Substance, Essence, Form

Here I will partially translate and briefly comment on Gwenaëlle Aubry’s analysis of the argument of book Zeta of Aristotle’s Metaphysics in chapter 3 of her Dieu sans la puissance. I think it is important to carefully capture a fair amount of the technical detail, especially because she is in part arguing against the most widely accepted traditional interpretation of a key point in the interpretation of Aristotle, which has to do with Aristotle’s ultimate attitude toward form.

(For the sake of the general reader, I have elided her precise citations, which use the standard Becker numbers for lines in the Greek text. English for much of book Zeta is reproduced in my own initial commentary on it. I have also omitted numerous accent marks that are sometimes used in romanization of Greek words.)

Aubry notes that whereas Aristotle uses the same word ousia for both primary and secondary substance in the senses of the Categories (a “this” and a universal, respectively), medieval Latin translations used substantia for primary substance and essentia for secondary substance. One important question raised in the discussion has to do with whether there are any cases where the “substance” and the “essence” of a thing are the same.

At the beginning of Zeta chapter 3, ousia is defined in terms very close to those of the Categories, as something that is not said of an underlying thing, but rather is the underlying thing of which other things are said.

“Matter being that which remains, it seems to be a substrate in the physical sense of the term…. But it also seems to satisfy the logical signification of the criterion of hypokeimenon [underlying thing]” (2nd ed., p. 77).

“But it is precisely the adequation of matter to the criterion of hypokeimenon, in its double acceptance logical and physical, that manifests the insufficiency of this criterion — and by that also the necessity of completing the analysis of the Categories” (ibid). She quotes Aristotle: “But this is impossible, for also to be separate and a this seem to belong to an independent thing most of all” (Sachs tr., p. 120). “No more than it suffices to respond to the question ‘what is ousia‘ that it is the substrate, does it suffice to respond… that ousia is matter” (Aubry, p. 77).

“This new criterion, that of khoriston kai tode ti [separate and a ‘this’], nonetheless conserves a trait of ousia as defined in the Categories: the capacity for independent existence. The initial analysis of Zeta thus has the effect at the same time of accentuating this trait, and of distinguishing the notion of a capacity for independent existence, or that of subsistence, from those of substrate and subject” (ibid).

“[T]here where one would expect to see the examination of form as a candidate developed, it is an analysis of to ti en einai [the what it was to have been] that is deployed, with respect to both the essence and the object of a definition (Zeta [chapters] 4-6). Of form, eidos, there is no question before Zeta 6″ (p. 78).

“This approach is qualified as logikos [logical]…. The logical approach to ousia will be governed by two questions: first, is there no essence but that of substance (Zeta 4-5)? Then, in what cases is essence identical to substance (Zeta 6)?” (ibid).

“One begins from the logical definition of essence as that which is said in accord with itself (kath auto). In the Posterior Analytics, the first sense of ‘in accord with itself’ names precisely what is mentioned in the definition of a given being and constitutes its ousia” (ibid).

“One goes on to conclude that there is an essence for everything for which one can give an account in a definition…. One does not affirm, nonetheless, that to ti en einai is the ousia, but only that it pertains to it first. According to the steps characteristic of Zeta, one goes on to establish not an exclusivity, but an order of priority: thus, essence belongs first and absolutely, protos kai haplos, to ousia. To the other categories, it belongs only secondarily…, in a certain way…, not absolutely” (pp. 78-79).

“Thus associating essence and definition, one remains in a Platonic logic…, even if Zeta 5 establishes that definition can give account not only of simple substances, but also of composite substances insofar as they are composite, on the condition that the composition is not accidental” (p. 79).

“The question thus arises to know whether there exist substances identical to their essence: for these are the sort of beings that the Platonists call ‘Ideas’…. Formulating this point, Aristotle clearly designates to ti en einai [what it was to have been], or the essence, as principle of intelligibility, and ousia as principle of being: if they were separated the one from the other, he writes, there would be no knowledge of the one, and the other would not exist” (ibid).

If being and intelligibility were not inseparable, there would be no knowledge of the one, and the other would not exist. But they don’t exactly coincide, either. Something similar could be said about being and value.

“Otherwise said, the guiding question is to know in what measure substance is identical to its essence, or to measure the division between a being and its principle of intelligibility: it is not again to know whether the essence can itself be considered a substance, that is to say capable of a separate existence” (ibid, emphasis in original).

(This relation of substance to essence bears some structural resemblance to the relation between existence and essence discussed by Aquinas. The criteria currently under discussion for ousia or “substance” (“separateness”, and being a “this”) indeed seem to have something to do with common notions of existence. But the ousia or substance is said to be the independent thing, whereas existence is commonly treated as an abstract property that can be said of things. And for Aquinas, God gives existence to an essence. But Aristotle starts by recognizing independent things that implicitly already exist.)

“But it is necessary, before arriving there, to establish the equivalence between essence and form, or between to ti en einai and the eidos. This is what the following chapters (Zeta 7-12), where the term eidos reappears, are concerned with” (p. 80).

