One, Many, Same, Different

Book Iota (X) of Aristotle’s Metaphysics extends the discussion in book Delta (V) of things said in many ways, going into detail on what makes things one, many, the same, or different. These are extremely important matters for any sound reasoning, though somewhat technical in nature. It also contains Aristotle’s sharp critique of the saying of Protagoras, “Man is the measure of all things”.

“[T]here are four senses in which something is said to be one primarily and in its own right, rather than incidentally” (ch.1, p. 185).

As to the first, “oneness belongs to what is continuous, either simply or, especially, by nature, and not by contact or a binding cord (and of these that is more so one and is more primary of which the motion is more indivisible and simple)” (ibid).

Continuity in a material is the lowest degree of something being one in its own right. That which is materially united by contact or by any artificial means would not be one in its own right.

As to the second, “[oneness] belongs still more to what is whole and has some form and look, especially if something is of that sort by nature and not by force, as those things are that are so by means of glue or bolts or being tied with a cord, but rather has in itself that which is responsible for its being continuous. And something is of this sort if its motion is one and indivisible in place and time; and so it is clear that, if something that has a source of motion that moves it in the primary kind of the primary class of motions (by which I mean a circular type of change of place), this is one magnitude in the primary sense” (ibid).

Being a whole is a higher degree of unity than being materially continuous. The association of circular motion with a strong unity is relevant to the upcoming argument in book Lambda (XII) about the first cause.

“So some things are one in this way, insofar as they are continuous or whole, but others are one because the articulation of them is one, and of this sort are those things of which the thinking is one, and this in turn is of this sort if it is indivisible, and an act of thinking is indivisible if it is of something indivisible in form or in number” (ibid, emphasis added).

As to the third, “a particular thing is one by being indivisible in number” (ibid, emphasis added).

These would include all the independent and non-independent things that were extensively discussed in book Zeta (VII).

He continues, “but that which is one by means of intelligibility and knowledge is indivisible in form, so [fourth] what is responsible for the oneness of independent things would be one in the primary sense” (ibid, emphasis added).

I expect that this last kind will turn out to be the first cause.

“But it is necessary to notice that one must not take the sorts of things that are spoken of as one as being meant in the same way as what it is to be one, or what the articulation of it is” (p. 186).

This is analogous to the distinction between saying something about something in general, and saying what something is, also discussed in book Zeta. He illustrates this below, with the example of fire.

“The same thing would also be the case with ‘element’ and ’cause’, if one had to speak about them, distinguishing the things to which the words are applied, and giving a definition of the words. For there is a sense in which fire is an element… and a sense in which it is not; for being fire is not the same thing as being an element…. And it is that way also with ’cause’ and ‘one’ and all such things, and this is why being one is being indivisible, just exactly what it is to be a this, separate on its own in either place or form or thinking, or to be both whole and indivisible, but especially to be the primary measure of each class of things, and, in the most governing sense, of the class of things with quantity, for it has come from there to apply to other things” (ibid).

Being one in the third sense above (being a particular thing) is now said to be “just exactly what it is to be a this“. This foreshadows an extensive one-to-one mapping he will develop below, between all the ways of the saying of being he elaborates in book Delta (V), and the ways of the saying of oneness.

He goes on to speak at some length about measures, which we would call units of measurement.

The most important point is that “a measure is always the same kind of thing as what it measures, for the measure of magnitudes is a magnitude, and in particular, that of length is a length, of breadth a breadth, of spoken sounds a spoken sound, of weight a weight, and of numerical units a numerical unit” (p. 188, emphasis added).

The distinction he makes here tracks perfectly with the way that different types, dimensions, and variables are handled separately in the operations defined by modern mathematics.

“And we speak of knowledge or sense perception as a measure of things for the same reason, because we recognize something by means of them, although they are measured more than they measure” (ibid).

The simultaneously humorous and serious caveat that “they are measured more than they measure” means that knowledge and perception are constrained by reality. More precisely, they are involved in mutual dependencies with the realities of things that they at once measure and are measured by.

“And Protagoras says a human being is the measure of all things, as if he were saying that a knower or perceiver were the measure, and these because the one has knowledge and the other perception, which we say are the measures of their objects. So while saying nothing, these people appear to be saying something extraordinary” (ibid).

Aristotle, at the end of his discussion of measure (longer and more detailed than included here), refers to Protagoras’ famous saying, commonly quoted as “Man is the measure of all things”. With uncharacteristic sharpness, he calls this “saying nothing”. Why? This seems worthy of a short digression.

Protagoras was a prominent Sophist, who appears in Plato’s dialogue of the same name. He wrote a controversial treatise entitled Truth, which began with the sentence, “Of all things the measure is man: of those that are, that they are; and of those that are not, that they are not”. Plato and Aristotle both took Protagoras to be asserting a kind of individualist relativism. Reportedly, the skeptic Sextus Empiricus also read him this way. Plato took him to deny any objective reality. Aristotle in book Gamma (IV) shows rare outrage at his other reported claim that “it is not possible to contradict”. I didn’t mention him by name in my account, but Aristotle names him there as well.

Aristotle implies it is a bit more plausible to much more specifically say that knowledge and perception are measures of things, but even that only with the caveat that really “they are measured more than they measure”.

But why go on to add with such sharpness that Protagoras is “saying nothing”? I suspect the answer may lie with the other part of Aristotle’s interpretation: “as if he were saying that a knower or perceiver were the measure, and these because the one has knowledge and the other perception”.

I’m inclined to think Aristotle would regard it as outrageous to transfer what may (ambiguously) be said of specific knowledge and perception, to an unqualified saying about one who is said to possess knowledge and perception in general.

Aristotle has just given an account of what a measure is, that it must be of the same kind as the things that it measures. How could one thing (“man”) possibly be the measure of countless things that have no common measure? That does sound like nonsense. Any measure has to be of one kind or another. Modern mathematics agrees that kinds, dimensions, variables can only be collapsed together if very specific criteria are met.

What Aristotle emphasizes here about knowledge and perception — that they have a remarkable involvement with things that also measure them — seems very consistent with his general views. But the way Protagoras implicitly presents “man” as their possessor makes the possessor stand apart from the mutual involvement with things that Aristotle emphasizes, in which knowledge and perception and things measure one another. In splendid isolation from all constraints of real measure, the possessor seems to have arbitrary freedom to claim whatever she wishes.

I intuitively associate Protagoras with the attitude that what’s true for you is true for you, but what’s true for me is true for me, so don’t tell me I’m wrong, and I won’t tell you you’re wrong! Then and now, such sentiments had and have a superficial appeal, because they seem to express a live-and-let-live attitude, which seems to be a good thing. But the way it is expressed, in fact it completely undermines any possibility of meaningful dialogue, which undermines reason itself, which undermines the very thing that makes us human.

Back to the text, Aristotle turns to illustrating the one-to-one mapping I mentioned between sayings about being and sayings about oneness.

“[S]ince not even being itself is an independent thing as though it were some one thing capable of having being apart from the many beings (since it is common to them), other than solely as a thing attributed to them, it is clear that oneness is not a universal either” (ch. 2, p. 189).

For Aristotle, neither Being nor the One is an independent thing in its own right. He will nonetheless argue in book Lambda (XII) that there is a first cause for all things.

“What’s more, what is true about oneness must hold true in a similar way for all things; and being and oneness are meant in equally many ways” (ibid).

“And the same account applies also to the other classes of things, … and [if] in all instances it is the case both that the number is a number of something and that oneness is some particular one thing, and oneness itself is not the thinghood of it, then it must also be the same way with independent things” (p. 190).

“[S]o too in thinghood, one independent thing is oneness itself; and that oneness in a certain way means the same thing as being, is clear from the fact that it follows along equally through the ways being is attributed, and is not any one of them (for instance, it is not what anything is, nor of-what-sort anything is, but stands similarly toward them just as being does), and from the fact that no other thing is predicated in ‘one human being’ over and above what is predicated in ‘human being’ (just as being is not something over and above what and of-what-sort and how-much a thing is), or in ‘being one’ over and above being any particular thing” (ibid).

Saying something is one human being is the same as saying it is a human being. In book Zeta, he analogously said that “good” and “being good” are the same.

