properties, rather than the thing as excluding incompatible ones. The tokenings of “here” that sensory consciousness understanding itself as sense certainty already saw as expressing a feature of its experiencings already plays this role, as well as the exclusionary one. Already in that primitive case we can see

the medium in which these determinations permeate each other in that universality as a simple unity but without making contact with each other, for it is precisely through participation in this universality that each is on its own, indifferent to the others—As it has turned out, this abstract universal medium, which can be called thinghood itself … is none other than the here and now, namely, as a simple ensemble of the many. [PG 113]

Along this dimension, too, thinghood, the idea of objects as an essential structural element of the structure that contains properties, shows up first in indexical form of here-and-nows, and is generalized first by the idea of anaphoric chains “recollecting” what is expressed by such unrepeatable indexical and demonstrative tokenings, on its way to the full-blown logical conception of particulars exhibiting universals.

The idea of sense experiencings that are determinately contentful in the sense of being not only distinguishable but standing in relations of material incompatibility turns out implicitly to involve a structural-categorial contrast between repeatable sense universals and something else. The something else is “thinghood,” or particularity. The notion of particularity then turns out itself to involve a contrast:

This simple medium is not merely an “also,” an indifferent unity; it is also a “one,” an excluding unity. [PG 114]²

These different but complementary roles reflect, within this ontological category, the distinction between compatible and incompatible differences, within the ontological category of properties (see Figure 5.4).

We have seen that determinateness demands that the identity and individuation of properties acknowledge not only compatible differences between them, but also incompatible differences. Does the identity and individuation of objects also depend on both the role of things as unifying compatible properties and their role as excluding incompatible ones? Hegel says:

[T]hese diverse aspects … are specifically determined. White is white only in opposition to black, and so on, and the Thing is a One precisely by being opposed to others. But it is not as a One that it excludes others from itself … it is through its determinateness that the thing excludes others. Things are therefore in and for themselves determinate; they have properties by which they distinguish themselves from others. [PG 120]

The first claim here is that the thing as a one is in some sense opposed to other things, or “excludes them from itself.” Talk of the thing as an excluding one invokes the role of objects as units of account for incompatibilities of properties.

But the sense in which objects exclude or are opposed to other objects cannot be the same as the sense in which properties exclude or oppose one another. What would the units of account for those exclusions be? More deeply, we have seen that the material contrariety of properties admits of the definition of opposites in the sense of contradictories. Property Q is the opposite of property P in this sense just in case it is exhibited by all and only the objects that do not exhibit P. This is how not-red is related to red. An argument due to Aristotle shows that objects do not have opposites in this sense of contradictories.3 The corresponding notion of an opposite in the ontological category of objects would have object b being the contradictory of object a just in case b exhibits all and only the properties not exhibited by a. But the properties not exhibited by any object always include properties that are incompatible with one another, and hence not all exhibitable by any one object. The red circular object does not exhibit the properties of being green, yellow, triangular, or rectangular. So its opposite would have to exhibit all of these properties (as well as all the other colors and shapes besides red and circular). That is impossible. The preceding figure has the properties of not being identical to my left little finger, and of not being identical to Bach’s Second Brandenburg Concerto. Its opposite would have to have the property of being identical to both. Since they are not identical to each other, this cannot be.

So although objects both differ from and in some sense exclude one another, there is a huge structural difference between how they do and how properties differ from and exclude one another—the distinction between two kinds of differences that kicks off the whole process of explicitation and elaboration we have been rehearsing. The Aristotelian argument unfolds what turns out to have been implicit all along in the distinction between the two ontological categories of properties and objects. The key to the difference, the distinction between them, lies in their relation to exclusive difference: the difference between their relations to this kind of difference.

How are we to think of objects as being identified and individuated, by contrast to the ways properties are? The answer Hegel offers in the earlier passage is surely right as far as it goes: they are identified and individuated by their properties. This response reinforces the order of explanation being identified here as Hegel’s: from (ur)properties (features) to objects—reversing the extensionalist Tarskian order of explanation. In virtue of their role as hosting cocompatible properties, objects as “also”s merely differ from one another insofar as they host different sets of cocompatible properties. In virtue of their role as excluding properties incompatible with those they host, objects as “excluding ones” exclude one another insofar as some of the cocompatible properties exhibited by one are incompatible with some of the cocompatible properties exhibited by another.

