Annamaria Schiaparelli has provided readers with a reliable translation and an informative commentary for book six of the Topics, the book in which Aristotle speaks at length on definition and how it may be (truly) predicated. As the core books of the Topics (i.e., books II–VII) have not been explored very much at all in the English-language commentary literature, this is a most welcome event. Much could be said about this book of the Topics and its place in Aristotle’s theory of definition and essential predication. Here I will limit myself to remarks on what one might hope to learn philosophically from reading Topics VI, how Schiaparelli develops the material in her commentary and handles its difficulties, and what this volume contributes to the state of current research on the development of Aristotle’s logical theorizing in the Topics.
In the beginning (or at least before Aristotle) was dialectic, the two-player argument game we find dramatized in Plato’s dialogues. Plato made various claims for what this conversational form of argument might accomplish. It can constitute knowledge of dividing genera correctly and knowing which kinds are the same or different (Soph. 253d1–3); it can even be the “coping-stone” of all forms of knowledge (Resp. VI, 534e2–3). Plato’s dialectician is expert in obtaining the definition of the essence of each thing (Resp. VI, 534b3–4); the better dialectician is better by virtue of the ability to discover “the explanation of things in definition” (Politikos 287 a3–4). Aristotle, by contrast, makes more modest claims for dialectic as a form of knowledge (see e.g., his remark in Met. Γ2, 1004b25 to the effect that dialectic can test what philosophy can know). But in the Topics he provides a method for training players for the game, the object of which (at least on Aristotle’s understanding) is to deduce in conversation and avoid self-contradiction (Top. I.1, 100a18–21).
In Aristotle’s method for dialectic, the definition of an item plays a prominent role. The definition is in a way the focal point of the core books of the Topics. These books are organized around the four predicables: Top. II–III concern accident, Top. IV genus, Top. V proprium or property, Top. VI definition. Aristotle introduces the predicables as the relations expressed by every dialectical premise-question or problem-question, i.e., by any proposition in dialectic offered for acceptance (Top. I.8, 103b2–19). They consist in the relations of predication between general terms. If one term A is (truly) predicated of another term B and B is (truly) counter-predicated of A, there are on Aristotle’s view two possible predication relations that could be involved. Either term A expresses the essence of B (in which case it is B’s definition), or it expresses a proprium of B—something which is not essential to B but which belongs only to the things which are B (103b9–12). If A is truly predicated of B but B is not truly predicated of A, there are again two possible predication relations. Either A is merely truly predicated of B but does not express anything essential about it—then A is an accident of B. Or A expresses a part of the definition of B. Then A is a genus-term or difference of B (103b12–19).
The relation of all this to, say, Socrates’ discussion with Euthyphro about definitions of piety might seem remote. How do definitions, as terms, actually enter the dialectical fray? You could think of the search for definition in conversation as a kind of Bildungsreise for the term under consideration. If, using the topoi of the accident, the term is confirmed to be truly predicated of the subject, we go on to the topoi of the genus and see if it is not merely truly predicated, but also predicated in the definition. If that holds, then we continue on to see if the term is counter-predicated with the subject. If the term withstands the tests for being a proprium and is confirmed as expressing the essence of the item to which it is predicated, it moves on to be tested as a definition—the ultimate goal and end-point of dialectical testing. Book VI features commonplaces, and with them rules, for this last stage on the term’s dialectical journey.
In her introduction Schiaparelli presents the system of the predicables in terms of four positive relations between two non-empty classes (10–11): 1. A includes B (A ⊆ B) but B does not include A (B ⊈ A), 2. B includes A but A does not include B (B ⊆ A and A ⊈ B), 3. A is co-extensive with B, and 4. A “overlaps” with B (A ∘ B). Schiaparelli is aware that Aristotle’s general terms are not classes and cannot be plausibly construed to represent them (11). Still, she includes a formalization of these relations and their derivable features in an appendix (357–358). As a model for the semantics of the predicables this interpretation has a defect: it cannot express the relation of essential predication, central to the predication relations of the genus and the definition (note that these two are different in their extensional features). In the commentary, definitional criteria which can be construed in terms of these extensional relations are highlighted (see e.g., 60). The thought is that extensional relations must be able to account for the features of whatever entities Aristotle has to discuss, as well as the logical rules that are based on them. It is a merit of the commentary that its author is aware of such relations, but does not get too distracted by them. She rightly concentrates her focus on reconstructing the “local”, contextual factors which determine the truth conditions for the predication of a definition in a given context of use.
