The final form of “supersensible world” that Hegel considers is the “inverted world”—or, better, the world as inverted. I have argued that this view is formally equivalent to contemporary possible-worlds semantics for modality. Instead of seeing the actual world as surrounded by merely possible alternatives to it, Hegel considers each property of every object as surrounded by the contrary properties that define it by strongly contrasting with it. That is a way of associating with each state of affairs all the states of affairs that it excludes, in the sense of being incompatible with. As one can in the possible-worlds framework easily construct for each proposition (set of possible worlds) all the propositions incompatible with it, so one can in Hegel’s framework construct the maximal sets of compossible states of affairs (possible worlds) from the association with each state of affairs of its noncompossible states of affairs (a partition of states of affairs into those that are and those that are not compossible with the state of affairs in question).

We have seen that his conceptual realism assigns great importance to what is expressed by the use of alethic modal vocabulary: the lawfulness of objective reality. But he objects to thinking of what is expressed by the subjunctive robustness essential to explanation as describing features of the world in the same sense in which making ordinary ground-level factual claims is describing the world. He regards the approach to modality shared by the inverted-world (IW) picture and the possible-worlds (PW) picture as unduly representational. They do not properly take into account the difference in expressive role that sets modal vocabulary apart from ordinary descriptive vocabulary. This is an extension of his criticism of the view of laws as stating superfacts. His idea is that what is made explicit by modal claims (including statements of laws) is implicit in what we are doing in making ordinary ground-level empirical claims, which do describe (represent) how things are. The key to understanding the relevant sense of “implicit” and “explicit” and the expressive relation between them is the idea that one cannot understand what one is saying in making modal claims without understanding what one is doing in making them. (The semantic content of alethic modal claims, what is claimed, is to be understood in terms of the pragmatic force of making those claims, the significance of modal claimings.) For this reason, one cannot understand the relation between modal and matter-of-factual claims (the relations between “law” and “force” that are the topics of both IW and PW) while remaining wholly on the objective side of the intentional nexus. One must think about how statements of laws (claims about what is necessary or possible) are used. This, Hegel says, is the inferential role they play in explanation.

Developing that line of thought is the principal interest of this chapter. Still, given what I have argued is Hegel’s prescient consideration of a version of contemporary possible-worlds approaches to necessity and possibility, it is worth exploring a bit further what he thinks is wrong with this last, most sophisticated version of a “supersensible world.” One point can be disposed of straightforwardly. Hegel thinks there is no go to the thought of developing this picture so as invidiously to distinguish the supersensible world as real from actuality, considered as mere appearance. Doing so is of course optional, but it was so also for the previously considered versions of supersensible worlds: that of invidious Eddingtonian theoretical realism and that of the calm realm of laws.

Looked at superficially, this inverted world is the opposite of the first in the sense that it has the latter outside of it and repels that world from itself as an actual world: that the one is appearance, but the other is the in-itself. [PG 159]

This superficial view is to be deplored and rejected.

More deeply, Hegel objects to understanding the semantogenic possibilia by contrast to which actual states of affairs are intelligible as determinate on the model of those actual states of affairs.

[S]uch antitheses of inner and outer, appearance and the supersensible, as two different kinds of actuality we no longer find here. The repelled differences are not shared afresh between two substances such as would support them and lend them a separate subsistence … just such a sense-world as the first, but in representation [Vorstellung]; it could not be exhibited as a sense-world, could not be seen, heard, or tasted, and yet it would be thought of as such a sense-world. But, in fact, if the one posited world is a perceived world, and its in-itself, as its inversion, is equally thought of as sensuous, then sourness, which would be the in-itself of the sweet thing is actually a thing just as much as the latter, viz. a sour thing, black, which would be the in-itself of white, is an actual black. [PG 159]

I think there are two principal objections to this view on offer. First, the reification of contrasting possibilia that is being rejected amounts to construing the modal articulation of actuality, which was originally presented in the shape of laws, on the model (allegorically) of further forces. That is, the possibilia are understood as further states of affairs, participants in what was allegorized as the play of forces, as being in some sense of the same kind as actual states of affairs, only not actual. Such a conception faces the same sort of difficulty that led to the postulation of laws as distinguished from the actual play of “forces” they govern. Understanding the relations between actuality and necessity-governed-possibilities threatens to require postulating a superlaw governing those relations. Material incompatibilities (what is not compossible) and consequences are treated as just more ultimately contingent (super)facts. Such a view, Hegel thinks, misconstrues the radically different role played in explanation by what is made explicit by modal claims.

From the idea, then, of inversion, which constitutes the essential nature of one aspect of the supersensible world, we must eliminate the sensuous idea of fixing the differences in a different sustaining element; and this absolute concept [Begriff] of the difference must be represented and understood purely as inner difference. [PG 160]

What specifically motivates the positive lesson we are to learn from the unsatisfactoriness of reifying semantogenic contrasting possibilia, though, is a fundamental conceptual difficulty in understanding the nature of necessary connections generally, which was raised to begin with in thinking about force, and then again more explicitly with respect to laws. The claim is that the IW picture does not resolve this difficulty. The issue is a version of Hegel’s master concern with conceptions of the relations between identity and difference. How can it be that the items related by a law are at once distinct from one another and necessarily related: joined in a necessary unity? This is Hume’s problem, and his response to it was the skeptical conclusion that the idea cannot be made intelligible. In Newton’s second law of motion, force, mass, and acceleration are related by F = m × a. That this necessary relation holds among them is essential to what force and mass are. But if the law is a definition of “force” and “mass,” then it does not relate independently intelligible magnitudes, because they are interdefined. The issue has an epistemological dimension: If F = m × a is a definition, then it is knowable a priori and does not require empirical investigation to establish. But the question is at base a conceptual question about how to understand necessary connections that are essential to the determinate contents of the properties (or concepts) related.

The law determining the distance a falling object traverses in a given time, d = k × t², governs a kind of motion by asserting a necessary (lawful) connection between space (distance) and time. Hegel says:

In the law of motion, e.g., it is necessary that motion be split up into time and space, or again, into distance and velocity. Thus, since motion is only the relation of these factors, it—the universal—is certainly divided in its own self. But now these parts, time and space, or distance and velocity, do not in themselves express this origin in a One; they are indifferent [gleichgültig] to one another, space is thought of as able to be without time, time without space, and distance at least without velocity … and thus are not related to one another through their own essential nature. [PG 153]

For both force and mass, the necessary relation of one to the other is an essential aspect of its identity. Each can be what it is only as standing in this necessary relation to something else. It is equally essential to the unity that is motion, according to its laws, both that it be split up into different components and that that partition be in some sense canceled by the assertion that the lawful relation among the components is necessary and essential to what they are.

The difference, then … is not a difference in its own self; either the universal, Force, is indifferent to the division which is the law, or the differences, the parts, of the law are indifferent to one another. [PG 154]

Hegel is far from wanting to claim that this kind of unity through difference, identity as necessarily involving relation to an other, is unintelligible. On the contrary. The task of developing an adequate way of talking about and understanding this holistic sort of identity or unity is at the very center of his project. Like Kant in his response to Hume’s skepticism about necessary nondefinitional relations and what is expressed by alethic modal vocabulary in general, Hegel thinks that what is expressed by lawlike statements of necessary connections cannot be understood in terms rigorously restricted to description of the objective world, but must involve recourse to talk about the cognitive activities of knowing subjects. The way the activities of knowing subjects come into his story is quite different from the way they come into Kant’s story, however. At this point in the text we have seen him express dissatisfaction with the invocation of supersensible modal superfacts as a response to the issue. He does not see that issue as adequately addressed by the claim that laws describe the layout of the space of maximal materially compossible states of affairs. A responsive answer along these lines would have to say a lot more about what makes states of affairs compossible or not, in the sense that matters for determining what constellations of states of affairs constitute genuinely possible worlds.