Here we see another aspect of the contrast in orders of explanation between the Tarskian extensionalist tradition and Hegel’s metaphysics of universals and particulars. The extensionalist tradition offers an answer to the question about how the identity and individuation of objects relates to that of properties: Leibniz’s Law (LL). It comprises two parts, a weaker and a stronger claim:

LL1: The Indiscernibility of Identicals.
LL2: The Identity of Indiscernibles.

LL1 says that identical objects must have all the same properties. LL2 says that objects with all the same properties are identical. The identity of indiscernibles is stronger than the indiscernibility of identicals in that it seems to depend on there being “enough” properties: enough to distinguish all the objects that are really distinct. As it arises in the extensionalist framework, Leibniz’s Law appeals only to the mere difference of properties and the mere difference of objects. It becomes controversial how to apply it when modally robust properties are in the picture.⁴ How do these principles look in an environment where exclusive difference of properties is also in play, as well as mere difference?

The Indiscernibility of Identicals says that mere difference of properties is sufficient for mere difference of objects. The Identity of Indiscernibles says that merely different objects have at least merely different properties. I think Hegel endorses these principles. But his talk of objects as excluding one another suggests that he also endorses a further, stronger principle: different objects not only have different properties; they have incompatible properties. We might call this principle the “Exclusivity of Objects.” Such a view would satisfy three criteria of adequacy, the first two of which are set by the passage most recently quoted.

It would underwrite talk of objects as excluding one another.
It would do so by appealing to the more primitive notion of properties excluding one another.
And it would respect the differences between property-exclusion and object-exclusion that are enforced by the Aristotelian argument showing that objects cannot have contradictories definable from their exclusions (in the case of properties, their contrarieties) in the way that properties do.

In effect, the Exclusivity of Objects says that it never happens that two objects are distinguished by their role as things-as-alsos combining different compatible properties, according to the discernibility of nonidenticals version of LL2 unless they are also distinguished by their role as things-as-excluding-ones. There is no mere difference of properties distinguishing objects without exclusive difference of properties (having incompatible properties) distinguishing them. This is a topic on which Leibniz’s Law is silent.

The principle of the Exclusivity of Objects holds even within the extensionalist context, provided logical vocabulary is available. For even there it is denied that two objects could differ (merely differ) just by having different merely or compatibly different properties. Taking our cue from the appeal to identity-properties used to illustrate the Aristotelian argument that objects cannot have contradictories, we can notice that if a and b are indeed not identical, then a will have the property of being identical to a and b will have the property of being identical to b. If a and b are not identical, then nothing can have both properties; they are not merely different properties, they are exclusively different. It is impossible for any object that has the one property to have the other.

So thinking about things from the extensionalist direction, beginning with mere differences of objects and identifying merely different properties in effect with sets of them, does yield a version of the principle of Exclusivity of Objects. If object a is red and object b differs from it by not having that property, then appeal to the notion of formal or abstract negation yields the result that b has the property that is the contradictory of red. It has the property not-red. That property is exclusively different from red, in that it is a property of formal negation that it is logically impossible for any object to have both properties simultaneously. Provided that logical vocabulary such as identity or negation is available to define complex properties, merely different objects will be exclusively different. The fact that the principle of the Exclusivity of Objects, that merely different objects will have not only compatibly different properties but also incompatibly different ones, arises early in the Hegelian order of explanation and late in the extensionalist one is a consequence and reflection of the two orders of explanation regarding the relations between material contrariety and formal contradictoriness that they adopt.