Things are often one in one respect, but many in another. The one and the many are “contraries, and not opposed as contradictories or as what are called relative terms” (ch. 3, p. 190). Next he turns to the meanings of same, other, and different.

“Since the same is meant in more than one way, in one way we sometimes speak of what is the same in number, but we say it in another sense if things are one in meaning as well as in number, as you are one with yourself in both form and material, and in another again if the articulation of the primary thinghood of things is one, for instance in the way equal straight lines are the same, … but in these equality is oneness” (p. 191).

In Fregean terms, things are what Aristotle calls one in number when they have the same reference. They are what Aristotle calls one in meaning when they have the same sense. Frege illustrates how they differ by saying that the morning star and the evening star have the same reference, but different sense.

“Things are alike if, not being simply the same, nor without difference in their composite thinghood, they are the same in form, just as a larger square is like a smaller one…. Other things are alike if they have the same form, and have it in them to be more and less, but are neither more nor less than one another. Other things, if they are the same attribute, and one in form, say white, more and less intensely, people say are alike because their form is one. Other things are alike if they have more things the same than different, either simply or superficially, as tin is like silver insofar as it is white, and gold is like fire insofar as it is yellow and fiery-red” (ibid).

“So it is clear also that other and unlike are meant in more than one way” (ibid).

“[B]ut difference is something other than otherness…. [W]hat is different from something is different in some particular respect, so it must necessarily be the same in some respect as that with which it differs” (p. 192).

For Aristotle, calling two things different presupposes that they can be meaningfully compared in the first place. This is not the case for things that are just “other” than one another. Black is different from white; they are both colors. But an apostrophe is just other than an aardvark.

This is followed by a ten-page discussion of technical details of contrariety, which I will mostly skip. Contrariety supports a definitive ruling out of some things based on other things. This has great importance for reasoning.

Incidentally, Aristotle explains why there is no essential difference between human beings with different colorings.

“And since one sort of thing is articulation while another is material, those contrarieties that are in the articulation make a difference in species, but those that are in what is conceived together with the material do not make such a difference. This is the reason that whiteness of a human being, and blackness, do not make such a difference…. For there is a difference between a white human being and a black horse, but that is not insofar as the one is white and the other is black” (ch. 9, pp. 201-202).

Finally, he argues that destructibility and indestructibility inhere in things by necessity. Whether a thing is destructible or not depends strictly on what genus of things its species belongs to.

“[A] destructible thing and an indestructible thing must be different in genus…. Therefore it is necessary that destructibility either be the thinghood or be present in the thinghood of each destructible thing; and the same argument also concerns the indestructible, since both are among things present by necessity” (ch. 10, p. 202).

Toward Potentiality and Actuality

With the discussion of independent things, the saying of what they are, and the provision for deriving sayings in the other categories from this, we have taken simple saying in the various senses of Aristotle’s Categories about as far as it can go. Although higher dialectical aspects will emerge in what is yet to come, I think the main results of Metaphysics book Zeta (VII) are qualified well enough to be counted by Aristotle as a permanent acquisition that will still be enhanced, but never rolled back.

Aristotelian saying is far from exhausted by saying in the syntactic senses of the Categories, however. We have yet to touch upon its all-important normative aspect, and the corresponding saying of things with an additional modal dimension of potentiality or actuality. This will be intimately involved with that-for-the-sake-of-which (see also Aristotle on Explanation). Book Eta (VIII), treated here, serves as a transition to the main discussion of potentiality and actuality that lies ahead in book Theta (IX).

For Aristotle (and Hegel as well), to say that something is actually X is to judge that it has achieved and is stably continuing to achieve a full expression of what it is to be X, which means it is actively fulfilling that for the sake of which X’s do what they characteristically do (see also Entelechy). In thinking about this, it is important not to set the bar too high — Aristotle thinks it is true of many things.

Then for something to be potentially X, at least within itself it has to be fully “ready” to undergo whatever is required by the process of becoming an actual X, though its becoming an actual X in fact will usually depend on conditions external to it, and in particular on the activity of some other actual X — parents in the case of offspring, and something like a Platonic “model” of the thing in the case of artificial things.

Book Eta begins with a summary of book Zeta, so here it is evident from the text itself that the two are intended to develop one continuous argument. Then book Theta will begin with a very short summary of both Zeta and Eta.

“Now one ought to reckon up the results of what has been said, and, putting them all together, to set out the final point to which they come. And it has been said that the causes, sources, and elements of independent things are being looked for” (ch. 1, Sachs tr., p. 155).

Here again we have a more refined statement of the goal of the inquiry. He then cheerfully points out what is in fact the big new impasse reached in the previous book, concerning the impossibility of defining independent things:

“But in one way it follows from the discussions that what it is for something to be, and what underlies something, are kinds of thinghood, and in another way that thinghood is the general class, more than the specific one, and the universal more than the particulars; and the forms are also connected with the universal and the general class (since it is by the same argument that they seem to be independent things). And since what it is for something to be is thinghood, and the articulation of that is a definition, for that reason distinctions were made about definition and about what something is in virtue of itself; and since a definition is a statement, and a statement has parts, it was also necessary to know about the parts — which sort are parts of an independent thing and which not, and if these are the same ones that are parts of the definition. And further, in the course of this, it turned out that neither the universal nor the general class is thinghood” (ibid).

He highlights the discussion of definition, saving till the end the major issue that the independent thing itself is a particular that cannot be the direct subject of a definition. The subtle cue that there will be something problematic in what is said is his “in one way it follows”.

It is typical of both Aristotle and Hegel to appear to endorse an argument for a while, only to eventually overturn it. This can be seen as preliminarily giving each current argument the benefit of the doubt, rather than attempting to anticipate its future refutation. Both Aristotle and Hegel consider it essential for learning to go through the process of an argument’s dialectical development, and not just anticipate ultimate conclusions, as if out of nowhere.

The last statement — that universals do not directly characterize substance-essence-thinghood, which is always particular — is one of the most important conclusions of the Metaphysics. It means that for Aristotle, knowledge (episteme) also will not apply to independent things, since independent things are particulars. This implies that for independent things, we have to rely on something like the practical judgment cultivated for ethical practice, which is directed at particulars.

Those who have wanted to treat “metaphysics” as a “science of being” are going in the opposite of Aristotle’s direction. First he characterizes “being” as having to do with what things are and what can properly be said about them. Then he says the inquiry is really about the causes of independent things. Then he eventually concludes that knowledge does not apply to independent things, because they are particulars. What he is after here is a kind of practical wisdom, not scholastic “science”.

“But now let us go over what concerns the acknowledged independent things. And these are the perceptible ones. And all perceptible independent things have material. And what underlies something is its thinghood, and in one sense this is the material (and by material I mean that which, while not being actively a this, is a this potentially), but in another sense what underlies something is its articulation and form, which, being a this, is separate in articulation; and a third sort of underlying thing is what is composed of these, of which alone there is coming into being and destruction, and which is separate simply. For of the independent things in the sense that corresponds to the articulation, some are separate simply, while others are not” (pp. 155-156).

Here he explicitly generalizes the notion of an “underlying thing”. In the previous book, he started with the accepted view that this must be some kind of material. Then he adopted a Platonic lesson that the form or articulation of things better characterizes what they are. Then he diverged from the Platonists and concluded that independent things are even more important than form.

He certainly discussed all three cases, but my reading of the previous book was that only the composite of both form and matter ended up fully and properly qualifying as an independent thing. In part, he is being extra generous here to his former colleagues in the Platonic Academy, as well as to common-sense views of material. But he is also setting the stage for a new conclusion we will see shortly.

At this point, I am a little mystified by the implication that both all composites and some forms (presumably, some forms of non-perceptible things, which have been mentioned in passing but not discussed yet) will turn out to be in the same way “separate simply”. His only developed argument about the applicability of “separateness” to forms so far has been against the separateness of the Platonic forms, at least in any context involving perceptible things.

However, it is also true that the previous book does in passing seem to defer discussion of the possibility that there are non-perceptible independent things. To anticipate, it does seem true that any first cause of all, analogous to the first cause of motion he argues for in the Physics, must also be independent, for by definition, “first” means having no dependencies.