The earlier “logical” approach is succeeded by a more physical approach in Zeta 7-9. “Form is the physical equivalent of essence…. Form is the essence that is found really instantiated in particular indviduals” (ibid).

“One indeed finds in form two traits characteristic of ousia, and more precisely of ousia as Plato had defined it” (ibid).

“Form can indeed pretend to the title of primary ousia. But (and this is essential), the text of Zeta itself distinguishes between ousia prote [primary substance] and ousia malista [what is substance most of all]. In the Categories, on the other hand, these terms are associated…. But while the denomination ousia prote is applied in Zeta to the form, that of ousia malista is applied to the composite, sunolon: that which is ousia malista is a human, a plant — not the ungenerated principle of generation that is form, but the concrete thing that is generated, mixed of form and matter” (p. 81).

“Ousia prote must be distinguished as much from ousia malista as from ousia said simply, or haplos, which is not the form [as such] but the immanent [instantiation of] form, associated with the matter together with which it constitutes the composite. This distinction is explicitly formulated in the preceding lines, in relation to the problem of definition: the definition does not include the matter” (ibid, emphasis in original).

“Form and ousia prote are nothing else than essence [to ti en einai, what it was to have been a thing]” (p. 82).

“If ousia prote is not the same in Zeta and in the Categories, it is because prote [primary] does not have the same sense in the two texts” (ibid). She has already noted that Zeta 1 explicitly recalls that “primary” or “first” is said in more than one way.

On the other hand, “The ousia malista of Zeta does correspond to the ousia prote of the Categories: it designates the individual.”

“From this, the form is clearly distinguished: the form signifies toionde, ‘of what species’; it is not a tode kai horismenon, an individual being subject to definition, but it produces and generates a being of that species in the individual…. No more than the matter does it correspond to the criterion of tode ti [being a ‘this’]” (ibid).

“The eidos is not fully ousia; it is only primary ousia, its anteriority being at once epistemological, as the logical analysis showed, and chronological, as the physical analysis showed. The form is only ousia in a Platonic sense, as the object of a definition, principle of intelligibility and of permanence, in short insofar as it is nothing other than essence comprising identity at the level of a species, and transmitted, by art or by generation, from one individual to another” (pp. 82-83).

“There is indeed a tension between ousia prote and ousia malista…. If the analysis of Zeta 7 manifests this, it indicates also, and already, the means to resolve it, in introducing, in the context of the study of generation, the notions of dunamis [potentiality] and entelecheia [entelechy]. Their substitution, in Eta, for those of matter and form, authorizes the reconciliation of the candidates, the criteria, and does so for both series of ousia, prote and malista: and it is at the end of Theta that the initial reflection of Zeta on this anteriority finds its culmination, since act is there said to be anterior both to to logo and te ousia, both from the point of view of the formula and from that of substance…. It will thus be possible to think the ousiai proterai not, in the manner of Plato, as forms-essences abusively separated from the matter they determine and the individual they define, but as acts having both an autonomous subsistence and a full intelligibility” (p. 83).

“Nonetheless, if we have on the one hand confirmed the identity between form, essence, and the object of definition and, on the other hand, qualified that between these three terms and ousia, we have up to now left aside another term fundamental to the Platonic equation: the universal” (p. 84).

“The universal meets neither the criterion of [full] determination, since it is common to many things, nor the criterion of being a substrate, since it is always affirmed of a subject…. Thus the universal cannot be called ousia in the qualified and reduced sense that essence is” (ibid).

“Once the pretention of the universal to the title of ousia has been eliminated, it remains to examine the question of its equivalence to form and essence. This is more complex, since form and essence are indeed a certain type of universal, a determinate one. But the fundamental point does not lie in this: the break with Platonism does not come, as maintained by the traditional reading, by way of the distinction between universal and form, and the affirmation that only the form would be ousia; it lies above all in the affirmation according to which form or essence itself is not fully ousia, the idea indeed according to which it does not suffice to be ousia kata ton logon [ousia according to what is said] to be ousia malista [ousia most of all]” (pp. 84-85, emphasis in original).

Aristotle in general does greatly emphasize the importance of what is said. Plato goes further, in making definition the very criterion of ousia. But for Aristotle, concrete things are not reducible to their definitions alone, and it is the concrete things that come first.

“The Platonic solution having been eliminated, we are brought back to the problem from which it was born (and which Beta calls the most difficult of all: how to think the relation between the individual and its principle of intelligibility” (p. 85).

“This problem is related to another…, how to think eternal and intelligible substances” (p. 86).

“Zeta 17 introduces a new point of departure… the point of view of principles and causes…. [I]n investigating the cause, it is first of all to ti en einai [what it was to have been a thing] that is researched” (ibid).

“But what is found there brought to light is not the nature of separate substance, as we might have hoped, but on the contrary the correlation of form and matter in the context of the composite substance” (ibid).

“These lines are generally read as the conclusion of Zeta, and as an ultimate affirmation of the identity between form and ousia. But it seems that they mark much more the insufficiency of this result” (ibid).