What is his response? It begins with the idea that understanding the sense in which force and mass are distinct but necessarily related by Newton’s second law requires thinking about how statements of the law function in explanation, to begin with, in inference.

[T]he law is, on the one hand, the inner, implicit in-itself [Ansichseiende] being, but is, at the same time, inwardly differentiated … this inner difference still falls, to begin with, only within the Understanding, and it is not yet posited in the thing itself. It is, therefore, only its own necessity that is asserted by the Understanding; the difference, then, is posited by the Understanding in such a way that, at the same time, it is expressly stated that the difference is not a difference belonging to the thing itself. This necessity, which is merely verbal, is thus a recital of the moments constituting the cycle of the necessity. The moments are indeed distinguished, but, at the same time, their difference is expressly said to be not a difference of the thing itself, and consequently is immediately cancelled again. This process is called “explanation” [Erklären]. [PG 154]

The kind of essentially differentiated necessary unity expressed by law can is to be understood in the first instance by considering the process of explanation. A law such as d = k × t² can be exploited according to two different orders of explanation, depending on what one takes as premise and what as conclusion in an inference. One can explain why the stone fell the distance it did by computing d from t, or one can explain why it took as long as it did to fall the fixed difference by computing t from d. Hegel calls making these inferences “reciting the moments” that are necessarily related by the law (the “cycle of necessity”). The difference in the moments, in spite of their necessary connection by the law, is manifest in the different orders of explanation, the difference in what understanding consciousness is doing in making the two different kinds of moves.

The exact nature of the relation between the distinction between two orders of explanation—inferring distance from time and inferring time from distance—on the one hand, and the distinction between the two necessarily related “moments” of the law, distance and time, is not yet clear to the shape of understanding consciousness being considered. It does not yet see how to understand the difference between distance and time as being a feature of the objective world. What it does appreciate, the new insight characteristic of this form of empirical consciousness conceiving itself as understanding, is that the differentiation into necessarily related moments that is essential to the articulation of the objective world expressed by laws is unintelligible apart from consideration of the inferential movement of empirical consciousness in explanations that traverse the moments in different directions. The idea is that the objective relations among theoretical entities that are codified in laws can be adequately understood only in a context sufficiently capacious as to include subjective inferential processes of explanation (“subjective” not in a Cartesian sense, but in the sense of being activities of knowing subjects).

II. Objective Idealism

The claim that the objective pole of the intentional nexus cannot properly be understood apart from an understanding of the subjective pole, and so of the whole intentional nexus, marks a decisive move in the direction of Hegel’s idealism. It is of the first importance to understand it correctly. As already indicated, Kant had a version of this thought. For he had the idea that in addition to concepts whose principal expressive role is to describe and explain empirical goings-on, there are concepts whose distinctive expressive role it is to make explicit features of the framework within which alone description and explanation are possible. Kant’s thought was motivated, as Hegel motivates his version here, by thinking about the distinctive expressive role played by the alethic modal concepts deployed in statements of laws and the subjunctive conditionals they support. (“If the stone had fallen for t seconds, it would have fallen d feet.”) The expressive role of such conditionals is in turn a matter of the kind of subjunctively robust reasoning (inferences) they support. Statements of laws and subjunctive conditionals are (in Gilbert Ryle’s phrase) inference-tickets. They codify patterns of reasoning. Understanding what it means to say that the objective world is lawful, that states of affairs stand to one another in relations of incompatibility and necessary consequence, requires understanding the patterns of reasoning that those claims license. This view is a kind of modal expressivism.¹

I see the move being made here as the second in a three-stage process of articulating ever more radical commitments that collectively constitute Hegel’s final idealist view. The first commitment is to what I have called “conceptual realism.” The second commitment is to what I call “objective idealism.” The third is to what I call “conceptual idealism.” I offer these claims as a tripartite analysis of Hegel’s idealism, claiming that his view is what you get if you endorse all of them. I take it they form a hierarchy, with each commitment presupposing those that come before it.

As I read it, conceptual realism appears on the stage already in the Introduction to the Phenomenology (though not, of course, in all the detail that will be filled in at subsequent stages). This is the view that the objective realm of facts about empirical (but not necessarily observable) things, no less than the subjective realm of thoughts about them, is conceptually structured. Only an account that underwrites this commitment, Hegel thinks, can satisfy what I have called the “Genuine Knowledge Condition”: that when things go right, what things are for consciousness is what they are in themselves. Hegel’s way of articulating conceptual realism depends on his nonpsychological conception of the conceptual. To be conceptually contentful is to stand in conceptual relations to other such conceptually contentful items. Conceptual relations are relations of material incompatibility (exclusive difference or contrariety) and consequence: Hegel’s “determinate negation” and “mediation.”

The picture of the intentional nexus at this stage is hylomorphic. One and the same conceptual content, functionally defined by the incompatibility-and-consequence relations it stands in to others, can take two forms: objective and subjective. In its objective form—for instance, as the intricate structure of facts about particulars exhibiting universals that emerges by the end of the Perception chapter—conceptual content is determined by alethic modal relations of incompatibility and consequence. They concern what is impossible and what is necessary. In its subjective form, conceptual content is determined by deontic normative relations of incompatibility and consequence. They concern what commitments one can be jointly entitled to, and when commitment to one content entails commitment to another.

The objective idealism that comes into view in the Force and Understanding chapter is a thesis about understanding. More specifically, it is a view about the relation between understanding the subjective pole of the intentional nexus and understanding the objective pole. It is a symmetrical claim: one cannot understand the objective pole without understanding the subjective pole, and vice versa. Though the dependences run in both directions, the dependence of the understanding of contentful thoughts on understanding the objective world they are thoughts about has been a theme throughout the Consciousness chapters. What is new with this shape of understanding consciousness is the dependence of understanding objectivity on understanding subjectivity.

There is a semantic distinction between two sorts of dependence relations that is fundamental to understanding the thesis of objective idealism. This is the distinction between reference-dependence and sense-dependence of concepts. This distinction begins with the Fregean distinction between sense and referent (his “Sinn” and “Bedeutung”). (In Chapter 12, the explication of a distinctively Hegelian version of these semantic notions takes center stage.) In Frege’s usage, a word such as “square” or “copper” expresses a sense, and that sense refers to some objective item, in this case, a property or substance-kind. Fregean thoughts (by which he means thinkables, not thinkings) are the senses expressed by sentential expressions. Grasping a thought is what subjects must do to understand what is expressed by a sentence. I depart from strict Fregean usage by sometimes talking about the senses expressed by locutions as “concepts.” (For Frege, concepts are the referents of predicates, not their senses.)

Xs are sense-dependent on Ys just in case one cannot in principle count as grasping the concept X unless one also grasps the concept Y. In this sense, the concept sunburn is sense-dependent on the concepts sun and burn, and the concept parent is sense-dependent on the concept child. As these examples show, sense-dependence can be either asymmetrical, as in the first example, or symmetrical, as in the second. Xs are reference-dependent on Ys just in case there cannot be Xs (referents of the concept X) unless there are Ys (referents of the concept Y). If Mrs. O’Leary’s cow kicking over a lantern was indeed the necessary and sufficient cause of the Great Chicago Fire of 1871, then the Great Chicago Fire of 1871 is reference-dependent on Mrs. O’Leary’s cow. Of course one could understand the former concept without understanding the latter. But the first concept would not refer to anything if the second did not. So there can be reference-dependence without sense-dependence. Sometimes the two relations do go together, as with parent / child or cause / effect, which are both reciprocally sense-dependent and reciprocally reference-dependent. And of course there are cases of concepts that stand in neither sort of relation to one another. Sloop and omelette are neither sense-dependent nor reference-dependent on one another.