“[I]t remains to say what the thinghood of perceptible things is in the sense of being-at-work. And Democritus seems to think there are three ways things differ (for he thinks that the underlying body, the material, is one and the same, while what differ are design, which is shape, twist, which is position, and grouping, which is order). But it is obvious that there are many differences; for instance, some things are spoken of by reference to the composition of their material, as are all those made by mixing, such as milk blended with honey; others by way of a binding-cord, such as a bundle, others by means of glue, such as a book, others by means of bolts, such as a box, others by more than one of these, others by position, such as a threshold and a capstone (since these differ by being placed in a certain way), others by time, such as dinner and breakfast, others by place, such as the winds, and others by the attributes of perceptible things such as hardness and softness, density and rarity, or dryness and fluidity, some things differing by some of these, some by all of them” (ch. 2, pp. 156-157).

As this passage makes clear for non-independent perceptible things, in no case does what he calls the “being-at-work” or “actuality” of things involve what we ordinarily think of as work (which is why I still guardedly use “actuality”). In the case of non-independent perceptible things, the “being-at-work” has to do with whatever makes a unified thing out of material components.

“So one must grasp the kinds of differences (since these will be the source of being)…. So it is clear from these considerations that if thinghood is the cause of each thing’s being, it is among these differences that one must look for what is responsible for the being of each of these things. None of these examples is an independent thing, but still there is an analogous structure in each of them” (p. 157).

As we saw in the previous book, Aristotle sees definitions not in the modern formalist sense of characterizations we simply posit in isolation, but as built up from an ordered series of essential differences that progressively distinguish something from other things. To define something for Aristotle is to clarify its relation to classifying distinctions from other things.

“Now it is clear from these examples that the being-at-work and the articulation are different for different materials” (p. 158).

Kinds of materials are a sort of universals, so we do expect their distinctions to be fully articulable. From his examples above, what is responsible for the unity of material things that are not independent living things is itself something material. What kind of thing this source of material unity will be varies according to the case.

“One must not ignore the fact that it sometimes escapes notice whether a name indicates a composite independent thing or its being-at-work and form” (ch.3, p. 158).

“[W]hat it is for something to be belongs to the form and the being-at-work” (p. 159).

Form establishes a what, though it is a universal what and not a particular what. So far we have only seen examples of the somewhat non-intuitive being-at-work of material, non-independent things, which I just called the “source” in Aristotle’s sense for their material unity.

“Now it is obvious to those who inquire about it that a syllable is not made of its letters plus combination, nor a house out of bricks plus combination…. Nor indeed is humanness animalness plus two-footedness, but there has to be something which is apart from these, since these are its material, and that something is neither an element nor derived from an element, but since people leave this out, they describe its material” (ibid).

Here he continues his dispute with Plato’s other students. Combination is not a material ingredient of anything, even in the sense of purely logical or “intelligible” material.

“But whether those things that are the thinghood of destructible things have being separately is not at all clear yet, except that it is clear for certain things at least that this is not possible, as many as are not capable of being apart from the particulars, such as a house or a piece of furniture. So presumably these things themselves are not independent things, nor is any of the other things that are not composed by nature, for one may posit that nature alone is the thinghood in destructible things” (ibid).

I find the above a bit perplexing. The previous book clearly seemed to assume that there are perceptible independent things, and that at least all earthly perceptible things are destructible, though he seems to assume the stars and planets are indestructible, since he sees no evidence to the contrary. But it seemed that animals and plants were implied to be independent things, and to have their own distinctive substance-essence-thinghood. He definitely said that “the soul of an animal… is its thinghood disclosed in speech”. Isn’t an animal a destructible thing?

“[I]t does not belong to an independent thing to be capable of a definition” (p. 160).

This again was a major conclusion of the previous book.

“[E]ach independent thing is a complete being-at-work-staying-itself [entelechy], and a particular nature” (pp. 160-161).

Here he explicitly associates the independence of independent things with the teleological notion of entelechy.

“[W]henever one is inquiring after what is responsible for something, one must state all the causes the thing admits of” (ch. 4, p. 162).

I silently passed over his discussion of his predecessors in book I, but his main argument there was that none of them took all the causes into account. In particular, even Plato resorted to treating the Good as a formal or efficient cause. Aristotle regards interpretation by that-for-the-sake-of-which as his own major innovation.

“And what is the cause in the sense of form? What it keeps on being in order to be. And what is the cause for the sake of which it is? Its end, though presumably both of the last two causes are the same. And one must state the nearest causes: What is the material? Not fire or earth but the material peculiar to the thing” (ibid).

I just pointed out that Aristotle regards the distinction of that-for-the-sake-of-which from a formal cause as of major importance. His identification of the two here therefore must be intended as less than fully general. Form has senses that do not primarily emphasize any normative component, such as the form of triangularity. But as we have seen, Aristotle also speaks of the souls of animals as forms.

One might say that the soul is the entelechy (literally, “in [it] end having”) of a living body. Entelechies may come in layers. More precisely, the soul would be a name for the “first entelechy” of the body, or its achieved and continuing organic functioning. For Aristotle, this is intrinsically a normative concept. To speak of the entelechy of a body implies that it is not only functioning, but functioning well in relation to its intrinsic ends. Higher ongoing functions — just insofar as they are well realized — involve higher entelechies.

He makes an important point about material. What is usually most relevant is “not fire or earth but the material peculiar to the thing“, such as an organic body or a particular mineral. The more specific a material is, the more form-like it is. We will see shortly that Aristotle takes this to the point of identity between the most specific material and the form of a material thing.

“[T]here will not be material in those things that are or are not without changing” (ch. 5, p. 163).

In the Physics, the material cause was originally developed as part of the explanation of change.

“[A]ll things that have more than one part, and of which the sum is not like a heap, but a whole that is something over and above the parts, have something responsible for them…. But a definition is one statement not by being bundled together like the Iliad, but by being of one thing” (ch. 6, pp. 163-164).

A form is normally treated as an integral whole. A definition implicitly refers to an integral whole.

“Now it is clear that, for those who approach defining and explaining in this way that they are accustomed to [crudely adding specifications together, as in “animal plus two-footed”], it is not possible to give an account of it and resolve the impasse. But if, as we say, there is one thing that is material and one that is form, and the former has being as potency and the latter as being-at-work, the thing sought after would no longer seem to be an impasse” (p. 164).

I think what he is saying here is that the definition applies to the form only, not to the composite. That is probably why he earlier mentioned the ambiguity between a name’s referring to the form, and its referring to the composite. This does resolve some of the earlier puzzles about the applicability of definitions (a definition applies to a form). It is important to recall, though, that he just said again that there is still no direct applicability of definitions — which are expressed in universal terms — to independent things, which are particulars.

“But as many things as do not have either intelligible or perceptible material, are each of them some very thing that is one, just as also some very thing that is, a this, an of-this-sort, a so-much (and this is why neither being nor one is included in definitions), and what it is for something to be is immediately a particular one and a particular being. Hence there is no other thing responsible for the being-one of any of these, nor of the being-a-being of each, since each is immediately a certain being and a certain one, not in the sense of being in a class of beings or ones, nor of being among things that have being apart from particulars” (pp. 164-165).

Now he begins to speak in general about things that have no material. What this will apply to is as yet unspecified.

“But as was said, the highest level of material and the form are one and the same thing; the former potentially, the latter actively, so that looking for what is responsible for their being one is like looking for a cause of one thing; for each of them is a certain one, and what is in potency and what is in activity are in a certain way one thing. Therefore there is nothing else responsible, unless in the case of something that moves it from potency to being-at-work, but everything that does not have material is simply something that is itself one” (p. 165).

Back again to things that do have material, here he makes a point I alluded to earlier. One aspect of Aristotle’s hylomorphism is this identity of the most specific material with the form (for things that have material). Each independent thing has its own entelechy that is the primary cause of its being what it is.

Finally, he reiterates that things without material do not require anything external to give them unity.