“Considered in its etiological, and not only logical, function, and taken as end, the form, in effect, is act. For the notion of act, insofar as it is substituted for that of form, but by way of completion, permits the reconciliation of the different criteria of ousia, as well as resolving the tension between ousia prote and ousia malista” (p. 87, emphasis in original).

“Act is ousia, absolutely, and in the full sense, from the logical and epistemological points of view as well as the ontological and etiological. If act allows ousia to be thought according to the double criterion of separation and intelligibility, it also allows the intelligible and separate substances to be thought, as Lambda will show. As for the notion of dunamis, its correlate, it serves to allow the reintegration of the candidate that Zeta has discarded: matter.”

“The notions of dunamis and energeia have something remarkable about them that allows a maximal extension of the notion of ousia to be given, without falling into equivocation, but on the contrary resolving the conflict between substance and essence, as well as that between simple and composite substances” (ibid).

Next in this series: Entelechy and Hylomorphism

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.

Next in this series: The Innovation of Potentiality-Actuality

The What-It-Is of Things

We’ve now reached the beginning of a much more sustained argument at the heart of Aristotle’s Metaphysics. The sequence of books Zeta, Eta, and Theta (VII-IX in Sachs’ translation) has a much tighter cohesion than the Metaphysics as a whole. These are commonly referred to by scholars as the “central” books. Here I will cover book Zeta (VII).

We have also reached the transition from initial questions about being (einai) to the development of answers that will be expressed entirely in terms of ousia (substance, essence, thinghood, the what-it-is of things). Neither Aristotle’s questions nor his answers have to do with being in the sense of existence.

“[Being] signifies what something is and a this, but also of what sort or how much something is, or any of the other things attributed in that way. But… the way that is first among these is what something is, which indicates its thinghood” (ch. 1, Sachs tr., p. 117).

“[S]omeone might be at an impasse whether each thing such as walking or healing or sitting is or is not a being, and similarly with anything else whatever of such a kind; for none of them is either of such a nature as to be by itself nor capable of being separated from an independent thing” (ibid).

I would call these “things”, but not “beings” or “independent things”.

Rather than attempting to speak about existence in general, he is concerned about the relative “independence” of particular things that are to be understood first in terms of what they are. This independence signifies both an internal cohesiveness associated with relative persistence in time, and a relative independence from us. Independent things are not just random phenomena, and they do not arbitrarily bend to our will. On the other hand, what they are can only be developed discursively, which implicitly involves us and our interpretation and judgment.

“[T]hinghood is primary in every sense, in articulation, in knowledge, and in time. For none of the other ways of attributing being is separate, but only this one; and in articulation this one is primary (for in the articulation of anything, that of its thinghood must be included); and we believe that we know each thing most of all when we know what it is…. And in fact, the thing that has been sought both anciently and now, and always, and is always a source of impasses, ‘what is being?’, is just this: what is thinghood?” (pp. 117-118).

Here he pretty much literally says that asking the famous “question of being” is asking the wrong question. From here on out, the inquiry will revolve around the status of definite “things” rather than of being in general — that is to say, it will focus on what things are, and on their “independence” as characterized above. We should still think of definite things in a higher-order way and not just one by one, but we will never leave definiteness behind.

Now the dialectical work begins in earnest. The first problem he addresses is that the preliminary separation of ousia from the more derivative senses of being was effected by treating the ousia as a kind of substrate in which all attributes inhere. This leads to the thought that it must after all be matter, but that cannot be right, because it is the form that allows something to be picked out as separate.

“But since at the start we distinguished in how many ways we define thinghood, and of these a certain one seemed to be what something keeps on being in order to be, one ought to examine that. And first let us say some things about it from the standpoint of logic, because what it is for each thing to be is what is said of it in its own right” (chapter 4, p. 120).

Again, it is vital to emphasize how questions of what things are are to be answered in terms of what is properly said about them. We will be concerned with proprieties of interpretation and judgment.

His concern with definiteness leads to a consideration of definition, and what it is to be a definable thing.

“Therefore there is a what-it-is-for-it-to-be of all those things of which the articulation is a definition. And it is not the case that there is a definition whenever a name means the same thing as a statement…, but only if the statement articulates some primary thing, and things of this kind are all those that are not articulated by attributing one thing to another” (p. 122).

Again, not being attributed to something else has to do with “independence”.

“This is clear: that a definition and a what-it-is-for-something-to-be belong primarily and simply to independent things. It is not that they do not belong to the other things in a way that resembles this, but only that they do not belong to them primarily…. And for this reason there will be a statement and a definition of a pale person, but in a different way than of pale, or of an independent thing” (p. 123).

“Therefore in one sense there will not be a definition of anything, nor a what-it-is-for-something-to-be present in anything, except of and in independent things, but in another sense there will be” (chapter 5, p. 124).

Independent things come first for Aristotle, but this emphasis is not exclusive. Derivative things — and corresponding things said in categories other than that of substance or thinghood — will also be taken into account.

“But one must investigate whether each thing is the same as, or different from, what it keeps on being in order to be” (chapter 6, p. 125).

