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?.)

Intention and Intuition

Husserl continues his passive synthesis lectures with more discussion of intuition as a confirmation of the concordance of intentions. It now seems pretty clear that intuition for Husserl is all about the “presentness” of presentations, and unlike the common usage does not involve any leaps. He distinguishes between intuitions that are “self-giving” (principally, external perceptions), and those that are not self-giving, but instead involve a “presentification”, like memories and expectations. He discusses at some length the question whether it is possible in advance to know which of our general intentions and presentations can potentially be confirmed in intuition.

He speaks of intentions “wanting” and “striving” to be fulfilled in present intuition, but contrasts this with a wish or will. Instead, it seems to be a more elemental directedness toward filling in the metaphorical hole in what he calls the “empty” intentions that are not correlated to a present object in intuition from external perception. Preconscious beliefs about an external object are subject to a kind of preconscious corroboration by comparison to direct impressions from sense perception.

I like the quasi-personification of intentions and intuitions here, as “wanting” or “giving themselves” (see Ideas Are Not Inert). Plato in the Republic compared the soul to a city or community of thoughts, feelings, and perceptions, thus suggesting that the kind of unity the soul has is comparable to the kind of unity a concrete community has. All our thoughts, feelings, and perceptions thus need not be attributed monolithically to a single, central agent; rather, our agency as individuals is the combined effect of numerous specialized, more or less cooperating but somewhat decentralized agencies.

All our intentions “want” to coalesce into the unity of a world.

“That we have a consciousness of our own life as a life endlessly streaming along; that we continually have an experiencing consciousness in this life, but in connection to this in the widest parameters, an emptily presenting consciousness of an environing-world — this is the accomplishment of unity out of manifold, multifariously changing intentions, intuitive and non-intuitive intentions that are nonetheless concordant with one another: intentions that in their particularity coalesce to form concrete syntheses again and again. But these complex syntheses cannot remain isolated. All particular syntheses, through which things in perception, in memory, etc., are given, are surrounded by a general milieu of empty intentions being ever newly awakened; and they do not float there in an isolated manner, but rather, are themselves synthetically intertwined with one another. For us the universal synthesis of harmonizing intentional syntheses corresponds to ‘the’ world, and belonging to it is a universal belief-certainty.”

“Yet as we already mentioned, there are breaks here and there, discordances; many a partial belief is crossed out and becomes a disbelief, many a doubt arises and remains unsolved for a time, and so forth. But ultimately, proper to every disbelief is a positive belief of a new materially relevant sense, to every doubt a materially relevant solution; and now if the world gets an altered sense through many particular changes, there is a unity of synthesis in spite of such alterations running through the successive sequence of universal intendings of a world — it is one and the same world, an enduring world, only, as we say, corrected in its particular details, which is to say, freed from ‘false apprehensions’; it is in itself the same world. All of this seems very simple, and yet it is full of marvelous enigmas and gives rise to profound considerations” (Analyses Concerning Passive and Active Synthesis, pp. 145-146).

Husserl on Perception

“External perception is a constant pretension to accomplish something that, by its very nature, it is not in a position to accomplish. Thus, it harbors an essential contradiction, as it were. My meaning will soon become clear to you once you intuitively grasp how the objective sense exhibits itself as a unity in the unending manifolds of possible appearances; and seen upon closer inspection, how the continual synthesis, as a unity of coinciding, allows the same sense to appear, and how a consciousness of ever new possibilities of appearance constantly persists over against the factual, limited courses of appearance, transcending them.”

“Let us begin by noting that the aspect, the perspectival adumbration through which every spatial object invariably appears, only manifests the spatial object from one side. No matter how completely we may perceive a thing, it is never given in perception with the characteristics that qualify it and make it up as a sensible thing from all sides at once. We cannot avoid speaking of such and such sides of the object that are actually perceived. Every aspect, every continuity of single adumbrations, regardless how far this continuity may extend, offers us only sides. And to our mind this is not just a statement of fact: it is inconceivable that external perception would exhaust the sensible-material content of its perceived object; it is inconceivable that a perceptual object could be given in the entirety of its sensibly intuitive features, literally, from all sides at once in a self-contained perception” (Husserl, Analyses Concerning Passive and Active Synthesis, pp. 39-40).

Adumbration is something like foreshadowing.

While many of his contemporaries were caught up in the logical empiricist enthusiasm for literal “sense data” as the supposedly rock-solid foundation for knowledge, Husserl was taking an extremely original approach to a more classical view of the inherent limiting and “transcending” features of sense perception, explicitly bringing out implicit characteristics of any possible seeing of physical objects that seem clear as soon as we bring them into focus and reflect on them.

We need not take something like Plato’s refusal to treat sensation as a source of knowledge as a case of repugnance toward physicality. With Husserl’s help we can “see” a more specific grounding of Plato’s view in reasons inherent to the subject matter. Husserl’s exceptionally clear examples in the realm of visual perception also provide a kind of model for understanding something like Hegel’s frequent complaints against “one-sided” points of view.

“When we view the table, we view it from some particular side…. Yet the table has still other sides” (p. 40). “It is clear that a non-intuitive pointing beyond or indicating is what characterizes the side actually seen as a mere side” (p. 41). “In every moment of perceiving, the perceived is what it is in its mode of appearance [as] a system of referential implications…. And it calls out to us, as it were, in these referential implications: ‘There is still more to see here, turn me so you can see all my sides, let your gaze run through me, draw closer to me, divide me up; keep on looking at me over again and again…'” (ibid).