Reflection and Dialectic

As with dialogue, reflection provides a kind of model for dialectic. Reflection can be understood as an either metaphorical or literal dialogue with ourselves. We “question ourselves”, which is to say we examine and potentially criticize or refine the basis of our own commitments. Further, actual dialogue is always implicitly dialogue among fellow rational beings, all of whom are engaged at least to some extent in their own reflective activity, just by virtue of being rational beings, so dialogue implicitly presupposes reflection.

Pippin quotes Hegel: “But at issue here is neither the reflection of consciousness, nor the more specific reflection of the understanding that has the particular and the universal for its determination, but reflection in general…. For the universal, the principle or the rule and law, to which reflection rises in its process of determination is taken to be the essence of the immediate from which the reflection began…. Therefore, what reflection does to the immediate, and the determinations that derive from it, is not anything external to it but is rather its true being” (Hegel’s Realm of Shadows, pp. 238-239).

And again: “In general, this means nothing but this: Anything which is, is to be considered to exist not as an immediate, but as a posited; there is no stopping at immediate determinate being [Dasein] but a return must rather be made from it back into its ground, and in this reflection it is a sublated being and is in and for itself. What is expressed by the principle of sufficient reason is, therefore, the essentiality of immanent reflection as against mere being” (p. 239).

In the first quote, Hegel is again emphasizing that what he means by reflection is not just looking in a figurative mirror, but rather something more like finding an orientation among (or building a synthesis of) the potentially infinite mutual reflections in a hall of mirrors. Reflection “in general” is a name Hegel gives to reflection with this kind of potentially infinite dimension. (That the infinity here should be called potential is my friendly Aristotelian interpolation.)

In the second quote, he is saying that this kind of reflection — lifted out from the distinction between reflective activity and what it reflects upon — is what he would call the “truth” of everything that appears to be immediately determinate.

The principle of sufficient reason as formulated by Leibniz effectively says that for everything that is in some definite way, there is a reason why it is that way. Hegel is saying more specifically that such “reasons why” emerge immanently from the reflective grounding of what he is in a nonstandard way calling essence. What Leibniz cannot show is how a particular essence or monadic point of view results in certain predicates and not others; despite great sophistication, he is still to some extent using essence and monads as unexplained explainers to avoid what Hegel calls the “problem of indifference”. Hegel on the other hand explicitly makes essence and explanation interdependent.

“[T]he ‘principles’ of identification and differentiation are deeply intertwined, not independent of each other” (p. 240).

“[A] thing’s determinate properties are not, cannot be, a mark of that thing’s unlikeness from other things, just by being those properties…. If one thing is red and another square, we do not thereby know one is unlike the other; they are just two different things. A locomotive has nothing to do with a melody; it is not unlike a melody. We are trying to account not for determinate otherness, as in the logic of being, but for how objects that share properties (are like) could be, even with an extraordinary degree of such likeness, still unlike” (p. 241).

“Some of this anticipates topics in the logic of the Concept. Two trees are alike in being trees but unlike in being two individual trees. The idea will be that just in their likeness, their way of being alike, that they are unlike (different trees), just in the way each distinctly instantiates ‘treeness’ that they are unlike. Such a different ‘way of being a tree’ is not another property but the way the tree-properties are ‘had’ by the individual” (p. 242).

“Hegel is thinking of the way in which the specifying work of ‘unlikeness’ cannot be a matter of individual properties, atomistically conceived, but unlikeness within likeness is best understood as some content, the unlikeness of which is strict, even within such likeness. Some charge can be both positive and negative; some number, 4, can be both +4 and -4; some quantity of money can be an asset and also a debt pending; some force can be attractive and repelling; some distance marched east is canceled by the same distance marched west, and all these are ‘opposed’ only within some common likeness” (ibid).

I find “either-or” language more appropriate to these cases than the “both-and” language above, but the intent is the same. The distinctions in each sub-case are concrete “opposites” applicable to some specific context, and each definable only in reference to the other. In each case, it is possible to abstract an indifferent thing being measured or assessed — “positive-or-negative-quantity” for the one, and “virtue-or-vice” for the other.

“The ‘world’s being contradictory’ means nothing more than that, as he says, virtue cannot be virtue just by being other than, different from, in comparison with, vice, but only by ‘the opposition and combat in it’ against vice” (p. 243, emphasis in original).

Pippin complicates the matter with this example, because “relative” seems to have a different significance in the context of virtue and vice than it does in, say, that of positive and negative numbers. But the intended point is a very abstract one about constitution of meanings that is common to both cases. Whatever the difference between the two “oppositions” (positive/negative, virtue/vice), in each case the two sub-terms are somehow measured or assessed “against” one another.

“Hegel is trying to specify how affirming contrary predicates (‘in opposition’) does not amount to a logical contradiction. That is the point of his discussion, to make this distinction, not to treat such oppositions as if they were logically contradictory and then to affirm them anyway. As [Michael] Wolff puts it, Hegel’s orientation… is not from sentence or predicate negation, but from developments in the understanding of negative numbers and from Kant’s defense of Newton on positive and negative magnitudes. In general, then, mathematical, not logical negation” (pp. 243-244).

This is extremely important. The status of negative numbers was still controversial in Hegel’s time. Kant and Hegel contributed to their acceptance. Hegel struggled to invent new language to distinguish ambiguous cases in his Logic and to say reasonable things about them, but readers (certainly including myself) have found his unique idioms very hard to follow. Most of the ink spilled over “contradiction” in Hegel has been based on fundamental misunderstandings. (See also Negation and Negativity.)

“To use an empirical example, if the question is something like ‘Why did the ball fall to the ground?’ we want to avoid two kinds of answers: ‘because whenever a heavy object is dropped from a height, it falls’; and ‘it is in the nature of heavy things to fall’. Doing so, avoiding these alternatives, will allow us to see that the relation between a ‘ground’ and ‘what it grounds’ must be understood as a dynamic relation, one whereby the determinacy of the ground and that of the grounded cannot be fixed in isolation from each other” (pp. 245-246).

He quotes Hegel: “But the being that appears and essential being stand referred to each other absolutely. Thus concrete existence is, third, essential relation; what appears shows the essential, and the essential is in the appearance. — Relation is the still incomplete union of reflection into otherness and reflection into itself; the complete interpenetrating of the two is actuality” (p. 246).

“The general point [Hegel] keeps making is: a strict separation of the two moments, and an insistence that the nature of an appeal to an essence, or to a causal law, or to someone’s reason for acting cannot be understood as punctuated moments on the billiard-ball model of causation, but involve a kind of unity, the development of a kind of unity, much closer (yet again) to Aristotle on energeia. This essential-being-as-activity, manifesting itself in its appearances, is what should count as ‘actuality’. This has the implication that many existing things have no actuality, are not really ‘anything’. A lump of dirt, a cough, a strand of wire” (ibid).

“The question for Hegel is the question of ‘actuality’, not ‘existence’, or the sensibly apprehensible, just as for Aristotle, the question is the ‘really real’, to ontos on.” (p. 247).

Pippin quotes from the Encyclopedia Logic, “The logical is to be sought in a system of thought-determinations in which the antithesis between subjective and objective (in its usual meaning) disappears. This meaning of thinking and of its determinations is more precisely expressed by the ancients when they say that nous [“intellect”, or thought in a non-psychological sense] governs the world” (p. 248).

Here “governs” is meant in a constitutive sense. The important point is that the “thought-determinations” here are indifferent to the ordinary distinction between a subjective “thinker” and an objective “thought content”.

In this context he speaks of “this dynamical relation, this Ur-relation of all relations” (ibid).

“I have tried to show in another book that the most important, most clarifying implications of this Ur-relation occur in Hegel’s practical philosophy, both in his account of human agency, and in the implications of that account for the practical theory of freedom in his Philosophy of Right and theory of objective spirit in general (ibid).

“[T]he full demonstration of the truth of this Ur-relation lies in what it actually illuminates, in the cogency and credibility of, for example, an account of agency based on it” (p. 249).

It was the outstanding (and very Aristotelian) account of Hegel’s view of agency in Hegel’s Practical Philosophy that first attracted me to Pippin’s work.

In his own idiom, Hegel says “thus the inner is immediately the outer, and it is this determinateness of externality for the reason that it is the inner; conversely, the outer is only an inner because it is only an outer” (quoted, ibid.)