The case that matters for thinking about what I am calling “objective idealism” is that of concepts that stand in a relation of sense-dependence but, unlike, say, superior and subordinate, not also in a relation of reference-dependence. As we saw in Chapter 2, one kind of example is provided by subjunctive response-dependent concepts and the properties they refer to. Suppose we define something as beautiful* just in case it would be responded to with pleasure were it to be viewed by a suitable human observer. (The asterisk distinguishing “beautiful*” from “beautiful” marks my not being committed to this as being the right definition, or even the right form of definition, for “beautiful” itself.) Then one cannot understand the concept beautiful* unless one understands the concept pleasure (as well as others such as suitable human observer). Then one can ask whether the existence of beautiful* objects depends on the existence of pleasurable responses by suitable human observers. For instance, were there beautiful* sunsets before there were any humans, and would there have been beautiful* sunsets even if there never had been humans? It seems clear that there were and there would have been. For even if the absence of suitable human observers means that sunsets are in fact not observed, and so not responded to by suitable human observers at all, never mind with pleasure, that had there been such observers they would have responded with pleasure. And that is enough for them to count as beautiful*. So there can be sense-dependence without reference-dependence.

That is the sort of relation I take Hegel to be claiming obtains between law and explanation. The concept law is sense-dependent, but not reference-dependent, on the concept explanation. In order to understand what a law is, one must understand how statements of laws function inferentially in explanations. Only grasping the latter, the process of “traversing the moments” in inferences explaining one fact in terms of another by means of lawful relations between them, can make intelligible the distinctive sort of necessary unity of what are nonetheless claimed to be distinct “moments” in a law such as Newton’s second law of motion. The claim is not that if there were no explanations, there would be no laws. Newton’s second law held before there were humans, and would still hold even if there never had been and never would be. Independence claims are determinately contentful only if the kind of dependence being denied has been specified. Objective idealism does claim that the objective world is not, in a specific sense, mind-independent. But since it is sense-dependence that is asserted and not reference-dependence, denying this sort of mind-independence is not saying that the existence of inferring, explaining subjects is a necessary condition of the existence of a lawful objective world. The relation of this objective idealism to Kant’s transcendental idealism, which understands lawfulness as a feature only of the phenomenal world and not of the noumenal world depends on how the latter is understood.

I take it that at least in the discussion of perceiving consciousness and in the discussion up to this point of understanding consciousness, Hegel has implicitly been accepting that one cannot understand these shapes of subjective consciousness without considering the character of the objective world that they take themselves to be consciousness of (to refer to or represent). Hegel shows by what he does in presenting these shapes of consciousness that, in the idiom of the Introduction, we (the phenomenological consciousness) cannot understand what the objective world is for one of these phenomenal shapes of consciousness without at the same time understanding what is to each shape how things are in themselves. Thus it is essential to the experience of empirical consciousness conceiving of itself as perceiving that it takes the world it is perceptually conscious of to have the aristotelian structure of particulars exhibiting universals. And it is essential to the experience of empirical consciousness conceiving of itself as understanding that the world it is thinking about is a world of unobservable theoretical objects and their observable expressions, or, at a later stage, allegorically simply a “play of forces” expressing an underlying “calm realm of laws.” If that is right, then Hegel is committed to the sense-dependence of the concepts articulating what things are for a shape of consciousness upon concepts articulating what is to it what things are in themselves. One cannot understand the concept explanation unless one also understands the concept law, and so on for the concepts that explicate more primitive forms of understanding, and perceiving consciousness. (What things are to empirical consciousness understanding itself as immediate sense certainty is sufficiently undifferentiated to make things more difficult in this case, but I take it Hegel also thinks one cannot understand the feature-placing language that would make explicit what what things are for sensing consciousness is to it without understanding also a world of immediately sensible features that is to it what things are in themselves.)

What is new with objective idealism is the converse sense-dependence claim: this form of understanding consciousness realizes that it cannot make sense of the notion of law except in terms that appeal to processes of explanation. The objective idealism that emerges for understanding consciousness is accordingly a reciprocal sense-dependence of the concepts articulating the objective things and relations and the concepts articulating the subjective thoughts and practices of understanding consciousness itself. Given what has gone before, this reciprocal sense-dependence is not limited to laws governing the objective world and the inferential manipulation of thoughts by subjects in explanation. So we can infer from the discussion of perceiving consciousness’s experience of an objective world with an aristotelian metaphysical structure that the concepts of property or universal, on the one hand, and the concept of what one is doing in classifying by applying predicates, on the other, are reciprocally sense-dependent. One cannot properly understand either one without understanding the other. Similarly, the concepts of object or particular, and the concepts of referring and singular terms are reciprocally sense-dependent. Given the notion of fact that perceiving consciousness bequeaths to understanding consciousness, we can add the reciprocal sense-dependence of that concept on the side of the objective world with that of the practice of claiming (or judging) using declarative sentences on the side of subjective practices.

So the fine structure of the commitment I am calling “objective idealism” is articulated into a triad of triads that stand to one another in relations of reciprocal sense-dependence:

Objective Ontological or Metaphysical Categories	Subjective Pragmatic Categories	Syntactic Categories
Objects / Properties or Particulars / Universals	Referring / Classifying	Singular Terms / Predicates
Facts	Asserting, Claiming, or Judging	Declarative Sentences
Laws	Explaining as Inferring	Universally Quantified Subjunctive Conditionals

Asserting the sense-dependence of the concepts object and particular on concepts articulating the use of singular terms is rejecting the possibility of general reductive explanations along the lines Quine suggests when he defines singular terms as expressions that “purport to refer to just one object.”² He takes it that the concept object is clear and independently accessible, and so can be appealed to in explaining that of singular term. Perhaps this is so for middle-sized bits of dry goods, but the idea begins to break down when pressed at the margins. Thinking about candidate objects such as musical notes, holes, ressentiment, theological phenomena such as irresistible grace, historiographical objects like the Enlightenment or modernity, concepts, cognitions, abstracta, and so on overloads intuitions about objects and particulars and drives one inevitably to thinking about the use of the terms in question. That is why in the Grundlagen, Frege finds it necessary to address the vexed question of whether numbers are objects by investigating whether numerals are used as genuine singular terms.

The concepts in question come as a package, are reciprocally sense-dependent. (This is one sense the metaphor of “two sides of one coin” can take—carefully to be distinguished from the reciprocal reference-dependence sense that that metaphor can also be used to convey.) The reciprocal sense-dependence of fact or state of affairs and the concept of what one is doing in asserting by uttering sentences explains why traditional grammar’s attempted definition of “declarative sentence” as “the expression of a whole thought” is of such profoundly little pedagogical use in helping students distinguish sentences from sentence-fragments and run-together sentences. (Are we to think that those who are slower to master the concept are devoid of “whole thoughts”? Or is coming to recognize them as such inseparable from learning how to use sentences?) Philosophers who think it is definitional of declarative sentences that they represent states of affairs make a corresponding mistake, as becomes clear from the metaphysical puzzlements that ensue (for instance, in the Tractatus) when we ask about the nature of the states of affairs represented by probabilistic or normative statements, by statements about future contingents or impossible objects like the least rapidly converging sequence. Invocation of truth-aptness or even truth-makers in this connection properly acknowledges, if only implicitly, the in-principle relevance of issues concerning the use of the sentences in question.