“For there is knowledge of anything only when we recognize what it is for it to be…. Therefore the good and being-good must be one thing, and so too the beautiful and being-beautiful…. So by these arguments, each thing itself and what it is for it to be are one and the same, in a way that is not incidental, and this follows also because knowing each of them is just this: to know what it is for it to be…. In what way, then, what it is for something to be is the same as each thing, and in what way it is not, have been said” (pp. 126-127).

Once again, he directs our attention to definite form (or meaningful “content”, in the way many contemporary philosophers speak). Whether we call it form or content, the idea is to focus on meaning, and on wherever meaning is concentrated.

Next he begins to raise issues related to becoming.

“Of the things that come into being, some come about by nature, some by art, and some as a result of chance, but everything that comes into being becomes something, from something, and by the action of something… [J]ust as is always said, coming into being would be impossible if there were nothing present beforehand” (chapter 7, p. 128).

This is Aristotle’s more specific version of what Leibniz calls the principle of sufficient reason. Next he explains that becoming applies only to composite wholes that include both matter and form. In the way that Aristotle thinks about these matters, it is not correct to say that the form or what-it-is-to-be a thing comes into being.

“[J]ust as one does not make the underlying thing, the bronze, so too one does not make the sphere, except in the incidental sense that the bronze sphere is a sphere, and one makes that…. Therefore it is clear that the form, or whatever one ought to call the shapeliness that is worked into the perceptible thing, does not come into being, and that coming-into-being does not even pertain to it, or to what it is for something to be (for this is what comes to be in something else…)” (chapter 8, p. 131).

“So it is clear from what has been said that what is spoken of as form or thinghood does not come into being, but the composite whole that is named in consequence of this does come into being; and it is clear that there is material present in everything that comes into being, so that it is not only this but also that…. So it is rather the case that one makes or begets a certain kind of thing out of some this, and when it has been generated it is this-thing-of-this-kind” (p. 132).

Aristotle maintains a delicate balance in speaking about form. He strongly endorses the broad Platonic thesis of the importance of form, while refusing to take literally the more specific Platonic suggestions about the independence of form, which Plato’s other students elevated to a dogma.

“Therefore it is clear that the causal responsibility attributed to the forms, in the sense that some people are in the habit of speaking of the forms, as if they are certain things apart from the particulars, is of no use, at least in relation to coming-into-being and independent things” (ibid).

According to Aristotle, by virtue of their very “independence”, the kind of forms advocated by the Platonists would be cut off from the world, and could not possibly serve as causes of anything.

“[I]n a certain way everything comes into being from something that shares its name, just as the things do that are by nature (for instance a house comes from a house, insofar as it comes about by the action of an intelligence, since its form is the art by which it is built)” (chapter 9, p. 133).

In the natural case, living beings beget other similar living beings.

“And it is not only about thinghood that the argument shows that the form does not come into being, but in the same way, the argument concerns in common all the primary things, such as how much something is, and of what sort, and the other ways of attributing being” (p. 134).

In general, Aristotle wants to insist that none of the determinations according to the Categories, considered just in themselves, “comes into being”. It is always the composite things that have such determinations that come to have them.

“But what is to be understood from these considerations as peculiar to an independent thing is that a different independent thing that is fully at work, and that makes it, must be present beforehand” (ibid).

Next he asks whether the articulation of the parts must be present in the articulation of the whole.

The conclusion is that “[A]ll those things that are parts in the sense of material, and into which something divides up as into material, are derivative from the whole; but either all or some of those that are parts in the sense of belonging to the articulation and to the thinghood that is disclosed in the articulation, are more primary than it” (chapter 10, p. 137).

“And since the soul of an animal (for this is the thinghood of an ensouled thing) is its thinghood as disclosed in speech, and its form, and what it is for a certain sort of body to be (at any rate, each part of it, if it is defined well, will not be defined without its activity, which will not belong to it without perception), either all or some parts of the soul are more primary than the whole animal as a composite, and similarly with each particular kind, but the body and its parts are derivative from the thinghood in this sense, and it is not the thinghood but the composite whole that divides up into these as material” (ibid).

The soul of an animal is its form. This is a profound but difficult teaching. As for Plato, for Aristotle too forms as such are not supposed to be subject to becoming. This would seem to make them static. But at the very least, souls belong to hylomorphic composites that are subject to becoming. And it seems that souls themselves are involved in actions and passions (except from the standpoint of Plotinus, which is not Aristotle’s).

Something is clearly being said in more than one way here. The apparently static character of form will eventually be superseded or supplemented in the account of potentiality and actuality that is to come in book IX.

“But a human being or a horse in general, and the things that are in this way after the manner of particulars, but universally, are not thinghood but a certain kind of composite of such-and-such an articulation with such-and-such material, understood universally, while the particular, composed of ultimate material, is already Socrates, and similarly in other cases” (ibid).

Here he carefully distinguishes between an abstract universal of a kind of composite, and the what-it is of composites of that kind — e.g., between “a horse” and the what-it-is of a horse. Putting this together with what was said earlier, we can conclude that the what-it-is of a horse will be equivalent to “being a horse”, but distinct from “the horse itself” as an independent thing and a composite.