Pippin comments, “He does not mean here anything as obvious as: when I do something, my ex ante intention is fulfilled and so becomes something outer, just as what was done, the bodily movement, counts as an action because it expressed this ex ante intention. The passage does not say that the inner becomes the outer, nor that the outer is the expression of the inner. It says: there is no ex ante intention except as outer. It is the outer. And there is no outer except as what must count as inner, nor that it expresses a separable inner. There is no such separation” (pp. 249-250; see also Hegel on Willing).

This concludes Pippin’s chapter on the logic of essence. Unsurprisingly, we have not uncovered any magic formula that would tell us which appearances manifest the essence in particular cases. Such a thing seems completely impossible to me; we should not expect to be able to find any general formula covering an unspecified collection of particulars. Any judgments involving particulars must in part at least come back to something like Aristotelian deliberation and practical judgment, which yield only particular results.

Nonetheless, in discussing the logic of essence we have ruled out some important classes of misunderstandings, and we have set the stage for the climax of Hegel’s Logic in the “logic of the concept”. The logic of the concept will take as a starting point the non-separation of “inner” and “outer” that has been shown in the logic of essence.

Otherness

I wanted to elaborate a bit on what I see “otherness” as doing in the part of Hegels’ text that formed the subject of the previous post. Cambridge University Press provided only a skimpy index, which scandalously includes no entry at all for this key term. I don’t specifically recall “otherness” being literally used in the main body of the Phenomenology, though it may well exist somewhere. What I find googling “Hegel otherness” seems entirely devoted to the relation of self-consciousness to other people. Quick review of top results failed to turn up a supporting quote from Hegel using the literal term “otherness” in that way, however. This leaves it unclear to me whether this more social usage of “otherness” is even literally Hegelian, or is rather a term interpolated by commentators.

Relations to other rational beings are essential to Hegelian self-consciousness, to the point where I have quipped that it might better be called other-consciousness. This social and ethical meaning of otherness is not irrelevant to the current context. However, I take Hegel’s use of “otherness” in the Phenomenology Preface to be primarily “logical” in his special sense, rather than social.

In the Preface, Hegel calls Anderssein (otherness; literally, “being-other”) the “element” and the “ether” in which knowing occurs. Hegel is using “knowing” in a very broad sense here, encompassing everything from the mere acquaintance of ordinary consciousness with objects, to the pinnacles of philosophy. He begins to develop otherness by way of implicit contrast with that other element of “familiarity” and “representation” that he mentions as an obstacle to the higher development of knowing.

He explicitly calls otherness the element of “science” (rational understanding) in knowing, while implying that familiarity and representation characterize a contrasting element of immediacy that he sees as an obstacle to “science”. For Hegel, “science” is first and foremost the “logic” that was to form the first part of the “system” the Phenomenology was to introduce, so it could equally be said that otherness here is the unfamiliar standpoint of Hegelian logic, for which the whole long detour of the Phenomenology is intended to gently and patiently prepare us.

Once again, I take a deflationary approach to his rhetoric about “science” and “system”. In general with Hegel, rather than starting with ordinary assumptions about what his terms mean, it is best to interpret them in light of what he does. Here otherness provides a first thematic anticipation of the general point of view Hegel wants to recommend, and in particular of what is at stake in Hegelian “logic”, “science”, and “system”.

As a first approximation then, we have otherness expressed as the “element of knowing” that the Science of Logic will later develop, initially expressed by way of a contrast with a point of view centered on immediacy, familiarity, and representation.

There seems to be a kind of analogy between this contrast and what I read as the Phenomenology‘s other big contrast between the standpoints of consciousness and self-consciousness. I think Hegel’s view is that neither of these latter is ever found entirely independent of the other in real life, but at the same time that the alienation inherent to the relation of ordinary consciousness to objects is eventually to be overcome by dwelling primarily in what he calls self-consciousness and spirit. The higher phases of self-consciousness and spirit will be characterized by an openness to otherness.

The contrast between the feeling of otherness and those of familiarity and immediacy gives us a first starting point that we can grasp even within the standpoint of the most naive ordinary consciousness. The second contrast between the standpoint of otherness and the standpoint of representation brings this into sharper focus.

In the Preface, Hegel only hints at his very strong reservations about the place of representation in early modern mainstream views of knowledge such as those of Descartes and Locke. But in the Consciousness chapter of the Phenomenology, the alienated relation of consciousness to objects broadly captures aspects of the views of Descartes and Locke, who were the two great representationalist promoters of “consciousness” in philosophy (literally in Locke, and its ancestor French conscience in Descartes; see Consciousness in Locke and Hegel).

We cannot communicate without representation, any more than we can exercise higher functions without consciousness. But Hegel’s implicit critique of representation in the Preface and his more developed critique of consciousness in the Consciousness chapter together constitute a vital thread of his argument. His repeated warnings against taking “fixed thoughts” at face value and against taking propositions in isolation are closely tied to this.

Otherness challenges both fixed representations of thoughts and an overly fixed notion of self. Self from the perspective of otherness is a contextual, relational and adverbial term, not an independently contentful noun with a reference fixed once and for all (see The Ambiguity of “Self”).

What I think he is suggesting is a strong conclusion that in explaining meaning, we ought as much as possible to subordinate the point of view associated with representation, consciousness, objects, immediacy, and familiarity, rather than treating all of these as foundational touchstones.

What we ought to subordinate them to is developed throughout the rest of the Phenomenology, but especially involves the actualization of self-consciousness, and of forms of spirit that are not merely what he calls substantial, but are self-conscious, and thus for Hegel depend essentially on relations of mutual recognition.

A fully developed self-consciousness will be “at home” in otherness.

Here in the Preface, I think he is suggesting an argument complementary to that of the Phenomenology‘s main thread. In the Preface, the accent seems to be on knowing as such, whereas I take the overall thrust of the main thread to be primarily ethical in intent. Here too, at least in a general sense the Preface is closer to the concerns of what Hegel calls “logical” inquiry. The critique of the classic early modern concept of representation falls in this area.

Foundational uses of representation are based on strong presuppositions about the identity of represented things (the “fixed thoughts” to which Hegel is objecting). Representationalist theories of meaning focus on the ways in which representations are supposed to unambiguously refer to objects, which basically reduces meaning to a kind of implicit pointing at things that are presumed to be unambiguously identifiable. But this is a huge presumption that Hegel wants to question.

Alternatively, the meaning of representations can be explained in terms of form, value, internal structure, and inter-relations, all of which I think for Hegel are potentially articulable complete in themselves “in the element of otherness”, without any pointing or presumption required. Otherness thus appears to stand for coherence over reference and difference over identity in the explanation of meaning. Again, that is not to suggest that reference is absent, just that it ought not to dominate or primarily drive our explanations.

Finally, Hegel would remind us that even pure difference or pure coherence also needs to be considered from the point of view of its becoming and not just one static view. Otherness as an orientation toward difference and coherence in their becoming gives us a first approximation of the concerns Hegel means to bring to the fore when he speaks of dialectic. (See also Pure Negativity?; Teleology After Kant.)

Hegel’s Preface

In Nature, Ends, Normativity I raised the question of what happens to Aristotelian teleology when we look at it through a Kantian critical lens, then made a preliminary gesture toward its resolution by invoking Hegel’s challenge and admonition to us in the Preface to the Phenomenology of Spirit to make ourselves at home in otherness. Just how making ourselves at home in otherness helps with the question about Aristotle and Kant may not be at all clear yet. For now it’s just a thought to keep in mind.

First I want to try to explore Hegel’s larger point in the Preface that I risked reducing to the phrase “make ourselves at home in otherness”, and let that lead where it may. This post won’t get to the point where the phrase is introduced. It’s even possible that I’m remembering it from a paraphrase in H. S. Harris’ outstanding commentary. I’ll walk through the Preface over the course of several posts, using Terry Pinkard’s translation published in 2018.

Hegel’s Preface is an extremely dense text that seems to very deliberately follow a non-linear order. It does have a development, but it doesn’t just proceed from beginning to middle to end. Rather, it seems to repeatedly circle around several key insights, adding a little more each time. Famously, he begins by rejecting the very idea that philosophical truth is the kind of thing that could be “introduced” or made easily digestible by a conventional preface.