For Hegel, all these issues come down to the concept of determinate negation. The metaphysical analysis by perceiving consciousness of particulars and universals in the aristotelian structure of objects with many properties stays as resolutely on the objective side of the intentional nexus as can be. As we saw, all he requires is the distinction, inherited from empirical consciousness understanding itself as sense certainty, between two kinds of differences: compatible or “mere, indifferent” difference and incompatible or exclusive difference (contrariety). This distinction, he takes it (by contrast to the British empiricists) is a feature of immediate sense experience. Appealing only to these two kinds of differences, Hegel is able, in a tour de force of analysis and construction, to elaborate, on behalf of perceiving consciousness, a richly articulated structure of facts about the possession by particulars of sense-universals: objects with many observable properties. (We have seen in the last chapter how the discovery that implicit in the idea of observable properties differing in the two basic ways is the idea of objects as bearers of those properties, objects that are not observable in the same sense the properties are, leads on to a generalized notion of theoretical entities, including properties and indeed facts, which are only inferentially accessible.)

This order of explanation shows that for Hegel if there is a reciprocal sense-dependence relation between the notion of material incompatibility that applies to properties, hence facts, and is expressed in laws in the objective realm, and the notion that applies to classification by applying predicates, making claims and judgments, and explanatory inferences in the subjective realm of thought, then corresponding sense-dependences will hold at all of the levels retailed in the preceding table. The idea that there is such a sense-dependence does not make its first appearance with the discussion of the relation between law and explanation. Even though the experience of perceiving consciousness is conducted to the extent possible, in accord with the self-understanding of that form of empirical self-consciousness, at the level of what is perceived, the perceiving of it plays a substantial role even there. This is registered in the title of the chapter, “Die Wahrnehmung; oder das Ding, und die Täuschung.” “Täuschung” here is invoking the experience of error, which does not just come in here at the phenomenological level, as we follow the development of various versions of perceiving consciousness driven from one to the next by the inadequacy of the first.³ The experience of error is also an important element of perceiving consciousness’s own understanding. For what one must do in order thereby to count as taking or treating two properties as incompatible in the objective sense made explicit by alethic modal locutions is precisely to acknowledge the obligation, when one finds oneself committed to attributing those properties to one and the same object, of rejecting at least one of those commitments. One does that by treating those commitments as incompatible in the sense made explicit by deontic normative locutions: one cannot be entitled to both commitments.

[T]he one who is perceiving is aware of the possibility of deception [Täuschung].… His criterion of truth is therefore self-identity, and his behavior consists in apprehending the object as self-identical. Since at the same time diversity is explicitly there for him, it is a connection of the diverse moments of his apprehension to one another; but if a dissimilarity makes itself felt in the course of this comparison, then this is not an untruth of the object—for this is the self-identical—but an untruth in perceiving it.⁴ [PG 116]

An object perceived as having objectively incompatible properties is perceived as in so far such not self-identical. The diversity in question must be a matter of exclusive difference, contrary properties, not merely or indifferently different ones. Perceiving an object as diverse in that weak sense of having merely compatibly different properties is not perceiving it as “not self-identical.” Only perceiving incompatible properties triggers the experience of “untruth.” Already here Hegel is asserting the sense-dependence of the objective alethic modal sense of “incompatible” (“exclusive difference”) on the deontic normative one. Grasping the concept of objective modal incompatibility of properties is treating the corresponding commitments as incompatible in the deontic sense that normatively governs the activities of knowing subjects. There could be modal incompatibilities of properties or facts without deontic incompatibilities of commitments. The concept of the former is not reference-dependent on the concept of the latter. But one cannot in principle understand the sort of modal incompatibility that will be codified in laws unless one understands what it is appropriate to do when confronted with deontically incompatible commitments. And what one must do is respond to the experience of error by making an inference that explains it, by rejecting at least one of the claims. Objective incompatibility and the experience of error are reciprocally sense-dependent concepts. Because they are, so are the concepts articulated and elaborated in terms of determinate negation, as retailed in the table.

Hegel does not (and has no reason to) deny the reference-dependence of the subjective pragmatic and syntactic categories on the ontological or metaphysical ones. Apart from laws governing facts about the exhibition of universals by particulars there would be no activities of inferring, asserting, referring, or classifying, and no subjunctive conditionals, sentences, terms, or predicates. He does not, and has no reason to, assert the reference-dependence of the categories articulating the objective world on those articulating the practices of empirical subjects. The dependence of the objective on the subjective he is asserting is a sense-dependence relation. The objective world is understood as semantically mind-dependent, not causally or existentially mind-dependent. The latter extravagant and implausible view is a kind of subjective idealism sometimes extrapolated from Berkeley and sometimes libelously attributed to Fichte. Whatever the justice of those associations, there is nothing of the sort in Hegel.

If this reading avoids pinning on Hegel an obviously crazy sort of idealism, it might be thought to court the converse danger of washing out his idealism to a view that is, to use the term Robert Pippin has used in raising this worry, anodyne. How exciting is it to be told that in order to understand lawfulness, what is made explicit by alethic modal vocabulary, one must understand the use of such vocabulary, the distinctive inferential role played by subjunctively robust conditionals? After all, anyone who has the concept law of nature has already mastered the use of a fairly sophisticated vocabulary and so can, in fact, use subjunctive conditionals. Anyone who talks or thinks at all about objects and properties (not even, perhaps, using terms corresponding to “object” and “property,” but only to “Fido” and “furry”), facts or states of affairs, must use singular terms, predicates, and declarative sentences. Surely that much is not a philosophical discovery.

It should be remembered to begin with that I am not identifying the “absolute idealism” Hegel propounds in the Phenomenology with objective idealism. As indicated in the preceding, I am analyzing absolute idealism as comprising three component theses: conceptual realism, objective idealism, and conceptual idealism. To assess the interest of absolute idealism as so conceived one must look at it whole. We will not be in a position to understand the final component of Hegel’s idealism, conceptual idealism, until the end of Reason—discussed here in Chapter 12. Nonetheless, the question of whether adding objective idealism as a reciprocal sense-dependence thesis to conceptual realism represents a substantial conceptual and doctrinal advance, and if so why, is a legitimate one. It can be addressed precisely by thinking of what it adds to conceptual realism.

Conceptual realism is the thesis that the objective world, the world as it is in itself, no less than the realm of subjective activity that shapes what the world is for consciousness, is conceptually structured. John McDowell is endorsing conceptual realism in this sense when he says in Mind and World that “the conceptual has no outer boundary,” beyond which lies a nonconceptual reality. [MW 27, 34–46] As I have been reading him, Hegel’s version of this thought has a hylomorphic shape. Conceptual contents can show up in two different forms: an objective form and a subjective form. The first is a matter of how things are in themselves, the second how they are for consciousness. These are reality and its appearance, the noumena and the phenomena. Because both forms are conceptually articulated, and because the very same content can show up in both forms, “[w]hen we say, and mean, that such-and-such is the case, we—and our meaning—do not stop anywhere short of the fact; but we mean: this—is—so,” as Wittgenstein puts the point. [PI §95] This is how the Genuine Knowledge Condition is to be satisfied: the criterion of adequacy on semantic theories that requires they not rule out on conceptual grounds the possibility that what things are for consciousness can be what they are in themselves.

Hegel fills in this hylomorphic picture by offering a nonpsychological conception of the conceptual. According to this conception, to be conceptually contentful is to stand to other such contentful items in relations of material incompatibility and consequence (“determinate negation” and “mediation”). This definition is sufficiently abstract and generic that it need not appeal to what it is to grasp a conceptual content in order to say what such contents are. It invokes only very general relations among contents. For objective states of affairs, including facts, these are alethic modal relations of noncompossibility and necessity. They are expressed by statements of laws of nature: mammalian life is impossible at 1085°C, and copper necessarily melts at 1085°C. For subjective thinkings of conceptually contentful thinkables, these are deontic normative relations of entitlement and commitment. The claim that the mammal is alive is incompatible with the claim that its average temperature is 1085°C in the sense that one cannot be entitled to both commitments. And the claim that the temperature of the copper is above 1085°C commits one to the claim that it is not solid.