“But the parts of a thing’s articulation belong only to the form, and the articulation is of the universal; for being a circle and a circle, or being a soul and the soul, are the same thing. But of the composite already there is no definition” (ibid).

All composites are particulars, and for Aristotle no particular as such is definable.

“But the material is not known in its own right. And one sort of material is perceptible, the other intelligible, the perceptible, for example, bronze or wood, or any movable material, while the intelligible is that which is present in perceptible things, taken not as perceptible, as for example mathematical things are” (p. 138).

What is known in its own right seems to be only form, the what-it-is. The qualification “in its own right” is important. It leaves space open for other things to still be known in an indirect way.

“One might reasonably be confused about what sort of things are parts of the form, and what sort are parts not of that but of the all-inclusive composite. And yet so long as this is not clear, it is not possible to define any particular thing, since the definition is of the universal and the form; so if it is not clear what sort of parts are present in the manner of material and what sort not, neither will the articulation of the thing be evident…. For example, the form of a human being always appears in flesh and bones and parts of that sort: are they then also parts of the form and of its articulation? Or are they not, but just material…?” (chapter 11, pp. 138-139).

He points out that it will not always be easy to distinguish what belongs to a form itself, and what belongs to a composite that has the form.

“[T]hat is why tracing everything back in this way, and taking away the material, is overly fastidious, for presumably some things are such-and-such in such-and-such, or such-and-such in such-and-such a condition…. For it is not a hand of any sort that is part of a human being, but one capable of accomplishing its work” (p. 140).

The example of the hand introduces a distinction by that-for-the-sake-of-which, that could be applied even if we said the form was the same. Here we have a first intimation that the what-it-is of something may after all not be adequately characterized by form alone.

“And it is clear too that the soul is the primary independent thing, while the body is material, and the human being or animal in general is what is made of both, understood universally; and if it is also true that the soul of Socrates is Socrates, then names such as Socrates or Corsicus have two meanings (for some people mean by them a soul, but others the composite), but if Socrates is simply this soul plus this body, then the particular is just like the universal” (ibid).

“What, then, the what-it-keeps-on-being-in-order-to-be-at-all of something is, have been stated in a general way that applies to everything…. For the thinghood of a composite is the form that is in it, and the whole that is made out of that and the material is called an independent thing” (p. 141).

Here he dips back to a more categorical identification of the what-it-is with form.

Next he raises the question, what makes a definition one? This seems to be a digression or supplementary remark, though possibly it anticipates further criticism of Platonism that lies ahead.

The discussion of definition is narrowed to “definitions that result from divisions” (chapter 12, p. 143), in which kinds of things are defined by their distinctions from other kinds within some common scope. This is sometimes known as Platonic division, and it is illustrated in Plato’s Sophist.

Definition will be explained in terms of difference, but Aristotle’s notion that gets translated as “difference” has an important nuance we might not anticipate. In book Delta (V) he says “All those things are called different that are other but the same in some respect” (p. 89). Naively, we might expect “different” to mean the same as “other”, but in the translation here Aristotle uses “other” for the unrestricted case that includes things with no relation at all to one another, and “different” only for things that are comparable in some way, and therefore must also have some underlying similarity. Thus he avoids what Hegel calls the “problem of indifference”.

“But surely it is necessary also to divide the difference into its differences; for instance, provided-with-feet is a difference belonging to animal, and next one must recognize the difference within animal-provided-with feet insofar as it is provided with feet, so that one ought not to say that of what is provided with feet, one sort is feathered and another featherless, if one is to state things properly (for one would do this rather out of ineptness), but instead that one sort is cloven-footed and the other uncloven, since these are differences that belong to a foot, cloven-footedness being a certain kind of footedness. And one wants to go on continually in this way until one gets to things that have no differences; and then there will be just as many kinds of foot as there are specific differences, and the kinds of animals-provided-with-feet will be equal in number to the differences. So if that is the way these things are, it is clear that the difference that brings the statement to completion will be the thinghood of the thing and its definition” (ibid).

“So if a difference comes into being out of a difference, the one that brings this to completion will be the form and the thinghood of the thing; but if a difference is brought in incidentally, such as if one were to divide what is provided with feet into one sort that is white and another sort that is black, there would be as many differences as cuts. Therefore it is clear that a definition is an articulation consisting of differences, and arising out of the last of these when it is right…. But there is no ordering in the thinghood of the thing; for how is one to think of one thing as following and another preceding?” (p. 144).

Here he omits the critique of the binary character of Platonic division that he makes in Parts of Animals book I. As he expounds here, in a hierarchical ordering of differences, it is the most specific difference at the bottom of such a hierarchy that picks out the what-it-is of a thing. But he also wants to say that the what-it-is itself is a simple unity without internal ordering. Next he moves to explicit criticism of some Platonic positions.

“[I]t seems to some people that the universal is responsible for a thing most of all, and that the universal is a governing source, and for that reason let us go over this. For it seems to be impossible for any of the things meant universally to be thinghood. For in the first place, the thinghood of each thing is what each is on its own, which does not belong to it by virtue of anything else, while the universal… is of such a nature as to belong to more than one thing” (chapter 13, p. 144).