Topics VI features not just rules concerning relations, but also points of style. Top. VI.1 introduces two parts of studying cases in which one has not defined well (139b12–18). One part concerns the extension of the definition and its asymmetry with the extension of the definiendum. But the other part of the study concerns the use of unclear expression (139b12–13). The points concerning the use of homonymous linguistic expression, metaphor, non-standard language, and jargon are not easily accounted for by Schiaparelli’s otherwise plausible thesis that the commonplaces of Top. VI are basically refutative. These seem to be points of criticism such as a judge or critic of dialectical bouts might make (see Top. VIII.11 for remarks on the critique of argument). This is a difficult feature of the style used in the Topics itself: the level at which certain commonplaces are entered is not homogenous, and there are relatively few signposts as to their bearing. Still, the criticism of unclear expression as well as Aristotle’s excursus on the norm that definition be from what is “more familiar” (Top. VI.4) have a distinctly pragmatic character. If someone defines by what is less familiar to the addressee or per se, they fail to meet a Gricean maxim of relation or relevance; if someone repeats the same element twice in the definition, they violate a maxim of quantity. To point this out is not refutative in the same way that showing a failure of extension would be.
Still, there is an abundance of material in Top. VI concerning the objects or items with respect to which definitions may be verified or refuted: genus (VI.5), difference (VI.6), relatives (VI.8–9), parts and wholes (VI.13–14). These passages have a metaphysical character, and to them Schiaparelli brings to bear extensive reading and thinking on Aristotle’s metaphysics. The work of sifting through various remarks scattered through the corpus on relatives or differentiae, for example, to square them with the relevant material in Top. VI is intricate and delicate. Schiaparelli does it well, and the parts of the commentary relating Aristotle’s dialectical observations to a larger metaphysical context I found especially illuminating. Still, the going can be hard. Readers seeking help with Aristotle’s difficult text might sometimes be discouraged to find relatively long notes on quite complex issues which do not make comprehension easier. In some parts of the commentary, shorter clarifying remarks might have been helpful. But the significant work of bringing together many strands for the better comprehension of quite difficult passages has been done diplomatically and well. There is much good, honest interpretive work in this commentary, and it will be an enduring resource for the study of this generally understudied text.
Where does this leave us with our understanding of Aristotle’s logic before the syllogistic? The commentary draws our attention to the many places in which the theorist of dialectic makes normative judgements about the appropriate use of language; it is almost as if the critic of dialectical exercises were making language better suited for valid (i.e., truth-preserving) inference. Aristotle sometimes recommends linguistic conservatism, in an attempt to reduce problems of meaning-opacity (Top. VI. 10, 148b16–22); Schiaparelli is very much attuned to the importance of such remarks. They are not offered only in the spirit of making our ideas clear, as Peirce once put it. The larger project of Aristotle’s theory of dialectic provides the means for evaluating conversational deductions by giving a wide array of standpoints or topoi from which they can be attempted, criticized, and evaluated. Moreover, Aristotle’s theory of essential predication as it appears in the Topics has been the basis for a reconstruction of the semantics of the modal syllogistic. By valorizing the semantics of the Topics, one has made the background metaphysics of this text much more important and interesting. Schiaparelli’s careful consideration of the metaphysical background assumptions of Aristotle’s theory of definition will be of interest also in this regard. It is to be hoped that the distinguished Clarendon Series will see to having more core books of the Topics covered, and covered so well.
Reviewed by Colin Guthrie King, Providence College