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?.)

Sellars on Kantian Imagination

The analytically trained Kantian pragmatist Wilfrid Sellars (1912-1989) is increasing recognized as one of the greatest American philosophers of the 20th century. It has been said that he played a central role in taking analytic philosophy from its empiricist beginnings to a new Kantian stage. He is known for his critique of the “Myth of the Given”, his work on material inference, and his concept of the space of reasons. I found an essay of his on the Kantian productive imagination.

He begins by contrasting two approaches to perceptual judgment. First is a standard empiricist notion that goes as far as possible in reducing judgment to grammatical predication, to the point where the perception itself is treated as a bare this, and all the cognitive work of judgment is concentrated in applying a predicate to the bare this.

“Traditionally a distinction was drawn between the visual object and the perceptual judgment about the object…. This suggested to some philosophers that to see a visual object as a brick with a red and rectangular facing surface consists in seeing the brick and believing it to be a brick with a red and rectangular facing surface: ‘This is a brick which has a red and rectangular facing surface’…. Notice that the subject term of the judgment was exhibited above as a bare demonstrative, a sheer this, and that what the object is seen as was placed in an explicitly predicate position (“The Role of Imagination in Kant’s Theory of Experience”, in In the Space of Reasons: Selected Essays of Wilfrid Sellars, Scharp and Brandom, eds., p. 455).

Rather than pretending that perception gives us only a bare this, we should recognize that at least we talking animals live always already immersed in meaningful content. The most primitive human sense perception involves taking something not just as this, but as something with definite characteristics. This will turn out to be what Kant calls a schema, as distinct from a concept.

“I submit, on the contrary, that correctly represented, a perceptual belief has the quite different form: ‘This brick with a red and rectangular facing surface’. Notice that this is not a sentence but a complex demonstrative phrase. In other words, I suggest that in such a perceptually grounded judgment as ‘This brick with a red and rectangular facing side is too large for the job at hand’ the perceptual belief proper is that tokening of a complex Mentalese demonstrative phrase which is the grammatical subject of the judgment as a whole. This can be rephrased as a distinction between a perceptual taking and what is believed about what is taken…. From this point of view, what the visual object is seen as is a matter of the content of the complex demonstrative Mentalese phrase” (ibid).

In a nonessential decoration of the argument, he mentions “Mentalese”, a term used by analytic philosophers for inner speech. We need not concern ourselves here with whether or not there is a “mental language” distinct from, but patterned on, natural language, as this term suggests. The important point is that in every human perceptual “taking”, there is a kind of linguistic or language-like articulation, which we can express with a phrase consisting of classifying terms and syntactic relations between them.

“We must add another distinction, this time between what we see and what we see of what we see…. How can a volume of white apple flesh [hidden inside the apple] be present as actuality in the visual experience if it is not seen? The answer should be obvious. It is present by virtue of being imagined (p. 457).

“Before following up this point, it should be noticed that the same is true of the red of the other side of the apple. The apple is seen as as having a red opposite side. Furthermore, the phenomenologist adds, the red of the opposite side is not merely believed in; it is bodily present in the experience. Like the white, not being seen, it is present in the experience by being imagined” (ibid).

Here he seems to recall Husserl’s perceptual “adumbrations” or foreshadowings. Sellars is a bit more straightforward and explicit in attributing these to imagination.

“Notice that to say that it is present in the experience by virtue of being imagined is not to say that it is presented as imagined…. Red may present itself as red and white present itself as white; but sensations do not present themselves as sensations, nor images as images. Otherwise philosophy would be far easier than it is” (pp. 457-458).

When we imagine something to be the case, we are most often not aware that we are doing so. We simply think or believe that it is the case. As soon as we already have experience, what Sellars in the thin modern sense calls the “actual” presence of the imagined content comes to us as primitively mixed in with that of the perceived content. It takes work to analytically separate them, and any such separation always has a hypothetical character.