For distinguishing at the outset compatibly from incompatibly different properties, as Hegel does, commits one to a picture of properties as coming in compatible families of incompatible properties, as in the paradigmatic case of shapes and colors of monochromatic Euclidean plane figures. If objects a and b differ merely in compatible properties, they differ in properties drawn from different families of incompatibles. For example, a is red and b is square. But for them to be distinguished from each other thereby, a must not also be square or b must not also be red. But if a is not square, it will exhibit some other shape, incompatible with being square, and if b is not red it will exhibit some other color, incompatible with being red. But then a and b will have properties that are not merely different from one another, but incompatible with one another. That is just what the Exclusivity of Objects claims. According to this picture, kinds of things are characterized by which compatible families of incompatible properties they must exhibit. Sounds can be shapeless and colorless—though they must have some pitch and volume. But any monochromatic Euclidean plane figure must have both shape and color on pain of not qualifying as a determinate particular of that kind.

In a sense, then, for the identity and individuation of objects, the exclusiveness of objects, which appeals to exclusive difference of properties, is more basic in the Hegelian order of explanation than Leibniz’s Law, which appeals to mere difference of properties.

VI. Ten Kinds of Metaphysical Differences

This observation completes the rehearsal of the argument that elaborates what is implicit in the idea of the contents of sensory consciousness as what would be expressed in a feature-placing vocabulary, through the consideration of what is implicit in the requirement that the features articulating those contents must be determinate, through the consideration of the relation of negation and universality, to the much more finely structured idea of those contents as presenting a world consisting of empirical objects with many observable properties. We are now in a position to understand what Hegel is after when, in the opening introductory paragraphs of the Perception chapter, he says such things as:

Perception … takes what is present to it as universal. [PG 111]

As it has turned out … it is merely the character of positive universality which is at first observed and developed. [PG 114]

Only perception contains negation. [PG 111]

Being … is a universal in virtue of its having mediation or the negative within it; when it expresses this in its immediacy, it is a differentiated, determinate property. [PG 113]

Since the principle of the object, the universal, is in its simplicity a mediated universal, the object must express this its nature in its own self. This it does by showing itself to be the thing with many properties. [PG 111]

In these passages Hegel describes a path from universality, through unpacking the requirement of the determinateness of universals, to negation (and mediation), fetching up with the universal / particular structure of the thing with many properties. I have told the story somewhat differently, but not, I think, irreconcilably so. The official result inherited from the Sense Certainty chapter is the realization by sensory self-consciousness that it must understand its immediate sense knowledge as having contents that are repeatable in the sense of being universal. (Not only in this sense, as we have seen.) So that is where Hegel picks up the story in Perception. I understand the subsequent invocation of determinateness and negation to be a reminder that what drove empirical consciousness understanding itself according to the categories of sense certainty to the realization that repeatability as universality must be involved was precisely considerations of the determinateness of sense knowledge as involving negation. So I have told the story of sensory consciousness understanding itself as perceiving starting with the distinction between two ways in which sense contents came to be seen to differ already in the experience of sense certainty.

The passage I want to focus on at this point is one in which Hegel summarizes what we will learn, by talking about

sensuous universality, that is, the immediate unity of being and the negative. [PG 115]

For here he is announcing that in this chapter we get our introduction to one of his master ideas, that determinateness should be understood as a kind of identity constituted by difference, unity articulated by disparity. (That it is determinate sensuous universality is why the sort of unity of being and the negative is characterized as “immediate.” I have glossed this as what I call “immediacy of origin,” the fact that the episodes of sensory awareness being considered are passively elicited by the exercise of noninferential differential responsive capacities.) Though he has other big ideas, this is the central structural innovation of his thought about what he calls “logic,” which only later in the story is differentiated into a semantics addressing the structure of the subjective realm of thought and an ontology or metaphysics addressing the structure of the objective realm of being. One of my main interpretive claims is that determinate negation or material incompatibility on the side of the thinking subjects is deontic incompatibility (a matter of commitment and entitlement) and on the side of the objects thought about is alethic incompatibility (a matter of necessity and possibility), and that Hegel’s idealism is a story about the unity constituted by these different kinds of differences. But that is a story for later on.

