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 non-logical, 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 is 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) don’t 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, and 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, isde 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 latecoming.
A particularly extreme version of the extensionalist order of explanation is that of the Tractatus. Not only does it not build modality into its modal primitives, it offers only the most attenuated version of it, 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, 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 meaning one cannot be B’s father. 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 mentioned above, 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.
Grafting on at the end substantive 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. Besides 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).
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 difference involves three distinct moves. Each one involves adding to the picture a further kind of difference, 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 difference, 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 onto” 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 that would be expressed by ‘then1’ stands to what would be expressed by ‘now1’, that is, as an anaphoric repeatable “holding onto” 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 ‘therei-and-thenj’s that are holdings-onto what would be expressed by any ‘herei-and-nowj’. 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 case we can see that the same anaphorically extended structure relating unrepeatable indexical or demonstrative experiencings plays the role of a unit of account excluding 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 repeatability structures they initiate.
So from the fact that what would be expressed by different ‘now’s can exhibit incompatible features 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 difference (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.”
One of Kant’s innovations is his introduction of Newtonian spatio-temporal identification and individuation of empirical objects, as a replacement of the traditional Aristotelian identification and individuation of individual substances through their essences and accidents. In the transition from the discussion of sensory consciousness understanding itself as sense certainty (immediate demonstrative awareness of sensible features) to sensory consciousness understanding itself as perception (sensory awareness of empirical objects with observable properties), Hegel is forging a conceptual link between Kantian-Newtonian spatiotemporal identification and individuation and the aristotelian structure of objects-and-properties (particulars-and-universals).
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.
Understanding functional units of accounts 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.31 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’.32 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 difference 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 [Entgegengesetzung] 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.33
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,
This 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.34
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.35
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-now’s, 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 turned 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.36
These different but complementary roles reflect, within this ontological category, the distinction between compatible and incompatible differences, within the ontological category of properties.
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:
...these 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.37
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.38 The corresponding notion of an opposite in the ontological category of objects would have object b being the contradictory of object ajust 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 chart above 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 difference 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 passage above 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 Hegels: from (ur)properties to objects—reversing the extensionalist Tarskian order of explanation. In virtue of their role as hosting co-compatible properties, objects as ‘also’s merely differ from one another insofar as they host different sets of co-compatible properties. In virtue of their role as excluding properties incompatible with those they host, objects as “excluding one”s exclude one another insofar as some of the co-compatible properties exhibited by one are incompatible with some of the co-compatible 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. 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.39 How do these principle 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 above.
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 non-identicals 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. 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. 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 and 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.
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.40
As it has turned out…it is merely the character of positive universality which is at first observed and developed.41
Only perception contains negation.42
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.43
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.44
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…45
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 called “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 another occasion.
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:
…the thing as the truth of perception reaches its culmination to the extent that it is necessary to develop that here. It is
) the indifferent passive universality, the also of the many properties, or, rather, matters.
ß) the negation generally as simple, that is, the one, the excluding of contrasted properties, and
) 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.46
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 difference. We began by distinguishing
mere or “indifferent” [gleichgültig] difference of compatible universals
exclusive difference of incompatible universals.
This brought into view the
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, since 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, two species that can be related by two opposing orders of explanation:
material contrariety, corresponding to determinate negation,
formal contradictoriness, corresponding to abstract logical negation.
There is then also the
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
difference between universals and particulars.
This is the the first intercategorial difference. It, too, is a kind of exclusive difference.
Implicit in the concept of particulars in relation to universals is the
difference between two roles they 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 stronglycompatibly different roles, since every particular not only can but must play both.
Corresponding to this difference on the side of particulars is the
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
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 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 list above. 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. Since 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.
This is the structure I take it that Hegel elaborates from the requirement of determinateness of the repeatable features characteristic of empirical consciousness understanding itself a 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 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.47
This means that
His criterion of truth is therefore self-identity, and his behavior consists in apprehending the object as self-identical.48
The trouble is that diversity (dissimilarity, diversity of moments) is also explicitly a feature of the content of sense perception as determinate.49 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 so long as empirical consciousness understanding itself according to the categories of perception seeks to its experience as exhibiting independent principles of unity and disparity (“these empty abstractons of a ‘singleness’ and a ‘universality’ opposed to it”50) that are somehow bolted together to yield a conception of the multifarious kinds of identity-through-difference (“ ‘being-for-self’ burdened with opposition”51) we have seen 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).
Since those sorts of unities are not intelligible according 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.52 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 form ourselves, and they fall asunder this way for us because the eye is quite distinct from the tongue…53
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 strategem cannot rescue perceiving consciousness’ 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,”54 the “diverse aspects for which consciousness accepts responsibility,” are still “specifically determined. White is white only in opposition to black….”55 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.56
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.”57 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 above 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 called 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.58
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.59
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
From 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.’60
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…61
When fully articulated, the result is the complex structure of particulars and universals involving ten different sorts of negation or difference expounded in sections V and VI above. 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 Conciousness section of the Phenomenology, called “Force and Understanding.”
A Spirit of Trust: A Semantic Reading of Hegel’s Phenomenology