“But while these [hidden] features are not seen, they are not merely believed in. These features are present in the object of perception as actualities. They are present by virtue of being imagined” (p. 458).

As with Husserl’s “presentified” contents, the contributions of imagination are not theoretical constructs, but part of the experience itself.

“We do not see of objects their causal properties, though we see them as having them…. To draw the proper consequences of this we must distinguish between imagining and imaging, just as we distinguish between perceiving and sensing…. Roughly imagining is an intimate blend of imaging and conceptualization, whereas perceiving is an intimate blend of sensing and imaging and conceptualization” (ibid).

I like the way Sellars recognizes the interweaving inherent to these “intimate blends” of imaging and conceptualization.

“Notice that the proper and common sensible features enter in both by virtue of being actual features of the image and by virtue of being items thought of or conceptualized. The applehood [by contrast] enters in only by virtue of being thought of (intentional in-existence)” (pp. 458-459).

“The upshot of the preceding section is that perceptual consciousness involves the constructing of sense-image models of external objects. This construction is the work of the imagination responding to the stimulation of the retina…. The most significant fact is that the construction is a unified process guided by a combination of sensory input on the one hand and background beliefs, memories, and expectations on the other. The complex of abilities included in this process is what Kant called the ‘productive’ as contrasted with the ‘reproductive’ imagination. The former, as we shall see, by virtue of its kinship with both sensibility and understanding unifies into one experiencing the distinctive contributions of these two faculties” (p. 459).

Here we have a very basic Kantian point about the nature of experience — all perception involves imaginative construction. Objects are not just given to us fully constituted.

“Notice once again that although the objects of which we are directly aware in perceptual consciousness are image-models, we are not aware of them as image-models. It is by phenomenological reflection (aided by what Quine calls scientific lore) that we arrive at this theoretical interpretation of perceptual consciousness…. Thus we must distinguish carefully between objects, including oneself, as conceived by the productive imagination, on the one hand and the image-models constructed by the productive imagination, on the other” (pp. 459-460).

In common with Plato, Kant is at pains to point out that everything we experience — including everything we apprehend in inner sense — is appearance. I would say we also have “contact” with reality underlying the appearances, but we do not easily get knowledge of that reality.

“Kant distinguishes between the concept of a dog and the schema of a dog…. [O]ur perceptual experience does not begin with the perception of dogs and houses…. But though the child does not yet have the conceptual framework of dogs, houses, books, etc., he does, according to Kant, have an innate conceptual framework — a proto-theory, so to speak, of spatio-temporal physical objects capable of interacting with each other; objects — and this is the crux of the matter – which are capable of generating visual inputs which vary in systematic ways with their relation to the body of the perceiver ” (p. 460).

Here he explains the important Kantian notion of a schema. Concepts express nonperspectival essences, but schemas are perspectival, involve potentially sensible content, and implicitly include a relation to a perceiver.

“Consider the example of a perceiver who sees a pyramid and is walking around it, looking at it. The concept of a red pyramid standing in various relations to a perceiver entails a family of concepts pertaining to sequences of perspectival image-models of oneself-confronting-a-pyramid. This family can be called the schema of the concept of the pyramid…. Notice that the pyramid-schema doesn’t follow from the concept of a pyramid alone. It follows from the complex concept of pyramid in such-and-such relations to a perceiver” (p. 461).

In a Kantian context, we have no access to a sensible world apart from a perceiver’s perception of it.

“However thin — as in the case of the child — the intuitive representation may be from the standpoint of the empirical concept involved, it nevertheless contains in embryo the concept of a physical object now, over there, interacting with other objects in a system which includes me. It embodies a proto-theory of a world which contains perceivers of objects in that world” (p. 465).

Here we have the basis of Kant’s “transcendental deduction”, which aims to show that perception and imagination effectively already presuppose the same categories that govern understanding. This is how Kant recovers the possibility of objectivity.

Logical Judgment?