What we have been exploring is the metaphysical fine structure of what Hegel invokes in this passage as “the negative.” One of Hegel’s own summaries is this:

[T]he thing as the truth of perception reaches its culmination to the extent that it is necessary to develop that here. It is

α) the indifferent passive universality, the also of the many properties, or, rather, matters,

β) the negation generally as simple, that is, the one, the excluding of contrasted properties, and

γ) the many properties themselves, the relation of the two first moments: The negation, as it relates itself to the indifferent element and extends itself within it as a range of differences; the point of individuality in the medium of enduring existence radiating out into multiplicity. [PG 115]

In fact, I have argued that Hegel’s metaphysical analysis of the fine structure of the aristotelian object-with-many-properties, and his derivation of it from the concept of determinate universality, is substantially more intricate than this summary indicates. As on offer in the Perception chapter, it is a constellation of no less than ten interrelated kinds of differences. We began by distinguishing

1. mere or “indifferent” [gleichgültig] difference of compatible universals

from

2. exclusive difference of incompatible universals.

This brought into view the

3. metadifference between mere and exclusive difference.

This is the first intracategorial metadifference, between differences relating universals to universals. It is a kind of exclusive difference, because the universals must be either compatible or incompatible. (One could use the terminology differently, so that exclusively different universals were also merely different. But this does not seem to be how Hegel uses the terms.)

Within exclusive difference, there are two species that can be related by two opposing orders of explanation:

4. material contrariety, corresponding to determinate negation,

and

5. formal contradictoriness, corresponding to abstract logical negation.

There is then also the

6. metadifference between determinate and abstract negation logical negation.

This is the second intracategorial metadifference, between differences relating universals to universals. These are not exclusively, but only compatibly different. Contradictories are a kind of contrary: minimal contraries.

Implicit in the concept of repeatables as universals is the

7. difference between universals and particulars.

This is the first intercategorial difference. It, too, is a kind of exclusive difference.

Implicit in the concept of particulars in relation to universals is the

8. difference between two roles particulars, or objects play:

particulars as “also”s—that is, as medium hosting a community of compatible universals—and
particulars as “exclusive ones”—that is, as units of account repelling incompatible properties.

This is the first intracategorial difference between roles played by particulars. These are what we might call strongly compatibly different roles, because every particular not only can but must play both.

Corresponding to this difference on the side of particulars is the

9. difference between two roles universals play with respect to particulars:

universals as related to an inclusive “One” in community with other compatible universals, and
universals as excluding incompatible universals associated with different exclusive “One”s.

Finally, there is the

10. difference between universals and particulars that consists in the fact that universals do and particulars do not have contradictories or opposites.

Unless the distinctions and intricate interrelations between these different ways in which things can be said to differ from or negate others are kept firmly in mind, nothing but confusion can result in thinking about Hegel’s logic and metaphysics of negation. As an illustration, both determinate properties and objects can be understood as, to use a favorite Hegelian phrase, “negations of the negation.” But in very different ways, accordingly as both what is negated and the negating of it must have senses drawn from different elements of the preceding list. For instance, the first negating of a negation is intracategorial, among universals, and the second is intercategorial, distinguishing particulars from universals. In the first case, the identity of a determinate property consists in how it negates or differs from all of its material contraries. Each is in sense 2 the negation of the property in question. And it is by being the contrary of, negating, all of its exclusive contraries that it is the determinate property that it is. This is one sense in which universals as such “contain negation within themselves,” which is why perception, which “takes what is present to it as universal,” thereby itself “contains negation.” In the second case, according to the order of explanation I have attributed to Hegel, particulars are understood in terms of their exclusive difference, of types 7 and 9, from universals. Because the universals are the determinate universals they are because of their negations of one another, particulars can be understood as negations of the negations that articulate those universals. They are of the category that does not negate others of its category in the way universals do negate others of their category. These two examples of kinds of identity that are intelligible as constituted by negating a negation are obviously quite different, due to the difference in the kinds of negation.

We have seen Hegel argue that the idea that sense experience has a determinate content implicitly involves the idea that such contents can differ from one another in two different ways. And we have seen how he argues that the aristotelian structure of objects-with-properties is implicit in the relations between these two sorts of differences, these two senses in which contents can negate one another. The result is a case study concerning how Hegel thinks a more complex structure can be understood to be implicit in a simpler one, in terms of the process by which one goes about making it explicit.