He goes on to repeatedly criticize two chief ways in which philosophy is made digestible and shallow — one that treats truth as something merely formal, and one that claims to leap into absolute knowledge by means of intellectual intuition. Especially in some of the later parts, Hegel gives a number of valuable hints at what he thinks serious philosophy ought to look like.

“[C]onventional opinion holds that the opposition between the true and the false is itself fixed and set…. It does not comprehend the diversity of philosophical systems as the progressive development of truth as much as it sees only contradiction in that diversity…. However, at the same time their fluid nature makes them into moments of an organic unity in which they are not only not in conflict with each other, but rather, one is equally as necessary as the other” (p. 4).

Hegel is not at all advocating some trite relativism or erasure of distinctions here. He is objecting to the artificially “fixed and set” way in which what he calls formalism sees the truth of propositions taken in isolation. More positively, he seems to be suggesting that we view the great philosophers as participants in a common, mutually enriching dialogue rather than as competitors.

“[T]he subject matter [of philosophy] is not exhausted in its aims; rather, it is exhaustively treated when it is worked out. Nor is the result which is reached the actual whole itself; rather, the whole is the result together with the way the result comes to be…. [T]he unadorned result is just the corpse that has left the tendency behind…. The easiest thing of all is to pass judgment on what is substantial and meaningful. It is much more difficult to get a real grip on it, and what is the most difficult of all is both to grasp what unites each of them and to give a full exposition of what that is” (p. 5).

Here Hegel makes a very Aristotelian point about the essential role of actualization. What he is directly applying it to is philosophical accounts of things. We should be interested not just in philosophy’s ostensible conclusions, but in how they were arrived at. (But an analogous point could be made about the actual working out of Aristotelian teleology in the world. What is relevant to this is not just pure ends by themselves, but the whole process by which ends are actualized by means of concrete tendencies.)

“In positing that the true shape of truth lies in its scientific rigor — or, what is the same thing, in asserting that truth has the element of its existence solely in concepts — I do know that this seems to contradict an idea (along with all that follows from it), whose pretentiousness is matched only by its pervasiveness in the convictions of the present age. It thus does not seem completely gratuitous to offer an explanation of this contradiction even though at this stage such an explanation can amount to little more than the same kind of dogmatic assurance which it opposes” (p. 6).

By “scientific” he basically means rational. Hegel here aligns himself with Kant’s emphasis on the conceptual and discursive character of rationality, and with Kant’s closely related rejection of claims to immediate knowledge by intellectual intuition. He is particularly alluding to claims of intellectual intuition in the philosophy of nature by followers of Schelling, as well as to the religiosity of immediate feeling promoted by followers of the German literary figure F. H. Jacobi, from whom Kierkegaard borrowed the image of the leap of faith.

The “true shape of truth” Hegel contrasts these with lies in conceptual elaboration — interpretation and explanation, not just asserted conclusions. The measure of truth is the insight and understanding it gives us. He also notes a difficulty that I often feel in attempting to summarize the results of a substantial development: summaries always run the risk of shallowness and dogmatism.

Hegel continues ironically that for his contemporary opponents, “The absolute is not supposed to be conceptually grasped but rather to be felt and intuited” (ibid).

“There was a time when people had a heaven adorned with a comprehensive wealth of thoughts and images. The meaning of all existence lay in the thread of light by which it was bound to heaven and instead of lingering in this present, people’s view followed that thread upwards towards the divine essence; their view directed itself, if one may put it this way, to an other-worldly present. It was only under duress that spirit’s eyes had to be turned back to what is earthly and kept fixed there, and a long time was needed to introduce clarity into the dullness and confusion lying in the meaning of things in this world, a kind of clarity which only heavenly things used to have; a long time was needed both to draw attention to the present as such, an attention that was called experience, and to make it interesting and to make it matter. — Now it seems that there is the need for the opposite, that our sense of things is so deeply rooted in the earthly that an equal power is required to elevate it above all that. Spirit has shown itself to be so impoverished that it seems to yearn for its refreshment only in the meager feeling of divinity, very much like the wanderer in the desert who longs for a simple drink of water. That it now takes so little to satisfy spirit’s needs is the full measure of the magnitude of its loss” (pp. 7-8).

Hegel was critical of traditional Augustinian other-worldliness, but saved his special disdain for followers of Schelling and Jacobi.

“The force of spirit is only as great as its expression, and its depth goes only as deep as it trusts itself to disperse itself and to lose itself in its explication of itself. — At the same time, if this substantial knowing, itself so totally devoid of the concept, pretends to have immersed the very ownness of the self in the essence and to philosophize in all holiness and truth, then what it is really doing is just concealing from itself the fact that instead of devoting itself to God, it has, by spurning all moderation and determinateness, instead simply given itself free rein within itself to the contingency of that content and then, within that content, given free rein to its own arbitrariness” (ibid).

It is not enough just to have a concept like the absolute Idea.

“However, just as little of a building is finished when the foundation is laid, so too reaching the concept of the whole is equally as little the whole itself. When we wish to see an oak tree with its powerful trunk, its spreading branches, and its mass of foliage, we are not satisfied if instead we are shown an acorn. In the same way, science, the crowning glory of a spiritual world, is not completed in its initial stages. The beginning of a new spirit is the outcome of a widespread revolution in the diversity of forms of cultural formation; it is both the prize at the end of a winding path as it is the prize won through much struggle and effort” (p. 9).

He implicitly recalls Aristotle’s argument that the oak tree is logically prior to the acorn, and cautions against assuming perfection in beginnings.

“Only what is completely determinate is at the same time exoteric, comprehensible, and capable of being learned and possessed by everybody. The intelligible form of science is the path offered to everyone and equally available to all” (p. 10).

When the Idea is kept vague, it becomes the province of claims of esoteric knowledge and special genius. Here he links the idea of rational “science” to a democratic tendency. But we should also beware of premature claims.

“At its debut, where science has been wrought neither to completeness of detail nor to perfection of form, it is open to reproach” (ibid).

He goes on at length about the formalism of the Schellingians’ insistence that all is one. The rhetoric is strong, but he is standing up for the importance of difference and distinction, which I completely support.

To condense a good deal, “when what is demanded is for the shapes to originate their richness and determine their differences from out of themselves, this other view instead consists in only a monochrome formalism which only arrives at the differences in its material because the material itself has already been prepared for it and is something well known…. [N]owadays we see the universal Idea in this form of non-actuality get all value attributed to it, and we see that what counts as the speculative way of considering things turns out to be the dissolution of the distinct and determinate, or, instead turns out to be simply the casting of what is distinct and determinate into the abyss of the void…. To oppose this one bit of knowledge, namely, that in the absolute everything is the same, to the knowing which makes distinctions… that is, to pass off its absolute as the night in which all cows are black — is an utterly vacuous naivete in cognition” (pp. 11-12).

(Remaining parts of this walk-through of the Preface are, in order, Substance and Subject; At Home in Otherness; Otherness; and Foreshadowing the Concept.)

Aristotle’s Critique of Dichotomy

Chapter 3 of the extraordinarily rich book 1 of Aristotle’s Parts of Animals contains a strong critique of the notion of classification by dichotomy, with implications reaching far beyond its original context. The idea that he criticizes is Platonic division into As and not-As, which is intended to result in a binary tree structure (i.e., a tree-shape in which all the branches are binary).

Platonic division was perhaps inspired by the two-sided character of Platonic dialectic, which was concerned with impartially examining the implications of both sides of some disputable question, particularly in the form of arguments for and against some thesis or other. Aristotle’s own dialectic has a more general form that is not bound to arguments for and against, but rather is simply concerned with an impartial examination of the consequences of hypotheses.

But in any case, classification in a world is a different problem from that of impartially examining a single hypothesis.

Ignoring Aristotle’s lesson, and strongly influenced by the more general impoverished notion of logical judgment as grammatical predication, early modern writers on natural history attempted to follow an a priori theory of univocal classification. But for Aristotle, there is no a priori theory of classification. Instead, the starting point is what Kant would call the implicitly schematized manifold of a concrete world.