It seems to me that “logical judgment” comes in a wide range of forms, from the preconscious syntheses of our evolved common sense that appear to us ready-made, to the most elaborately explicit works of interpretation. I see judgment as referring principally to a process, and only secondarily to the outcome of the process — to the deliberation more than to the verdict, as it were.

There is a traditional use of “judgment” as a synonym for “logical proposition”. I find this a bit odd; it would make more sense to think of a judgment as at the very least an assertion or denial of a proposition, even in contexts where the connotation of interpretive, deliberative process is suppressed, and the focus is only on an outcome.

In combination with traditional ideas about predication, this identification of judgments with propositions led to a notion of acts of logical judgment in which acts of grammatical predication such as construction of the sentence “Socrates is a human” were viewed as prototypical.

Even Kant’s discussion of the application of concepts in the first Critique bears noticeable traces of this predicative analysis of logical judgment. I think Kant across the larger body of his work played a major role in developing alternatives to the predicative approach that narrowly construed “judgment” as the application of a predicate to a subject. Indeed Brandom argues that Kantian concepts are only intelligible in terms of their contribution to the activity of judging. Nonetheless, when Kant talks about subsuming particulars under universals, the discussion still recalls the predicative approach. Certainly the application of universals to particulars is important, but it is only one of several dimensions that come into play in the constitution of meaning, and it is not the most fundamental.

In referring to the constitution of meaning, I have already implicitly moved beyond the predicative analysis. The problem with the predicative analysis is that it takes meanings for granted, and really only addresses their syntactic combination as pre-existing units. We need to address the broader territory of judgments about meaning and value that go below the level of pre-existing units and preconceived identities. Meanings of terms in context turn out to depend on judgments, which in turn depend on others, and it is the ties of mutual dependency that bind together this open-endedly expanding network that give relative definiteness to our determinations.

Predication

It is extremely common to see references to “predication” as if it were a central concept of Aristotelian logic. We are so used to a grammatical interpretation in terms of relations between subjects and predicates that it is hard to disengage from that. However, historically it was Aristotelian logic that influenced ancient Greek accounts of grammar, not vice versa.

Modern logicians distinguish between a neutral proposition — which might be merely mentioned, rather than asserted — and the assertion of the proposition. Grammatical predication in itself does not imply any logical assertion, only a normatively neutral syntactic relation between sentence components. But “said of” in Aristotle always refers to some kind of meaningful assertion that has a normative character, not to grammatical predication.

Aristotle talks about what we might call kinds of “sayables” (“categories”). He famously says that we can only have truth or falsity when one kind of sayable is “said of” another. Mere words or phrases by themselves don’t assert anything, and hence cannot be true or false; for that we need what modern writers have referred to as a “complete thought”.

The ordinary meaning of “to categorize” in ancient Greek was “to accuse in a court of law”. Aristotle used it to talk about assertions. It didn’t originally connote a classification. The modern connotation of classification seems to stem from the accident that independent of what “category” meant in his usage, Aristotle famously developed a classification of “categories”.

Aristotle also talks about logical “judgment” (apophansis, a different word from practical judgment or phronesis). Husserl for instance transliterated this to German, and followed the traditional association of logical judgment with “predication”. But the ordinary Greek verb apophainein just means to show or make known. Aristotle’s usage suggests a kind of definite assertion or expressive clarification related to demonstration, which makes sense, because demonstrations work by interrelating logical judgments.

All of Aristotle’s words and phrases that get translated with connotations of “predication” actually have to do with normative logical assertion, not any connecting of a grammatical subject with a grammatical predicate. Nietzsche and others have complained about the metaphysical status foisted on grammatical subjects, implicitly blaming Aristotle, but all these connotations are of later date.

The great 20th century scholar of ancient and medieval logic and semantics L. M. de Rijk in his Aristotle: Semantics and Ontology (2002) argued at length that Aristotle’s logical “is” and “is not” should be understood as not as binary operators connecting subjects and predicates, but as unary operators of assertion and negation on whole propositions formed from pairs of terms. (See also Aristotelian Propositions.)