Objective idealism adds to this hylomorphic version of conceptual realism a thesis about the interdependence—in the sense of sense-dependence—of these two forms that conceptual contents can take: alethic modal and deontic normative, objective and subjective. In order to grasp the concept conceptual content, which can take the two forms, it turns out one must grasp those two forms in their inter(sense-)dependence. On my analysis, the objective idealist reciprocal sense-dependence thesis takes on its substantial and distinctive significance for Hegel in the context of the three other strategic commitments already mentioned: conceptual realism, an understanding of conceptual articulation as consisting in relations of material incompatibility and consequence, and the hylomorphic rendering of that latter view as a response to the requirement set by the Genuine Knowledge Condition. It is the latter that brings the intentional nexus into play, in the form of the relation between what things are in themselves and what they are for consciousness. Against this background, in asserting the reciprocal sense-dependence of the alethic modal metaconcepts we use to make explicit the conceptual structure of the objective pole (what things are in themselves) and the deontic normative metaconcepts we use to make explicit the conceptual structure of the subjective pole (what things are for consciousness), objective idealism marks a significant advance. For it provides additional clarification and substantial development of this hylomorphic form of conceptual realism. It tells us something important about the relations between the two different readings (alethic and deontic) of “incompatible” and “consequence”—namely, that one crucial such relation is reciprocal sense-dependence. For Hegel, the necessary relation between the two different alethic modal and deontic normative senses of “relations of material incompatibility and consequence”—the kind of unity-through-difference they stand in as forms of one kind of content—is just the intentional nexus: the relation between thought and what it is about, between sense and referent.

Objective idealism tells us we cannot understand the ontological structure of the objective world (its coming as law-governed facts about the properties of objects) except in terms that make essential reference to what subjects have to do in order to count as taking the world to have that structure—even though the world could have that structure in the absence of any subjects and their epistemic activities. The sort of unity-through-essential-difference that objective idealism attributes to conceptual contents by explaining how their objective (alethic nomological) and subjective (deontic normative) forms are related is fundamentally different from that grasped by understanding consciousness in its thought about force and its expression and force and law. Those both concerned only the objective pole of the intentional nexus: what is known or represented. Objective idealism concerns both poles, the relation between what things are objectively, or in themselves, and what they are subjectively, or for consciousness. And both of those conceptions of understanding consciousness concerned themselves with reference-dependence relations as well as sense-dependence relations. (That is part of what is wrong with reifying laws as superfacts. They are represented in a sense that is assimilated to the sense in which ordinary empirical facts—whether immediately observable or not—are represented.) So it is not the case that the relation of law to explanation and the distinctive kind of identity between its moments it involves should be thought of as modeled on those earlier relations and the kind of identity they involve. Rather, a kind of self-referential metaclaim is being made. It is only by understanding the kind of identity of content requiring diversity of form characteristic of the reciprocal sense-dependence of concepts articulating the structure of the objective represented world and concepts articulating the structure of the epistemic activity of representing subjects that one can understand the kind of identity constituted by the necessary relation of diverse moments characteristic of the objective pole of that intentional relation: the relation of force to its expression, the play of forces, and of both to the laws that govern them. (Or, of course, the subjective activity of epistemic subjects, but that direction in which the reciprocal sense-dependence can be exploited is hardly surprising or controversial.) That is the lesson of this experience of understanding consciousness.

There is one more aspect of the way the activity of explanation “traversing the moments” in inference bears on understanding the sort of objective law-governed holistic unity through necessarily related diverse components represented allegorically by the “play of forces” that should be noted. I take it that the use of “moment” throughout Hegel’s writings is itself motivated by the allegory of forces. It is of the essence of Newtonian physical analysis to represent the parabolic motion of a thrown object, for instance, as the vector produced by two forces (gravity and the throw) that are described as “moments” of the resulting motion. They are not self-standing “elements” that are bolted together to result in the parabolic motion, but components into which it useful to analyze the unity that is the motion, each equally operative at every point in the trajectory. The motion is the observable expression of the “play” of these forces. Hegel raises questions about how we are to understand this sort of holistic identity. I have described the move from force to law as a shift of attention from relata to the relations they stand in to one another. Once it is understood that each is what it is only in (meta)relation to the other—the law essentially governing these forces and the forces being what they are only as governed by this law—the question becomes how to understand the whole comprising the related relata without considering one or the other as antecedently identified and individuated.

The answer is to understand this structure as the objective relational correlate of the process of inferentially traversing the moments in explanation, as when the distance fallen by an object is calculated from the time elapsed since it was at rest, or the elapsed time from the distance covered. That epistemic inferential activity depends not only on actual commitments (initial boundary conditions), but also on the manipulation of terms, in thought, speech, or writing, that are immediately identifiable and individuated. The sign-designs involved in the statement of a law, say “d = k × t²,” are not holistically individuated. They are immediately perceptible and distinguishable. In virtue of the deontic role those signs play in inferences, how it is appropriate to manipulate them in explanation, they can be understood as standing for or expressing conceptual contents, which in virtue of the relations of material incompatibility and consequence they stand in, are holistically related to one another: different, but essentially and necessarily related. The intelligibility of the thoroughly mediated moments and the kind of relational unity they constitute essentially depends on the epistemic immediacy of the actual vehicles used in making statements and manipulating them in inferential moves. The distinctness of the necessarily related moments in the play of forces is sense-dependent on the immediately (observably) distinct vehicles that come to express conceptual contents by standing in normative subjunctively robust relations of deontic incompatibility and consequence that govern actual inferential activities of manipulating those vehicles in explanation.⁵

III. “Infinity” as Holism

The last five paragraphs of Force and the Understanding sketch the final shape of empirical consciousness conceiving itself as understanding, and the lessons we, the phenomenological consciousness, are to learn from the achievement of this form of phenomenal consciousness, as the culmination of the process of development of the others that have been rehearsed. The discussion is maddeningly compressed and telegraphic, both in its characterization of understanding conceiving itself under the concept of infinity, and in its account of how our understanding of that form of consciousness motivates turning our attention from consciousness to self-consciousness, in the sense of consciousness of ourselves as norm-governed beings. That is what motivates the first big expository transition in the book, from Consciousness to Self-Consciousness.

“Infinity” [Unendlichkeit] is Hegel’s term for a distinctive holistic structure of identity constituted by necessary relations among different “moments,” each of which is what it is only in virtue of its relations to the others and its being comprised by the whole it is a moment of. It is the final form of understanding consciousness. The alarming term “infinite” has mathematical connotations that are actively misleading (for us post-Cantorians), and theological ones that are largely unhelpful. It is probably best regarded, to begin with, as a merely suggestive label.

What is finite is what is limited, what has boundaries. The suggestion seems to be that insofar as the different “moments” comprised by a whole of the sort being considered are defined as what they are only by their relations to one another, there is a sense in which they lack boundaries. And insofar as the whole that comprises them is also defined by the internal relations among its “moments,” rather than by relation to anything external, it, too, is not defined by boundaries. So both the whole and the holistically related moments it comprises are not finite in the sense in which things as ordinarily conceived are. But to say this is more to gesture vaguely at a possible motive for choosing the term “infinite,” than to offer a satisfying explanation of what it means. Compare Hegel’s related term “absolute.” “Solvere” is Latin for “loosen.” What is absolute is indissoluble: its parts cannot be loosened from one another, so tightly and intimately bound up with each other are they. These are holistic metaphors.

The kind of holistic structure of identity and difference labeled “infinite,” we are told “has no doubt all along been the soul of all that has gone before.” [PG 163] That is, it is the fully adequate conception both of the actual conceptual structure of consciousness, of which all the shapes considered up to this point (under the rubrics of empirical consciousness conceiving of itself as sense certainty, as perceiving, and as understanding) are less adequate conceptions, and of the objective world as conceived by understanding consciousness.