“These indications are at the same time tendencies that push us toward the appearances not given…. They are pointers into an emptiness since the non-actualized appearances are neither consciously intended nor presentified. In other words, everything that genuinely appears is an appearing thing only by virtue of being intertwined and permeated with an intentional empty horizon, that is, by virtue of being surrounded by a halo of emptiness with respect to appearance. It is an emptiness that is not a nothingness, but an emptiness to be filled-out; it is a determinable indeterminacy” (p. 42).

“In spite of its emptiness, the sense of this halo of consciousness is a prefiguring that prescribes a rule for the transition to new actualizing appearances…. This holds time and again for every perceptual phase of the streaming process of perceiving…. There is a constant process of anticipation, of preunderstanding” (pp. 42-43).

“[A]s soon as a new side becomes visible, a side that has just been visible disappears from sight….But what has become non-visible is not cognitively lost for us…. Having already once seen the back side of an unfamiliar object and, turning back to perceive the front side, the empty premonition of the back side now has a determinate prefiguring that it did not have previously” (pp. 45-46).

“The fact that a re-perception, a renewed perception of the same thing, is possible for transcendence characterizes the fundamental trait of transcendent perception, alone through which an abiding world is there for us, a reality that can be pregiven for us and can be freely at our disposal” (p. 47).

Here “transcendence” just refers to the various characteristics of the incomplete perception of spatial objects he is pointing out.

“[W]e see that every perception [implicitly] invokes an entire perceptual system; every appearance that arises in it implies an entire system of appearances” (p. 48). “What is already given to consciousness in a primordial-impressional manner points to new modes of appearance through its halo which, when occurring, emerge as partly confirming, partly determining more closely…. Advancing along this line, the empty intentions are transformed respectively into expectations” (p. 49).

Perception gives us the very opposite of isolated sense data. Every perception is connected to other perceptions.

“If we ask, finally, what gives unity within every temporal point of the momentary appearance… we will also come across reciprocal intentions that are fulfilled simultaneously and reciprocally” (p. 50).

Substance in the elementary sense of something persisting through change emerges from networks of mutually reinforcing cross-references.

“We can never think the given object without empty horizons in any phase of perception and, what amounts to the same thing, without apperceptive adumbration. With adumbration there is simultaneously a pointing beyond what is exhibiting itself in a genuine sense. Genuine exhibition is itself, again, not a pure and simple possession on the model of immanence with its esse = percipi [to be = to be perceived]; instead, it is a partially fulfilled intention that contains unfulfilled indications that point beyond” (p. 56).

“[I]n the process of perceiving, the sense itself is continually cultivated so in steady transformation, constantly leaving open the possibility of new transformations” (p. 57).

Everything we perceive reaches beyond itself, raising new questions.

“We always have the external object in the flesh (we see it, grasp, seize it), and yet it is always at an infinite distance mentally. What we do grasp of it pretends to be its essence; and it is it too, but it remains so only in an incomplete approximation, an approximation that grasps something of it, but in doing so also constantly grasps into emptiness that cries out for fulfillment” (pp. 58-59).

I suggested above that what Husserl illustrates so clearly about visual perception can serve as a model for other things. In particular, I think both facts and beliefs share the perspectival character of visual perception of spatial objects, because they revolve around analogous issues of correspondence with something external.

The very best and most complete facts about anything at best resemble a collection of still views of a tree from different angles, like the sides of the table in Husserl’s example. The virtue of facts is that they are supposed to be individually self-contained, and individually verifiable by correspondence to states of affairs. Even leaving aside all questions of interpretation that tend to unravel this putative self-containedness, by virtue of their isolation all individual facts still remain “one-sided” or perspectival, like individual still views of the tree.

Even the most complete collection or sequence of still views fails to capture the simultaneous many-sided unity-in-diversity of the concrete tree. The real concrete unity of the tree is not factual but teleological and “transcendental”, forever out of reach of a merely factual approach.

If this is true of the best possible facts, I would say it must also be true of the best possible beliefs, because both revolve around a kind of correspondence to states of affairs. The difference is that beliefs are just assertions of correspondence between what we say and what “is”. But to qualify as a fact, an assertion must also be verifiable by correspondence.

But verification by correspondence can only apply to what appears, not to what “is”, so facts only apply to what appears about states of affairs. Facts in effect just are verifiable appearances. They are an instance of what Plato called “true opinion”. They are objects of justified true belief, and potentially of a kind of subjective “certainty”.

Beliefs on the other hand usually reach beyond appearances toward what is, so although they assert a kind of correspondence, they cannot in general be verified by correspondence. Their well-foundedness in the general case has to do with a goodness of reasons. Well-foundedness by reasons falls short of certainty in one way, but it reaches deeper. It is potentially less subject to perturbation, because it does not directly depend on appearances or correspondence.

I think knowledge is something stronger than well-founded belief. Unlike facts and beliefs, I want to say that knowledge in the proper sense has nothing to do with correspondence to something outside itself. Also, well-founded beliefs may depend on assumptions that could eventually be refuted, but “knowledge” in the sense I want to give it does not depend on any assumptions either.

Contrary to common usage, then, I want to say that facts are not knowledge, and even certainty about appearances is not knowledge.

Judgments of correspondence — including beliefs and facts and certainties about appearance — seem to me to be inherently perspectival in the way that Husserl talks about. On the other hand, that rare thing called knowledge, in the way I am using the term, would be immune to perspectival limitations, because it does not depend on correspondence at all. (See also Husserl on Passive Synthesis; Opinion, Belief, Knowledge?; Sense Certainty?; Taking “Things” as True; Berkeley on Perception; Platonic Truth; Everyday Belief; A Criterion for Knowledge?; McDowell on the Space of Reasons; The Non-Primacy of Perception.)