As in similar cases, by no means do I wish to suggest that all the work done on the basis of the common translation of “predication” is valueless; far from it. But I think we can get additional clarity by carefully distinguishing the views and modes of expression of Aristotle himself from those of later commentators and logicians, and I think Aristotle’s own more unique perspectives are far fresher and more interesting than even good traditional readings would allow.

Judgments

I usually think of judgment as a process of interpretation or a related kind of wisdom, but at least since early modern reformulations of Aristotelian logic, “a” judgment has also traditionally meant a logical proposition, or an assertion of a proposition.

An older, but still post-Aristotelian notion is that what the early moderns called a judgment “A is B” should be understood (on the model of its surface grammar) as the potentially arbitrary predication “A is B”. Such a potentially arbitrary predication by itself does not contain enough information for us to assess whether it is good or bad. The predication model was associated with a non-Aristotelian notion of truth as simple correspondence to supposed fact.

L. M. De Rijk, arguably the 20th century’s leading scholar on medieval Latin logic, developed a very detailed textual argument that the understanding of logical “judgments” in such grammatical terms is actually an unhistorical misreading of Aristotle. In the first volume of his Aristotle: Semantics and Ontology, De Rijk concluded that Aristotle’s own logical or semantic use of “is” or “is not” should be understood not in the traditionally accepted way as a “copula” or binary operator of predication, but rather as a unary operator of assertion on a compound expression — i.e., on the pair (A, B), as opposed to its two elements A and B.

I also want to emphasize that Aristotle himself did not admit simple, potentially arbitrary predications as “judgments”. The special form of Aristotelian propositions makes them express not arbitrary atomic claims as is the case with propositions in the standard modern sense, but two specific ways of compounding subclaims. Aristotle’s two truth-value-forming operations of combination and separation (expressed by “is” and “is not”) limit the scope of what qualifies as a proper Aristotelian “judgment” to cases that are effectively equivalent to what Brandom would call judgments of material consequence or material incompatibility (see Aristotelian Propositions). What the moderns would call Aristotelian “judgments” thus end up more specifically reflecting judgments of what Brandom would call goodness of material inference.

Proper Aristotelian “judgments” thus turn out to express not just arbitrary predications constructed without regard to meaning, but particular kinds of compound claims that can in principle be rationally evaluated for material well-formedness as compound thoughts, based on the actual content of the claims being compounded. (Non-compound claims are just claims, and do not have enough content to be subject to such intrinsic rational evaluation, but as soon as there is some compounding, internal criteria for well-formedness come into play.)

So, fortuitously, modern use of the term “judgment” for these ends up having more substance than it would for arbitrary predications. For Aristotle, truth and falsity only apply to what are actually compound thoughts, because truth and falsity express assessments of material well-formedness, and only compound thoughts can be assessed for such well-formedness. The case for the fundamental role of concerns of normativity rather than simple surface-level predication in Aristotelian truth-valued propositions is further supported by the ways Aristotle uses “said of” relations.

Independent of this sort of better reading of Aristotle, Brandom in the first of his 2007 Woodbridge lectures points out that Kant also strongly rejected the traditional analysis of judgment in terms of predication. Brandom goes on to argue that for Kant, “what makes an act or episode a judging in the first place is just its being subject to the normative demand that it be integrated” [emphasis in original] into a unity of apperception. This holistic, integrative view of Kantian judgment seems to me to be strongly supported by Kant’s discussion of unities of apperception in the second edition of the Critique of Pure Reason, as well as by the broad thrust of the Critique of Judgment.

Thus, a Kantian judgment also has more substance than the standard logical notion, but while an Aristotelian “judgment” gets its substantive, rational character from intra-propositional structure, a Kantian judgment gets it from inter-propositional structure.