The principal lesson we are to learn from the final experience of understanding consciousness is that the holistic structure of identity and difference that results from this progressive process of making explicit what is implicit in empirical consciousness (the structure Hegel calls “infinity”) is the structure of self-consciousness. It is the discovery that the key to understanding empirical consciousness lies in the norm-governed activities of self-consciousness that motivates for us the expository transition in Hegel’s narrative that takes us from the Consciousness chapters to the Self-Consciousness chapter.

It is true that consciousness of an “other,” of an object in general, is itself necessarily self-consciousness, a reflectedness-into-self, consciousness of itself in otherness. The necessary advance from the previous shapes of consciousness for which their truth was a Thing, an “other” than themselves, expresses just this, that not only is consciousness of a thing only possible for a self-consciousness, but that self-consciousness alone is the truth of those shapes. [PG 163]

There are three claims here. Each of the “shapes of consciousness” considered up to this point, including the final one, is a conception of, a way of understanding, empirical consciousness. As such, they are forms of self-consciousness: ways of being conscious of consciousness. Further, “consciousness of a thing is possible only for a self-consciousness.” That is, any empirical consciousness must have some such “shape.” For it must be aware of the distinction between what to it things are in themselves and what to it they are for consciousness.⁶ It is taught that by the experience of error. That aspect of consciousness incorporates a conception of consciousness, and hence constitutes a form of self-consciousness. This much of Hegel’s picture was already on offer in the Introduction. What is new is a third claim, that self-consciousness is the “truth” of all forms of empirical consciousness of an objective world.

Empirical consciousness understanding itself under the concept of infinity understands consciousness as

consciousness of a difference that is no less immediately cancelled … it is a distinguishing of that which contains no difference, or self-consciousness. I distinguish myself from myself, and in doing so I am directly aware that what is distinguished from myself is not different [from me]. I, the selfsame being, repel myself from myself; but what is posited as distinct from me, or as unlike me is immediately, in being so distinguished, not a distinction for me. [PG 164]

The only feature of self-consciousness that is being invoked as that on which consciousness is now modeled is that the distinction the latter involves, between consciousness and what it is consciousness of, is a difference that essentially involves assimilating the distinguished items, as the self that is self-conscious is both nominally distinguished from and also necessarily identified with the self of which it is conscious. The functions of self as subject of self-consciousness and self as object of self-consciousness can be distinguished, as for instance, when we say, or Hegel says, of a less than fully self-conscious subject that there are features of the object of self-consciousness of which the self-conscious subject is not aware. That is compatible with nonetheless claiming that the two selves are identical. (After all, the morning star is the evening star.) The task of understanding these passages is accordingly a matter of understanding what sort of identity-in-and-through-difference empirical consciousness understanding itself as infinite takes to characterize the intentional nexus: the distinction that (as we were reminded already at the beginning of the Introduction) consciousness essentially involves, between what things are in themselves and what they are for consciousness.

What sort of assimilation of the two distinguished elements, one on the side of the objective world, the other on the side of subjective activity, is it that consciousness conceiving itself as having the structure Hegel calls “infinity” performs, which Hegel is telling us amounts to taking the two to be two ways of regarding one thing, as the self that is self-conscious and the self of which it is conscious are one self? Two sorts of assimilation are already on the table: conceptual realism and objective idealism. Conceptual realism says that what things are in themselves, no less than what things are for consciousness, is always already in conceptual shape. So when he says that in its final form “the Understanding experiences only itself,” [PG 165] Hegel could mean just that what is to it what things are in themselves is already in conceptual shape, just as its thoughts are. I think this is indeed part of what is meant. But only part of it. Objective idealism says that the concepts articulating what is to understanding consciousness what things are in themselves and the concepts articulating what is to it what things are for consciousness are reciprocally sense-dependent. One consequence of the objective idealist thesis is that a necessary condition of understanding the ontological structure of the objective world empirical consciousness is consciousness of is that one must also understand the epistemic activities by which consciousness becomes conscious of it. That (like the conceptual realist thesis) is certainly a sense in which, in experiencing the world, “Understanding experiences itself.” It was just pointed out that conceptual realism also offers a sense in which “Understanding experiences only itself”: it experiences only conceptual contentful states of affairs, whose content can also be the content of thoughts. Objective idealism then adds the claim that the metaphysical categorial structure of the objective world (for instance, that it takes the form of facts related by laws) cannot be understood apart from understanding what consciousness does in understanding it. The paradigm of what understanding consciousness does is “traversing the moments” in explaining.

The argument of the closing passages of Force and Understanding has three phases. It starts with a characterization of the lessons to be learned from consideration of the final form of the supersensible world understanding takes itself to confront: the inverted world. The second phase consists of remarks about the holistic structure of identity in and through difference that Hegel calls “infinity.” The concluding phase is the claim that we can see (though it cannot yet) that in conceiving its object on the model of such an infinite structure, phenomenal understanding consciousness has put itself in a position to recognize itself in its object—that it has actually become a form of consciousness that does not merely presuppose self-consciousness, but is, to itself, but not explicitly for itself, a form of consciousness as self-consciousness.

Specifying the exact register of the state of understanding (self-)consciousness is a delicate matter. I would put it like this: Infinity has been “no doubt all along the soul of all that has gone before,” [PG 163] in-itself. Consciousness, however it understands itself (as sensuous certainty, as perceiving, as understanding), has no doubt always been self-consciousness, in the sense we finally come to understand it. None of the forms of (self-)consciousness considered in Consciousness, including the final form of understanding consciousness, which takes its object to be infinite, recognizes itself in its object and so is for itself self-consciousness in the sense Hegel tells us we can recognize consciousness as being. But the self-conception of that final form of understanding consciousness is self-consciousness not only in itself, but also to itself, even though that is not what that conception is for understanding consciousness. That is to say that it must implicitly take or treat itself as self-consciousness, by something it practically does, even though that implicit, practical self-understanding is not explicitly thematized. The task of understanding these crucial, gnomic passages is accordingly the task of understanding the three lessons being taught first about the inverted world as the final form of supersensible world, second about infinity, and third about consciousness being in a position implicitly to recognize itself in its object, as well as the rationales that move us from one to the other of these three thoughts.

Here is the first thought, leading into the second:

From the idea, then, of inversion, which constitutes the essential nature of one aspect of the supersensible world, we must eliminate the sensuous idea [Vorstellung] of fixing the differences in a different sustaining element; and this absolute Notion of the difference must be presented and understood [darstellen und auffassen] purely as inner difference.…

Certainly, I put the “opposite” here, and the “other” of which it is the opposite there; the “opposite,” then, is on one side, is in and for itself without the “other.” But just because I have the “opposite” here in and for itself, it is the opposite of itself, or it has, in fact, the “other” immediately present in it. Thus the supersensible world, which is the inverted world, has at the same time overarched [übergriffen] the other world and has it within it; it is for itself the inverted world, i.e. the inversion of itself; it is itself and its opposite in one unity. Only thus is it difference as inner difference, or difference in its own self, or difference as an infinity. [PG 160]⁷