Aristotle points out that if classification were reducible to the assignment of predicates, then to consistently classify a world or any given collection, there would have to be some one order in which we divide things by one predicate, then another, and so on. By examples he illustrates the fact that by this method, it is impossible to arrive at the division of animal species that we recognize in nature.

He also makes the more general argument that half of the classifying terms in any classification by sequential predication will be negatives, and that negative terms cannot be properly subdivided.

“Again, privative [negative] terms inevitably form one branch of dichotomous division, as we see in the proposed dichotomies. But privative terms in their character of privatives admit of no subdivision. For there can be no specific forms of a negation, of Featherless for instance or of Footless, as there are of Feathered and of Footed. Yet a generic differentia must be subdivisible; for otherwise what is there that makes it generic rather than specific? There are to be found generic, that is to say specifically subdivisible, differentiae; Feathered for instance and Footed. For feathers are divisible into Barbed and Unbarbed, and feet into Manycleft, and Twocleft, like those of animals with bifid hoofs, and Uncleft or Undivided, like those of animals with solid hoofs. Now even with the differentiae capable of this specific subdivision it is difficult enough so to make the classification that each animal shall be comprehended in some one subdivision and not in more than one (e.g. winged and wingless; for some are both — e.g. ants, glowworms, and some others); but far more difficult, impossible, is it to do this, if we start with a dichotomy into two contradictories. For each differentia must be presented by some species. There must be some species, therefore, under the privative heading. Now specifically distinct animals cannot present in their substance a common undifferentiated element, but any apparently common element must really be differentiated. (Bird and Man for instance are both Two-footed, but their two-footedness is diverse and differentiated. And if they are sanguineous they must have some difference in their blood, if blood is part of their substance.) From this it follows that one differentia will belong to two species; and if that is so, it is plain that a privative cannot be a differentia.” (Complete Works, Barnes ed., vol. 1, p. 1000).

Aristotle’s positive conclusion is as as follows:

“We must attempt to recognize the natural groups, following the indications afforded by the instincts of mankind, which led them for instance to form the class of Birds and the class of Fishes, each of which groups combines a multitude of differentiae, and is not defined by a single one as in dichotomy. The method of dichotomy is either impossible (for it would put a single group under different divisions or contrary groups under the same division), or it only furnishes a single differentia for each species…. As we said then, we must define at the outset by a multiplicity of differentiae. If we do so, privative terms will be available, which are unavailable to the dichotomist” (pp. 1001-1002, emphasis added).

This is consistent with Plato’s more general advice that classifiers, like butchers, should “cut at the joints”, i.e., look for natural distinctions rather than imposing artificial ones. Dipping back again to the negative argument, Aristotle adds:

“Now if man was nothing more than a Cleft-footed animal, this single differentia would duly represent his essence. But seeing that this is not the case, more differentiae than this one will necessarily be required to define him; and these cannot come under one division; for each single branch of a dichotomy end in a single differentia, and cannot possibly include several differentiae belonging to one and the same animal.”

“It is impossible then to reach any of the ultimate animal forms by dichotomous division” (p. 1002; see also Classification; Hermeneutic Biology?.)

Neoplatonic Critique of Identity?

A common theme of much 20th century continental philosophy was criticism of presumed identities of people and things. Writers like Theodor Adorno and Michel Foucault, to name but two, systematically questioned the role of identity in our understanding of the world. Edmund Husserl had recommended suspending judgments of existence in favor of the concrete description of essences; starting especially from a historiographical point of view, Foucault recommended suspension of judgments of pre-existing unity in favor of a concrete description of differences.

Later neoplatonism like that of Proclus (412-485 CE) is commonly associated with an extreme “realist” multiplication of metaphysical entities that implicitly had their own presupposed identities. The positive side of this is a rich view of differentiation metaphysically underpinning the diversity of concrete being. But the neoplatonic technical term hypostasis is the etymological source of our verb “to hypostasize”, which basically means to attempt to artificially impose more unity on something than it really has.

But especially if we go back to Plotinus (204/5 – 270 CE), and also in later authors, there is a strong strand of what might be called “negative henology” in neoplatonism. Plotinus was the main originator of so-called negative theology in the West. Negative theology indirectly gives meaning to the notion of transcendence by pointing out how every definite description falls short of adequately characterizing God. Hen is Greek for “one”, so by analogy with negative theology, a negative henology would be an account of how everything falls short of the pure unity of the One — in other words, how things that we think of as pre-existing unities are less unified than we suppose.

Hand in hand with this perspective comes the recognition that unity has many degrees. There are a few strong unities and many weak ones, and many degrees in between. As Plotinus recognized, nothing real has the pure unity of the One. (See also Power of the One?; Plotinus Against the Gnostics; Subjectivity in Plotinus.)

Pure Difference?

A common theme here is the conceptual priority of difference over identity. I think that identity is a derived concept, and not a primitive one (see also Aristotelian Identity).

The French philosopher Gilles Deleuze (1925-1995) in Difference and Repetition and other works argued that a pure notion of difference is by itself sufficient for a general account of things. In information theory, information is explained as expressing difference. In Saussurean structural linguistics, we are said to recognize spoken words by recognizing elementary differences between sounds. In both cases, the idea is that we get to meaning by distinguishing and relating.

Deleuze initially cites both of these notions of difference, but goes on to develop arguments grounded largely in Nietzsche and Kierkegaard, whom he uses to argue against Plato and Hegel. His very interesting early work Nietzsche and Philosophy was marred by a rather extreme polemic against Hegel, and in Difference and Repetition he announces a program of “anti-Platonism” that reproduces Nietzsche’s intemperate hostility to Plato. Nietzsche blamed Plato for what I regard as later developments. Neither Plato nor Aristotle made the kind of overly strong assertions about identity that became common later on.

In The Sophist and elsewhere, Plato had his characters speak of Same, Other, and the mixing of the two as equally primordial. Hegel took great pains to elaborate the notion of a “difference that makes a difference”. But Deleuze wants to argue that Plato and Hegel both illegitimately subordinate difference to identity. His alternative is to argue that what is truly fundamental is a primitive notion of difference that does not necessarily “make a difference”, and that come before any “making a difference”. (I prefer the thesis of Leibniz that indiscernibility of any difference is just what identity consists in.)

This is related to Deleuze’s very questionable use of Duns Scotus’ notion of the univocity of being, both in general and more particularly in his interpretation of Spinoza. For Deleuze, pure difference interprets Scotist univocal being.

I frankly have no idea what led to Deleuze’s valorization of Scotus. Deleuze is quite extreme in his opposition to any kind of representationalism, while Scotus made representability the defining criterion of his newly invented univocal being. It is hard to imagine views that are further apart. I can only speculate that Deleuze too hastily picked out Scotus because he wanted to provocatively oppose the 20th century neo-Thomism that had considerable prominence in France, and Scotus is a leading medieval figure standing outside the Thomist tradition.

For Deleuze, univocal being is pure difference without any identity. Difference that doesn’t make a difference seems to take over the functional role that identity has in theories that treat it as something underlying that exceeds any discernibility based on criteria. I don’t see why we need either of these.

I think Deleuze’s bête noir Hegel actually did a better job of articulating the priority of difference over identity. Hegel did this not by appealing to a putative monism of difference and nothing else, but by developing correlative notions of “difference that makes a difference”, and a kind of logical consequence or entailment that we attribute to real things as we interpret them, independent of and prior to any elaboration of logic in a formal sense.

In Hegel’s analysis as explicated by Brandom, any difference that makes a difference expresses a kind of “material” incompatibility of meaning that rules out some possible assertions. This is just what “making a difference” means. Meanwhile, all positive assertions can be more specifically analyzed as assertions of some consequence or entailment or other at the level of meaning (see Material Consequence). Every predication is analyzable as an assertion of consequence or entailment between subject and predicate, as Leibniz might remind us. It is always valid to interpret, e.g., “a cat is a mammal” as an inference rule for generating conclusions like if Garfield is a cat, then Garfield is a mammal.