“Again, thinghood is what is not attributed to any underlying thing, but the universal is always attributed to some underlying thing…. And what’s more, it is impossible and absurd that what is a this and an independent thing, if it is composed of anything, should have as a component… an of-such-a-sort…. So for those who pay attention, it is clear from these things that nothing that belongs to anything universally is thinghood, and that none of the things attributed as common properties signifies a this, but only an of-this-sort” (p. 145).

Platonic forms are generally considered to have universal import, although I think Plotinus argues that there are also forms of individuals.

“But there is an impasse. For if no independent thing can be made of universals, … and no independent thing admits of being composed of active independent things, every independent thing would not be composed of parts, so that there could not be an articulation in speech of any independent thing…. Therefore, there will be no definition of anything; or in a certain way there will be and in a certain way there will not. And what is said will be more clear from things said later” (p. 146).

More generally, independent things seem to be particulars, and Aristotle says that properly speaking, there are no definitions of particulars. That of course does not prevent dialectical inquiry and clarification about them.

“But it is also clear from these same things what follows for those who say that the forms are independent things and separate, and at the same time make the form be a compound of a general class and its specific differences…. [I]f it is impossible for things to be this way, it is clear that there are not forms of perceptible things in the way that some people say there are” (chapter 14, pp. 146-147).

Another paradox about Platonic forms — seemingly acknowledged by Plato himself in the first part of the Parmenides — is that they are supposed to have universal import, but themselves to be a kind of immaterial particulars.

“[T]here is destruction of all those things that are called independent things…, but of the articulation there is no destruction…. And this is why there is no definition of nor demonstration about particular perceptible independent things…. For this reason it is necessary, when one is making distinctions aiming at a definition of any of the particulars, not to be unaware that it is always subject to be annulled, since the thing cannot be defined” (chapter 15, pp. 147-148).

Independent things are destroyed, but their what-it-is is not. Here he mentions explicitly that particulars cannot be defined, though this does not stop us from inquiring and making judgments about them.

“But neither can any form be defined, since they say that the form is a particular and is separate; but it is necessary that an articulation be composed of words, and that the definer will not make up a word (since it will be unknown), but the words must be names given in common to everything, so that they must also belong to something else” (p. 148).

Strictly speaking, all definitions without exception implicitly depend on other definitions. If the words used in the definition of a thing did not themselves have definitions, we could not understand them. The larger our web of connected, consistent definitions, the greater the confidence we can have in it. I think another relevant point is that we don’t have knowledge of the correctness of any isolated definition, though we could have knowledge of the compatibilities and incompatibilities of one definition with others. Definitions in general are a matter of dialectic and judgment.

He mentions problems involved with the definition of unique things. The errors here are an instance of more general errors in specifying too much or too little for sound identification of unique instances of kinds.

“For people miss the mark not only by adding things of a sort such that, if they were taken away, the sun would still be the sun, such as ‘going around the earth’, or ‘hidden at night’ (for if it were to stand still or shine at night it would no longer be the sun, but it would be absurd if it were not, since ‘the sun’ signifies a certain independent thing), but also by including things that admit of applying to something else, such that, if another thing of that kind came into being, it would clearly be a sun; therefore the articulation is common, but the sun was understood to be among the particular things” (p. 149).

“And it is clear that most of what seem to be independent things are potencies, not only the parts of animals…, but also earth and fire and air, since none of them is one, but just like a heap, until some one thing is ripened or born out of them (chapter 16, p. 149, emphasis added).

The seeming is all-important here. He actually means to deny that these are independent things. Only when “some one thing is ripened or born” might there then be an independent thing.

“And since one is meant in just the same way as being, and the thinghood that belongs to what is one is also one, and those things of which the thinghood is one are one in number, it is clear that neither oneness nor being admits of being the thinghood of things…. [B]eing and oneness are thinghood more so than are sourcehood and elementality and causality, but it is not at all even these…; for thinghood belongs to nothing other than itself and that which has it, of which it is the thinghood” (p. 150).

Aristotle here clearly emphasizes a self-containedness of the what-it-is of a thing. This seems to be motivated by a concern correlative to that for independence in things. Leibniz would later take this to an extreme with his monadology. Hegel goes in the other direction, questioning the self-containedness of a what-it-is. I think Aristotle is implicitly maintaining a Kant-like duality between the self-containedness of an undefinable indemonstrable what-it-is in itself, and his view of the difference-based character of definitions and knowledge, which I think also ought to extend to what I have called relatively well-founded belief. We could perhaps then resolve the duality between self-containedness and knowledge, somewhat in the way that Hegel resolves the Kantian ones, while at the same time preserving an Aristotelian respect for the independence in things.

“And yet, even if we had not seen the stars, nevertheless I suppose there would have been everlasting independent things besides the ones we know, so that now too, even if we cannot say what they are, it is still presumably necessary that there be some. That, then, none of the things attributed universally is an independent thing, and that no independent thing is composed of independent things, is clear” (pp. 150-151).

Now he really sounds like Kant: “even if we cannot say what they are, it is still presumably necessary that there be some.”