VII. From Perception to Understanding

The structure comprising these ten sorts of difference or negation is what I take it that Hegel elaborates from the requirement of determinateness of the repeatable features characteristic of empirical consciousness understanding itself as sense certainty. It is introduced in the first five paragraphs of Perception. In the body of the chapter, he recounts three large movements of the experience of empirical consciousness understanding itself as perceiving. Here we, Hegel’s phenomenological consciousness, look on at how this underlying structure manifests itself to the phenomenal consciousness by showing the inadequacy of the abstractions that articulate its self-understanding. The overall difficulty is that this sort of self-consciousness still understands the sense in which the properties it perceives are given to it immediately: not only in terms of immediacy of their origin, but still also in terms of the supposed immediacy of their content. As Hegel puts it, according to its self-conception:

It has only to take it, to confine itself to pure apprehension of it.… If consciousness itself did anything in taking what is given, it would by such adding or subtraction alter the truth. [PG 116]

This means that

[the subject’s] criterion of truth is therefore self-identity, and his behavior consists in apprehending the object as self-identical. [PG 116]

The trouble is that diversity (dissimilarity, diversity of moments) is also explicitly a feature of the content of sense perception as determinate. The three movements of the experience of perceiving consciousness are conceptual strategies—each ultimately unsuccessful—for explicitly reconciling the elements of unity and diversity, self-identity and difference, implicit in ground-level determinate sense experience. In accordance with its self-conception, Hegel says, any failure to reconcile these diverse moments must be attributed not to a feature of what is perceived, but to the perceiving of it.

In general, what we see is that because empirical consciousness understanding itself according to the categories of perception seeks to understand its experience as exhibiting independent principles of unity and disparity (“these empty abstractions of a ‘singleness’ and a ‘universality’ opposed to it” [PG 130]) that are somehow bolted together to yield a conception of the multifarious kinds of identity-through-difference (“ ‘being-for-self’ burdened with opposition” [PG 130]) that turned out to be implicit in the notion of determinateness, it is doomed to confusion and failure. In its first experience, it notices that what it takes to be the immediately simple, self-identical unity it experiences essentially involves multiplicity, diversity, and difference. (Hegel walks us through several of the dimensions of identity-through-difference retailed in the previous section.) Empirical consciousness understanding itself as perceiving cannot understand how on this basis e pluribus unum, one arising out of many, is possible. Identity and diversity are exclusively different features. So it must be impossible for one single, self-identical content to exhibit both. In particular, one cannot conceive of objects as determinate apart from their relation to their properties, and one cannot conceive of the properties, in terms of which objects are determinately what they are, as determinately what they are apart from their relations (of exclusion) to other properties. So one cannot understand either objects or properties as both determinate and independent of their relations to other things (properties to other properties, objects to properties, and objects to other objects).

Because those sorts of unities are not intelligible according to its guiding metaconception, perceiving consciousness takes it that it must be making some sort of a mistake in its taking in of what is given to it. Either the object of perception is unified and self-identical, and multiplicity is being spuriously added by the perceiving subject, or what is perceived is really diverse and a spurious unity is being conferred by the perceiving subject. What drives the second experience of perceiving consciousness is the question of where to locate responsibility for diversity or unity.⁵ This is really the issue throughout the body of the chapter. The first metaexperience sought for both in the objective realm of what is perceived. In the second, the loci of responsibility considered are the perceived object and the perceiving subject. The second strategy of perceiving consciousness—still laboring under an understanding of identity as requiring autonomy, excluding essential relation to something other—is to respond to the failure of its first strategy by assigning a role to consciousness in making sense of the complex constellation of unity and diversity required by determinateness.

One way to do that is to take the thing experienced to be indeed one and autonomous, but to be experienced as exhibiting diverse properties only because of its relation to our various senses.

We get the entire diversity of these aspects, not from the Thing, but from ourselves, and they fall asunder this way for us because the eye is quite distinct from the tongue. [PG 119]

The idea here is the one Shelley expresses in a passage in Adonais where he imagines the “white radiance of Eternity” refracted through the multicolored stained glass of the mind to yield the multiplicity we see:

The One remains, the many change and pass;

Heaven’s light forever shines, Earth’s shadows fly;

Life, like a dome of many-coloured glass,

Stains the white radiance of Eternity.