What is missing from Deleuze’s account is anything like entailment, the idea of something following from something else. This notion of “following”, I am convinced, is prior to any notion of identity applicable to real things. Without presupposing any pre-existing identities of things, we can build up an account of the world based on the combination of differences that make a difference, on the one hand, and real-world entailments, on the other. Identity is then a result rather than an assumption. Meanings (and anything like identity) emerge from the interplay of practical real-world entailments and distinctions. It is their interplay that gives them definition in terms of one another.

Deleuze was a sort of ontological anarchist, who wanted being to be free of any pre-existing principles. While I agree that we can’t legitimately just assume such principles, I think this is very far from meaning that principles are irrelevant, or actually harmful. On the contrary, as Kant might remind us, principles are all-important. They aren’t just “given”. We have to do actual work to develop them. But if we have no principles — if nothing truly follows from anything else, or is ruled out by anything else — then we cannot meaningfully say anything at all.

Taking “Things” as True

The second standpoint examined by Hegel in the Phenomenology is Perception, or in the literal etymological sense of the German word for it, “true-taking”. This etymology has an intriguing but probably accidental resonance with the notion of taking things as thus-and-such that Brandom emphasizes in Kant. In Perception, emphasis is more on the things than on the taking.

Harris in his commentary associates Perception with the philosophy of healthy common sense. Even the peasant woman of the previous chapter “must follow the ‘leading’ of language at least one step beyond the naming of [things]. She identifies her cows not just by their names, but by their color-patterns; and she knows her apple trees from her plum trees or her neighbor’s peach, etc. Hers is a world not just of singular [things], but of perceptible types; but for her, the process of classification with its universal names is an instrumental shorthand for dealing with the ‘real things’ that can be identified and pointed to. She does not want to take the leading of language seriously, but only to get back to her life, and to get on with it” (Hegel’s Ladder I, p. 238).

Perception at least begins to take up the nuances of how things interrelate that are ignored by sense certainty. “Sense-Certainty is rich only in positive things to be certain of…. Only perception can say what is, because it names universal things that are perceived through the changing sequence and variety of their properties”(p. 239). “Perception is the being grasped together of the moments that unfold in perceiving as process…. The perceiving we are concerned with is a process in which the universal self takes itself to be a rational being, and the truth of its object to be a universal truth” (p. 238). By “universal self” he means an individual self taken as an instance of a rational self, not anything like a world soul.

Harris continues, “Our situation as philosophical observers is different in its ‘object’ from the perceiving consciousness. Our object has been logically determined for us, whereas the object of the perceiving consciousness simply ‘falls out of the world of Sense-Certainty’ for it… It knows that the object is a universal essence; but it does not know that ‘universality’ is an activity of the perceiving mind” (pp. 238-239).

“We know that the ‘thing’ is a result of this process…. Our perceiving is the process, of which the object is the result. Perception… is an interpretation of sense-certainty in which the knowing consciousness is no longer concerned about the truth of the copula ‘is’, but about what is…. Sense-Certainty was already implicitly perception in its examples” (p. 239).

He quotes Hegel saying “Being is a universal in virtue of having mediation or the negative in it” (p. 240). As Harris says a bit later, “There is no nameable property of anything that is not part of a range of alternative properties. Some variations of properties are consistent with the thing continuing to count as the ‘same thing’ — and some are not” (ibid).

“[T]he singular property of ‘being salt’ is known to us as immediate sensation only when we taste it (and that is when the salt itself is necessarily dissolved back into the flux of sense-immediacy). Thus, in the white cube that is the ‘thing’ I perceive, the character of being salt is a not-this; it is not immediately sensed, but it is stably preserved for the sensation whenever I want to sense it…. It is a potentiality for sensation…. As this potentiality, this ‘otherness’ than what it is (the cubical whiteness etc.), it is a universal” (pp. 240-241).

(I am delighted to see Harris stressing the importance of potentiality in this crucial transition out of immediacy in Hegel. I don’t recall Hegel using the word “potentiality” much, but thought he ought to have.)

“What is ‘truly taken’ is an essence that is the negative ‘property’ which determines and holds together all the positive ones. But it is also truly taken as the positive property of filling a certain space. All of the properties cohere together in the space that the thing occupies…. ‘Thinghood’ as directly given for perceiving is the persisting spatial togetherness of many independent qualities…. The ‘thing’ is not just a loose collection of properties inhering somehow in the same identifiable region of space at the given time. It is a thing because of what it excludes; and its exclusiveness is what particularizes each of its properties” (p. 241).

“I know that I do not passively perceive what is true, in the way that I seem to apprehend the fact that ‘this is Lisa, and this is Ursel’ passively. My reflective capacities are involved. Perceiving is an activity of consciousness” (p. 245). “But it ought to be consistent” (p. 246).

“The attempt to claim that the manifold of sensation is simply subjective ignores its interpersonal objectivity. Every identifiable property is an objective essence…. Not just the oneness of the thing is objectively real, but its ‘difference’ from everything else” (p. 247).

“The essence of being a thing is to be ‘for another'” (p. 249). “Everything is specified by its difference from others” (p. 250). “The determinacy which is the ‘essential’ or ‘absolute’ character of a thing on its own account is essentially a relation to others (which negates the thing’s independence)” (p. 251).

Here we begin to see the limits of Perception. “The standpoint of Perception presupposes an absolute community of ‘things’. But the definition of ‘thinghood’ that the perceptual consciousness set up for itself contains no necessary reference from one thing to another for its being. The independent being of the thing is what makes it the ‘object’ that can be ‘truly taken’…. We have now seen that in any consistent formulation of the perceptual standpoint, this is logically impossible. It is the independence that is a sham” (p. 252).

“What is ‘essential’ and what is not ‘essential’ is a function of our supposedly external observation” (p. 253).

“Hegel… aims to show us that the naive empiricism which wants to conceive of perception causally (as analogous to mirror-reflection) cannot succeed.”

“We have already seen how we could not stand still at the concept of the ‘one thing’ with ‘many properties’. We had to admit that the multiplicity was founded in the ‘thing’, and not simply generated by the perceiving mind; and on the other hand, the ‘unity’ was an actively negative exclusion, which could not be simply contributed by the mind as it sorted the perceived ‘properties’ into things” (p. 254).

The standpoint of perception treats logic and philosophy as mere “game[s] with verbal counters” (p. 256). Its mistake is “to assume that ‘cognition’ is an activity that supervenes on an object that is already there; but actually it is the construction of ‘the object’ in a process of interpretation” (p. 257).

Adverbial Otherness

Hegel’s German word Anderssein has a more concrete feel than its usual English “otherness”. Literally it is more like “being differently”, a noun made from an adverb applied to a verb. Hegelian difference is not only constitutive, but has an adverbial character.

He says in a passage near where the term is introduced, “[True reality] is the process of its own becoming, the circle which presupposes its end as its purpose, and has its end for its beginning; it becomes concrete and actual only by being carried out, and by the end it involves…. Precisely because the form is as necessary to the essence as the essence to itself, absolute reality must not be conceived of and expressed as essence alone, i.e. as immediate substance, or as pure self-intuition of the Divine, but as form also, and with the entire wealth of the developed form. Only then is it grasped and expressed as really actual” (Phenomenology, Baillie trans., pp. 80-81; I seem to have misplaced the Pinkard and Miller translations).

In this very Aristotelian passage, he invokes ends, form, actuality, and actualization, while pointing out the inadequacy of what are really modern contractions of the notions of substance and essence.

Harris notes that for Hegel, “a self-thinking substance must necessarily be a community of rational equals within the natural order who recognize themselves in one another as a spiritual community that transcends that order. This is Hegel’s concept of ‘Spirit’…. Here it is called die Reflexion im Andersssein in sich selbst, ‘the reflection within the otherness into [or within] itself'” (Hegel’s Ladder I, p. 56, brackets in original). Otherness is the native element of self for Hegel.

Harris’ abstract of paragraph 19 reads, “Divine knowledge is the interplay of divine love. But the loving must comprehend its own opposite, the suffering, patience, and labor of human experience. Logically it is untroubled, but this peace is abstract. The form of its realization is as important as its logical essence (since it belongs to the essence)” (p. 57).