“But what one ought to say thinghood is, and of what sort it is, let us speak again, as though making another start; for perhaps from these discussions there will also be clarity about that kind of thinghood that is separate from perceptible independent things. Now since thinghood is a certain kind of source and cause, one must go after it from that starting point. And the why of things is always sought after in this way: why one thing belongs to something else” (chapter 17, p. 151).

Now he explicitly suggests that there is something separate from perceptible independent things.

“Now why something is itself is not a quest after anything…. But one could search for the reason why a human being is a certain sort of animal…. For example, ‘why does it thunder?’ is, ‘why does noise come about in the clouds?’, for thus it is one thing’s belonging to another that is inquired after…. It is clear, then, that one is looking for what is responsible, which in some cases, as presumably with a house or a bed, is that for the sake of which it is, but in some cases it is that which first set the thing in motion, since this too is responsible for it. But while the latter is looked for in cases of coming into being and destruction, the former applies even to the being of something” (pp. 151-152).

Identity by itself cannot be a reason for anything. Meanwhile, he mentions that that-for-the-sake-of-which also applies to things outside of becoming.

“But the thing in question escapes notice most of all in those cases in which one thing is not said to belong to another, as when the thing one is seeking is what a human being is, because one states it simply and does not distinguish that these things are this thing. But it is necessary to inquire by dividing things at the joints; and if one does not do this, it becomes a cross between inquiring after nothing and inquiring after something…. Accordingly, it is clear that in the case of simple things, there is no process of inquiry or teaching, but a different way of questing after such things” (p. 152).

Knowledge for Aristotle is concerned with things “belonging” to other things. It is expressed by things said of other things. Of particulars or singular things taken in isolation, may we have acquaintance or experience. We may have dialectical inquiry, and perhaps good judgment, but not knowledge.

Next in this series: Independent Things

Totality

The last post suggests another nuance, having to do with how “total” and “totality” are said in many ways. This is particularly sensitive, because these terms have both genuinely innocent senses and other apparently innocent senses that turn out to implicitly induce evil in the form of a metaphorically “totalitarian” attitude.

Aiming for completeness as a goal is often a good thing.

There is a spectrum of relatively benign errors of over-optimism with respect to where we are in achieving such goals, which at one end begins to shade into a less innocent over-reach, and eventually into claims that are obviously arrogant, or even “totalitarian”.

Actual achievements of completeness are always limited in scope. They are also often somewhat fragile.

I’ll mention the following case mainly for its metaphorical value. Mathematical concepts of completeness are always in some sense domain-specific, and precisely defined. In particular, it is possible to design systems of domain-specific classification that are complete with respect to current “knowledge” or some definite body of such “knowledge”, where knowledge is taken not in a strong philosophical sense, but in some practical sense adequate for certain “real world” operations. The key to using this kind of mathematically complete classification in the real world is including a fallback case for anything that does not fit within the current scheme. Then optionally, the scheme itself can be updated. In less formal contexts, similar strategies can be applied.

There are also limited-scope, somewhat fragile practical achievements of completeness that are neither mathematical nor particularly ethical.

When it comes to ethics, completeness or totality is only something for which we should strive in certain contexts. About this we should be modest and careful.

Different yet again is the arguably trivial “totality” of preconceived wholes like individuals and societies. This is in a way opposite to the mathematical case, which worked by precise definition; here, any definition is implicitly suspended in favor of an assumed reference.

Another kind of implicit whole is a judgment resulting from deliberation. At some point, response to the world dictates that we cut short our in principle indefinitely extensible deliberations, and make a practical judgment call.

“What” by Inferential Semantics

Brandom’s inferential semantics can be seen as providing a general framework for answering “what is…” questions. Semantics is about meaning — especially of concrete things said — and inferential semantics is about understanding meaning as a kind of practical doing involved with reasons. Looked at this way, a meaning reflects an inferential role, or role in real-world reasoning. Such roles always have two sides — conditions for appropriate use, and consequences of using this rather than that. Brandom identifies conceptual content with such inferential roles, and focuses on a contrast between these and simple definition, but I want to emphasize instead that all simple definition should be understood as a kind of summary of what implicitly distinguishes a particular inferential role from others.

The kind of meaning of interest here is in principle shareable rather than subjective, private, or psychological. Meaning is social and essentially involved with communication, but it is not a matter of empirical fact. Rather than explaining communication in terms of empirical facts, we should ultimately explain what we call empirical facts in terms of well-founded shareable meaning. The more we are able to explicitly spell out conditions of use and consequences of things that are said, the more substantive content we can share with others.

The “what is…” questions classically asked by Plato and Aristotle have an open-ended character because they are concerned with what something means for a reasoning being in general, which is an open-ended context. To have meaning for a reasoning being is to make a difference in the way the being reasons in life. In this way, Plato and Aristotle also were deeply concerned with the inferential roles of things, and practiced a kind of inferential semantics. This is ultimately inseparable from questions of goodness of reasoning. Here, too, inferential semantics depends on normative pragmatics.