The Shelleyan stratagem cannot rescue perceiving consciousness’s commitment to understanding identity as involving no substructure of difference from or relation to others, though. For the “various properties which seem to be properties of the Thing” [PG 119], the “diverse aspects for which consciousness accepts responsibility,” are still “specifically determined. White is white only in opposition to black.” [PG 120] So the difficulty of understanding identity as constituted through (exclusive) difference is not solved on the subjective side of perceiving consciousness. And on the side of the objective perceived thing, whose unity or identity construed in terms of autonomy is supposed to be preserved by relegating manyness to consciousness,

it is in its determinateness that the thing excludes others. Things are … in and for themselves determinate; they have properties by which they distinguish themselves from others. [PG 120]

The way in which exclusive intracategorial difference is essential to the identity both of properties and of things remains a problem even after responsibility for the diversity of properties has been assigned to one pole of the intentional nexus and responsibility for the unity of the thing has been assigned to the other.

And the converse Kantian version of this second strategy fares no better. The idea here is that “the Thing itself is the subsistence of the many diverse and independent properties,” and that “positing these properties as a oneness is the work of consciousness alone.” [PG 121] For Kant, what is given is a sensory manifold of intuition. Imposing unity on that manifold is solely the responsibility and the result of the work of the understanding. But once again, the identity of each of the diverse properties consists in its exclusive difference from others, and the specific unity imposed on some compatible set of them when they are gathered together into an object as a one as “also” is distinguished from other such specific unities only by the exclusive difference of some of their various properties.

So dividing responsibility for unity and responsibility for diversity between subjective and objective poles of the intentional nexus, between the act of perceiving and what is perceived, will not solve the underlying problem. Both perceptual experiencings and what is perceptually experienced must be understood as determinate. That means both must exhibit the aristotelian structure of particularity and universality, which implicitly, but essentially, exhibits a fine structure articulated by different sorts of difference or negation, a complex constellation of kinds of categorial identity constituted by relations of different sorts of difference.

Hegel sees one last desperate strategy as available to empirical consciousness understanding itself according to the metaconceptual commitments of perceiving, in attempting to salvage its hopelessly simple-minded atomistic understanding of identity as consisting solely in self-relation, so excluding any essential relation to what is different from it. Interestingly enough—given the account I have offered in the preceding of the metaphysical analysis of the aristotelian structure of objects-with-properties I take Hegel to be offering, and its alternatives—the third strategy he considers is what I there call the Tractarian version of the Tarskian extensionalist order of explanation. This begins with mere difference of simple (“elementary”) objects, and construes the variety of their properties in terms of their inessential (optional, contingent) relations to one another.⁶

This third strategy, too, is bound to fail. Each thing is supposed to be the determinate thing it is, and so distinguished from other things. But what makes it determinately different is just its properties, now conceived as its relation to other things. So those relations, the way it exclusively differs from others, are essential to its being the thing it is.

The thing is posited as being for itself, or as the absolute negation of all otherness, therefore as purely self-related negation; but … the Thing has its essential being in another Thing. [PG 126]

The atomistic conception of identity as involving no essential differences must be abandoned.

Rehearsing the lessons of the three experiences of perceiving consciousness, Hegel says that it begins when

[f]rom sensuous being it turned into a universal … but a universal afflicted with an opposition; for this reason the universality splits into the extremes of singular individuality and universality.… These pure determinatenesses … are only a “being-for-self” that is burdened with a “being-for-another.” [PG 129]

What is required is a shift in understanding the relations between “the universality which is opposed to and conditioned by singular being”:

But these two contradictory extremes are not merely alongside each other but in a single unity, or, in other words, the defining characteristic common to both, viz. “being-for-self” is burdened with opposition generally. [PG 130]

When fully articulated, the result is the complex structure of particulars and universals involving ten different sorts of negation or difference expounded in this chapter’s Sections IV through VI. The holistic way in which the intricately interrelated items in it must be understood in terms of their relations to one another is what Hegel calls “understanding,” and the objects understood he calls “forces.” They are the topic of the final chapter of the Consciousness section of the Phenomenology, called Force and Understanding.

Chapter 5

Understanding the Object / Property Structure in Terms of Negation