What is wrong with the inverted world [verkehrte Welt] is not the inversion, but the reification of it into a world—just as what was wrong with the conception of a supersensible “calm realm of laws” was the reification of laws into superfacts. In that case the mistake was to assimilate statements of laws to ordinary empirical statements, taking the former to represent something in the same sense in which the latter represent facts. The representational semantic paradigm of representings and represented (the name “Fido” and the dog Fido) is extended beyond ground-level empirical (but not necessarily observable) statements and states of affairs to include modal statements of necessity in the form of laws or of impossibility and necessity in the case of the inverted world. The difference between the two cases is diagnosed as a difference in the kind of state of affairs that is represented. This is what Hegel means by the “sensuous representation fixing the differences in a different sustaining element.” The supersensible worlds are thought of as worlds that are just like the world of empirical facts—only supersensible. Merely possible states of affairs (worlds) are thought of as just like the actual world—only merely possible. (Compare the boggling Cartesian response to Leibniz’s idea of “petites perceptions,” described as just like Cartesian episodes of conscious awareness—except “inconscient.”⁸ As though anything at all is left of a Cartesian pensée when awareness of it is subtracted.) The inverted world is the result of inverting a world. But the result of that is not a world. It is the world—the actual world, the only world, which is partly supersensible—as inverted. “Inverting” the world is explicitly including in it the subjunctively robust relations of material incompatibility and consequence that properties and states of affairs must stand in to other properties and states of affairs in order to be the determinate properties and states of affairs they are—to have the conceptual contents they do. Hegel is here laying down a marker: we are not to understand the relation of those concept-articulating relations and relata to the actual world on the model of representation, but on the model of expression. They are in a sense yet to be specified implicit in the actual properties and states of affairs. We will eventually come to understand how representation and expression are two sides of one coin, two aspects of subjects’ relations to the objective world they know about and act on and in that both are established by and show up for consciousness in the course of the process that is its recollective rational reconstruction of its empirical experience. That lesson lies far ahead of us at this point in Hegel’s text. What we are given here is a quick sketch, the rendering of some outlines to be filled in and color added later.

IV. Expressivism, Objective Idealism, and Normative Self-Consciousness

Hegel’s discussion of the inverted world turns on diagnosing the mistake that Sellars calls “descriptivism.”⁹

[O]nce the tautology “The world is described by descriptive concepts” is freed from the idea that the business of all non-logical concepts is to describe, the way is clear to an ungrudging recognition that many expressions which empiricists have relegated to second-class citizenship in discourse are not inferior, just different. [CDCM §79]

To be a descriptivist about a vocabulary or kind of discourse is to take its characteristic expressive role to be describing (representing) how things are. One should, of course, be a descriptivist about descriptive discourse. Hegel is rejecting descriptivism, or representationalism, for alethic modal discourse (which, as we have seen, is the approach characteristic of contemporary possible-worlds metaphysics for semantics).

The alternative he is recommending in place of descriptivism is a kind of expressivism. The image Hegel is working with in the preceding passage is that instead of picturing the exclusive contrasts in virtue of which actual states of affairs are the determinate states of affairs they are as further states of affairs, separated from the actual by being across some ontological boundary (“jenseits”), we picture them as within the actual, as implicit in it. Alethic modal statements, about what is impossible (incompatible) or necessary express explicitly something that is implicit in ordinary descriptive statements about actuality. Part of what it is to be copper, a necessary feature of copper, is to be an electrical conductor. That excludes the possibility of being an electrical insulator. Those modal features of copper are internal to it, implicit in something’s being copper. Thinking of them as facts about another world, a shadow world over and above the actual world is mislocating them. Modal claims, it is true, do not simply describe the actual. (Laws are not superfacts.) But that is not because they describe something else. What we are doing in making modal claims is something other than describing. We are making explicit something that is implicit in applying ordinary, ground-level concepts to describe how things actually are. Modal statements express the exclusive differences in virtue of which any actual state of affairs is the state of affairs it is. They articulate the conditions of determinate conceptual contentfulness of the ordinary empirical concepts deployed in description and explanation.

Another aspect of the point Hegel is making, and of the antidescriptivism Sellars is recommending, is precisely an insight about the intimate relations between description and explanation. Sellars puts it like this:

Although describing and explaining (predicting, retrodicting, understanding) are distinguishable, they are also, in an important sense, inseparable. It is only because the expressions in terms of which we describe objects, even such basic expressions as words for perceptible characteristics of molar objects, locate these objects in a space of implications, that they describe at all, rather than merely label. The descriptive and explanatory resources of language advance hand in hand. [CDCM §108]

The subjunctively robust inferential relations between descriptions (the “space of implications”) exploited in explanation (“traversing the moments”) are semantically essential to the descriptions being the descriptions they are, having the content they do. One misunderstands the intimate relation between describing and explaining if one assimilates explaining to describing. That is the descriptivist mistake. It is an intelligible mistake precisely because description and explanation are inseparably intertwined. Hegel is promising an account of their relation that takes a different, nonrepresentational, expressive shape. The final sentences of the long Hegel passage quoted in the previous section say that understanding the sense in which the content-determining exclusive differences are implicit in and constitutive of the determinate identity of any describable thing or state of affairs will be understanding the structure he is calling “infinity.” That structure is the model for a nondescriptivist expressivist semantics that encompasses representational structure but is more comprehensive, extending to the use of concepts whose principal expressive role is not to describe how things are.

We will have all the raw materials needed to understand Hegel’s recollective expressivism only by the end of Part Two of this work, after discussing the Reason section of the Phenomenology in Chapters 11 and 12. At that point the third element of Hegel’s pragmatist form of idealism, the conceptual idealism that builds on but extends beyond conceptual realism and objective idealism, will be on the table. It is based on a notion of recollection that we first got a glimpse of in discussing Hegel’s Introduction. Recollection is the final phase of episodes of experience, which begin with the detection of anomalies, in the form of acknowledgment of the incompatibility of commitments. As part of the “emergence of the second, new, true object,” the endorsements that result from the reparative phase of experience must be recollectively vindicated. To do that, one must retrospectively rationally reconstruct the course of experience from which they emerged, exhibiting it as expressively progressive: as the gradual, cumulative becoming (more) explicit of what then shows up as having been implicit all along, in the form of a norm governing and guiding the process of experience. Hegel thinks that we should understand what is implicit in terms of the process of expressing it: the process of making what is implicit explicit. That process is recollection. Hegel ends the Consciousness chapters by foreshadowing and advertising the account of expression in terms of recollection that will eventually provide cash for his gesture at an expressive alternative to reifying representational ways of understanding the modal relations that articulate conceptual content, in both its objective and its subjective forms, as well as the relations between them. It is only at the end of Hegel’s story, when we understand Hegel’s account of representation in terms of expression, and the expressive relation between what is implicit and what is explicit in terms of recollection, that we will be in a position to appreciate all of the dimensions of the holistic conception of identity constituted by difference that he here labels “infinity.”

But it is possible to say a bit more at this point about some of the clues we are given at the end of Force and Understanding. A first step toward understanding the expressivism Hegel is recommending is noting that it is a version of Kant’s fundamental claim that some concepts—paradigmatically those expressed by alethic modal vocabulary in subjunctively robust conditionals such as those underwritten by laws—have as their principal expressive role not empirical description but making explicit features of the framework that makes empirical description possible. That framework includes the in-principle availability of descriptions to figure in explanations appealing to counterfactual-supporting laws. Because every empirical description presupposes what those concepts express, Kant says they must be knowable a priori—that is, in a way that does not depend on knowing whether any particular empirical description actually applies to something. They are his categories. In Hegel’s version, empirically describable states of affairs (possible and actual) are intelligible as determinate only insofar as they stand in relations of material incompatibility and consequence (“determinate negation” and “mediation”) to one another. Those content-conferring relations are what are expressed explicitly by statements of law and of the relations articulating what is misunderstood as the inverted world. So they play that framework-explicating nondescriptive expressive role that Kant discovered (even though Hegel’s account of the nature and significance of that discovery is different from Kant’s).¹⁰

A further step toward understanding how Hegel’s notion of infinity differs from the Kantian idea on which it is built shows up in this passage (already cited earlier in a different context):

Infinity, or this absolute unrest of pure self-movement, in which whatever is determined in one way or another, e.g. as being, is rather the opposite of that determinateness, this no doubt has been all along the soul of all that has gone before … but it is as “explanation” that it first freely stands forth. [PG 163]