Definition

The deeper Hegelian truth of a conceptual content can only be approached diachronically, via a historical recollective expressive genealogy. But in passing in the course of his world-historically groundbreaking interpretation, Brandom says Hegel rejects the very possibility of conveying a conceptual content by defining it, without saying what definition is or elaborating on what this denial means for the status of definition (Spirit of Trust, p.7). I find this to be ambiguous, and potentially a little misleading. At least within any given synchronic context and to some extent even more broadly, I believe definition in the sense of an Aristotelian “what it is” still has a positive role to play. It would not be reasonable to suppose that Brandom really means to ban the philosophical use of definitions; otherwise, we would have an extreme nominalism incompatible with his stated goals, which include what he calls conceptual realism. (See also Abstract and Concrete.)

The ambiguity in the passage has to do with how strong a sense we give to “conveying”. We should not expect a run-of-the-mill definitional representation to literally convey conceptual (inferential) content in its explicit form. But such a representation absolutely does address or concern conceptual content, and therefore can still “convey” that content in the weaker sense of referring to it or reliably picking it out. (We could also atypically construct definitions in terms of explicit material incompatibilities and consequences. These would presumably in a stronger sense convey the conceptual content isomorphic to them. We could even atypically construct definitions in terms of the current best expressive genealogy, so I don’t really see these as counterposed.)

I do not think Hegel would go so far as to deny the high pragmatic value of definition in synchronic contexts. This is part of the necessary moment(s) of determinacy (and Understanding) in the larger process of the development of Spirit. He just wants to make the larger point that diachronically, any realized ground-level definition is ultimately just a stopping point along the way. That does not mean we should not attempt to sum up the best understanding we have achieved at each moment. I think we are deontically obligated to do just that. Every ground-level definition is contextualized by its historical situation and therefore subject to change, but at every moment we should still strive to speak and act in accordance with the best definitions we can achieve. Representational clarity is imperfect and always dependent on other considerations in the background, but it is still a moment to be preserved.

We should distinguish the conceptual-content-related doing associated with developing a definition from the representation produced. Further, I find it difficult to separate a concern for definition from a methodological concern for problems of definition, as evinced by Plato and Aristotle for instance. From this perspective, definition has more to do with a line of questioning than a putative answer. The question of the “what” or conceptual content of things is actually far more substantial and interesting than those of mere fact or abstract existence. Even if it aims at a representation, definition as a practical task is all about inquiry into that whatness of things. The norm to which synchronic representation of whatness is responsible comes down to the best achievable view of the relevant difference and mediation, or material incompatibility and material consequence (as Brandom would put it) in the circumstances of that logical moment. This I think is actually independent of the diachronic moves of expressive genealogy.

Hegel’s “Substance that is also Subject” is explicitly presented as an extension of Aristotle’s (expressive meta) concept of ousia, and I think Aristotle anticipates even more than Hegel recognizes. (Expressive genealogy is distinctively Hegelian, but Substance certainly not, and Hegel himself notes in the History of Philosophy lectures that the concerns he groups under “Subject” were significantly addressed by Socrates, Plato, and Aristotle.)

If Brandom is right that Hegel intended to exclude such expressive metaconcepts from the general prognosis that all (ground-level) concepts eventually elicit their own negation, then it is at least logically possible that Aristotle’s metaconcept had already achieved the requisite stability to be incorporated by Hegel without negating the subordinate aspect of ousia that for Aristotle corresponds to a definition.

Without prejudice to claims about what Hegel added, I would argue that Hegel did in this way intend to incorporate all the multiple nuances of Aristotelian ousia, including the definitional one. With due respect for Brandom’s distinction between determination as Hegelian process and determinateness as Kantian/Fregean property (and the importance of the process as a superior point of view), I also think we need to forgivingly recollect all best attempts at determinateness. (See also Classification.)

I wonder what Brandom would say about the role of definitions in the articulation of mathematical conceptual content. The doing of mathematics seems to join the doing of history as problematic for simple subsumption under a genealogical approach as Brandom has described it. Mathematics needs definitions, and history needs to evaluate data without Whiggish filtering. (But Brandom does not exactly disallow either, and I can’t imagine that he would want to. The meaning of mathematical theorems can certainly be expressed in terms of material incompatibility and consequence, and the concepts used in non-Whiggish historiography could themselves be Whiggishly genealogically grounded.)

We should think about the functional inferential role of stipulative definitions, as well as the definitions of empirical concepts that I expect Brandom has foremost in mind. We could say that in both cases, the meaning sought by definition — as distinct from the definiens — is actually constituted through material incompatibility and material consequence. But a stipulative definition is a making rather than a taking. It in a sense starts a whole course of reasoning, whereas empirical concepts implicitly summarize results of reasoning.

Also, mathematical definition is mostly concerned with structures and structural properties. I believe a case could be made that in general, such structures and structural properties are expressive metaconcepts in much the same sense that logical concepts are.

I don’t think it’s historically right that expressive metaconcepts are a “discovery or invention” of German Idealism (p.5). Aristotle already had quite a few expressive metaconcepts, as at least partially exhibited in this blog. I believe Hegel himself recognized this.