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.”