I have referred to infinity as a “structure,” and in the broadest sense I think that is appropriate. But it is correct only if the term is not restricted to something static. This key claim is that infinity can be understood only in terms of the movement of understanding consciousness, something it does, which first shows up as “traversing the moments” inferentially in explanation. Statements of necessary lawful consequence and expressions of exclusive difference as noncompossibility play their distinctive role in expressing norms governing these explanatory movements of the understanding. In this game, empirical descriptions specify positions, while modal statements of necessity and possibility constrain moves. The reifying descriptivist mistake Hegel diagnoses in the last two conceptions of supersensible worlds, the realm of laws and the inverted world, is to think of specifications of the moves on the representational model of specifications of further positions—which then must be thought of as positions of a special kind. Thought of this way, the mistake Hegel is diagnosing belongs in a box with that made by the Tortoise in Lewis Carroll’s “Achilles and the Tortoise”: treating rules in accordance with which to reason as though they were premises from which to reason.¹¹

This is the lesson Hegel draws for us from consideration of the reifying “two worlds” views, which treat the consequences and incompatibilities as more determinate things, like those described by empirical statements of fact, just things located “jenseits,” in a kind of supersensible world, whether the calm realm of laws or the inverted world. The mistaken line of thought behind these conceptions begins with the idea that the facts about which objects exhibit which properties are modally insulated—in that sense, extensional. This is the thought that they are intelligible as the determinate facts they are independently of what else might, or must, or cannot be true. Statements expressing those additional modal relations are then construed as descriptive, fact-stating statements, generically like the ordinary ground-level empirical descriptive claims that state how things merely are. It is just that they describe a specifically different kind of world, state a different kind of fact. The proper conception, Hegel tells us, is rather one in which the conceptual articulation of objective facts, made explicit in statements of necessary consequence and noncompossibility, is implicit in the objective determinate facts described by ground-level empirical statements of how things are.

The crucial insight Hegel is offering, as I read him, is that all objective empirical properties (a class we have learned is not to be taken to be restricted to observable properties) are modally involved. Asserting that they obtain always essentially involves committing oneself to subjunctive consequences, to what would, could, and could not happen if other states of affairs were to obtain. The culprit here is the idea that there is a distinction between modally insulated and modally involved properties, and further that the former are antecedently intelligible independently of the latter. This is the fundamental idea on which the Tarski-Quine extensional order of semantic explanation is based, and through it, the Lewis-Stalnaker possible-worlds picture of modality built on it. This is what Hegel is prophetically, if proleptically criticizing under the rubric of the “inverted world.” It is this conception I used in Chapter 6 as the starting point of the recollective sketch of an expressively progressive development from a Tarskian order of semantic explanation through a Fregean one to the Hegelian—counterchronological though this rational reconstruction is.

Understanding consciousness conceiving itself and its object as having the structure Hegel calls “infinity” has won through by its metalevel experience (as Hegel recollects it for us) to the realization that objective facts are conceptually structured. They and the properties they involve are determinate only insofar as they stand in a holistic structure of modal relations of necessary consequence and incompatibility to each other and to other possible states of affairs and properties. All properties are modally involved because being determinate is incompatible with being modally insulated. It is in this sense that the alethic modal relations made explicit by statements of laws are implicit in the objective facts, whatever they are. On Hegel’s hylomorphic conception of conceptual content, this same structure visible in the objective pole of the objects of knowledge is mirrored on the deontic side of the subjects of knowledge. Doxastic commitments as to how things really, objectively, are have the determinate conceptual contents they do only in virtue of being articulated by commitments to the goodness of subjunctively robust material inferential relations and relations of material incompatibility. On the side of the cognitive activity of subjects, these are deontic normative relations: norms according to which a commitment with one content necessarily commits one to endorsing other contents that follow from it, and precludes one from entitlement to still others. In each case the modal relations of consequence and incompatibility, whether alethic or deontic, are to be understood as implicit in, as conceptually articulating, the contents of thinkables, both facts and judgments. Both forms that conceptual content can take, the objective form made explicit by alethic modal vocabulary and the subjective made explicit by deontic normative vocabulary, exhibit the holistic structure Hegel calls “infinite.”

We have seen that this bimodal hylomorphic conceptual realism is explicated further by the claims of objective idealism. It asserts the reciprocal sense-dependence of concepts expressing the ontological structure of objective reality, concepts such as object, property, fact, and law, on the one hand, and concepts expressing framework-constituting features of norm-governed discursive activities, practices, or processes, such as referring, classifying, asserting, and inferring, on the other hand. The Perception chapter explains the sense in which relations of material incompatibility and consequence must be thought of as implicit in taking the objective world to consist of facts about properties characterizing objects, and the Force and Understanding chapter does the same for a broadened conception of facts and the subjunctively robust consequential and incompatibility relations implicit in them.

To understand the sense in which the modal articulation of the objective empirical world is not to be understood to be something alongside the actual world (even in a universe of merely possible worlds) but as something within it, something implicit in it, then, we must focus on the process that Hegel calls the “movement of the understanding,” which is explaining. For engaging in the process of explaining exploits and so practically acknowledges the implicit articulation of empirical concepts by modal relations of necessitation and preclusion. That broadly inferential activity is essentially norm-governed. Offering some claims as reasons for or against others is appealing to norms that settle what claims entitle and commit us to which others, and which further claims they preclude us from being entitled to. To understand what we are saying about the objective world when we say that it consists of facts standing in lawful relations to one another, we must understand our cognitive practices, what we are doing in judging and reasoning (describing and explaining, taking up a position and making a move).

The progressive evolution of empirical consciousness conceiving itself as understanding that Hegel has rationally reconstructed and rehearsed for us has brought it to this objective idealist insight. When consciousness conceiving itself as understanding realizes that, when it achieves the conception of objective idealism, it achieves a new kind of self-consciousness. It is aware that, to understand the structure of the objective world, it must understand our own discursive activities. This is the third sense in which consciousness presupposes self-consciousness.

As readers following Hegel’s rational reconstruction of the progressive development of empirical self-consciousness, we realize something that the understanding self-consciousness does not. Bimodal hylomorphic conceptual realism tells us that in order to understand ourselves as describing and explaining, we will have to understand what is made explicit by normative vocabulary. The activity of explaining empirical goings-on is an essentially norm-governed activity. Explaining, inferring, asserting, describing, referring, and predicating all involve both the exercise of authority and the undertaking of responsibility. The positions empirical consciousness takes up in judging or describing are normative stances: commitments. The moves empirical consciousness takes up in inferring or explaining (which functionally, and therefore holistically, confer contents on the positions) are normative moves: they are subject to normative assessment as moves the subject is entitled or committed to, according to standards set by what is a reason for and against what. So to follow out the lesson of understanding consciousness’s aspiration to understand itself as a knower and describer, hence as a reasoner and explainer, we see (though it does not) that we must come to understand it as a normative subject: the subject of normative statuses.

It is the achievement of this sort of self-consciousness by the phenomenal consciousness being considered that provides the rationale for us, the phenomenological consciousness looking at it from a metaconceptual level, to turn our attention to understanding normativity and the kinds of selves or subjects who live and move and have their being in a normative space of authority and responsibility. This is shifting focus to the subjective, deontic normative practices that complement the objective, alethic modal relations, according to both bimodal hylomorphic conceptual realism and objective idealism. It is why Hegel’s book moves from considering knowing from the side of what is known to considering it from the side of the knowers, from Consciousness to Self-Consciousness.

Chapter 7

Objective Idealism and Modal Expressivism

I. Explanation and the Expression of Implicit Laws

II. Objective Idealism

III. “Infinity” as Holism

IV. Expressivism, Objective Idealism, and Normative Self-Consciousness