Definition and Essence from Aristotle to Kant

For all the effort that philosophers have put into defining things, there is surprisingly little modern attention paid to the question of what a definition is. Over the centuries, however, there has been a great deal said about what definitions are and what purpose they serve. From an historical point of view, such discussions have opened up rich avenues of inquiry into foundational issues in metaphysics and epistemology. We historians, taking our lead from contemporary concerns, have not taken much notice of these long-running disputes. The topic is ripe for exploration.

Peter Anstey and David Bronstein have assembled an admirable collection of papers that seeks to do just this, based on a conference held in Sydney in 2019. As one might expect, Aussies are well represented, but overall the contributors are an impressively international group. The volume exemplifies all the virtues of an edited collection. First, it offers an awesomely wide scope, not just chronologically but also topically, inasmuch as the chapters range variously over science, mathematics, logic, language, and core questions of M&E. Second, it achieves this range without sacrificing expertise: chapter by chapter, we are delivered into the hands of first one expert and then another. To be sure, the volume also exhibits the constraints of the genre. The historical coverage is full of gaps, the specific topics discussed are a haphazard mix, and—in keeping with the unfortunate convention of this genre—none of the chapters engages with any of the others. Still, the quality of each individual chapter makes the volume as a whole a tremendous success.

The chapters are roughly equally split among ancient, medieval, and early modern material (all European), and nine of the twelve are focused squarely on definition. On the face of things, it is an oddity that the volume begins with Aristotle, and so omits what one might take to be the most historically important treatments of definition in the whole canon, those of Socrates and Plato. But this turns out to be a good-making feature, because it allows the volume to focus more squarely on the Aristotelian theory and reactions against it, which is how conversations about definition mostly take shape in the philosophical traditions that emerge from ancient Greece.

Although the notion of essence appears in the title, essences generally play a secondary role in the volume. That role is important, however, because one of the hallmarks of the Aristotelian approach is that the object of a definition is an essence. (P. 14 of Bronstein’s opening chapter quotes Topics 101b38 on a definition as “an account [logos] signifying the what it is to be [to ti ēn einai].”) Accordingly, one of the overarching themes of the volume is the way in which philosophers variously seek to respect or reject the relationship between definitions and essences. One mark of philosophy’s gradual drift away from Aristotle is the growing number of authors who abandon the goal of defining essences. Calvin Normore explains that, by the time of the nominalists of the fourteenth century, the object of a definition is always a word (151). Some definitions nevertheless are real, expressing the quid rei, which is to say that they define a word in such a way as to capture the essences of things. A nominal definition, in contrast, yields only the quid nominis, which is to say that it offers merely an expression that can be used synonymously with the term being defined. By the time of Hobbes, the very notion of an essence falls into doubt: an essence is simply “that accident for which we give a certain name to any body” (as quoted by Normore, 156).

According to the volume’s introduction, “Aristotle is the first figure in the Western intellectual tradition to articulate a theory of definition” (2). No doubt, Aristotle has no earlier rival in setting out a theory in such explicit and systematic detail. Crucial to that project is the role definitions play in science (i.e., epistēmē). According to Posterior Analytics 99a21, “all the sciences come about through definition”. Bronstein quotes that remark (37) and works out in careful detail what it means. Definitions are of special importance to Aristotle because of the crucial role they play in demonstration. Some definitions are the indemonstrable starting points of a demonstration, whereas others fall out as the conclusion of a demonstration (Bronstein, 19–21). The Posterior Analytics offers a handful of familiar toy examples of how this goes but, across Aristotle’s corpus, one famously finds few developed examples of the method being put to work.

That lacuna gives extra value to James Franklin’s chapter on definition in Euclid. Definitions are of course a crucial feature in the Elements, and Franklin offers examples of what work they do there. Against those who suppose that all definitions are nominal, Franklin argues that the case of mathematics, in antiquity and in modern times, makes a case for the significance of the search for real definitions. Interestingly, though, he argues that what makes this search tractable in the mathematical case is that such definitions pursue objects in the category of Quantity. Outside of mathematics and allied fields, those who have sought to advance their accounts more geometrico have involved themselves in “wild goose chases”, producing work that is “close to useless” (52). Franklin goes on to assess why these projects can succeed in quantitative domains but not when we seek to define the essences of substances.

The many and varied lights that the volume shines on the Aristotelian tradition make clear that the dream of a demonstrative science founded in real definitions had its critics from the start. Katja Vogt shows that the Stoics reject the very idea of a single privileged definition, and regularly deploy multiple non-exclusive definitions for the same thing. This is of a piece with their rejection of the very idea of forms or essences. If we jump ahead to Thomas Aquinas, as discussed by Gabriele Galluzzo, we find a view that embraces the Aristotelian methodology of demonstration grounded in definition. But even Aquinas thinks that our definitions fail to grasp the essences of things. When we seek to frame a real definition in terms of genus plus differentia, we in practice can do no better than offer accidental differentiae that serve as signs of the unknown essential differentia (Galluzzo, 143). So, yes, human beings can be defined as rational animals, but that complex expression merely points at the unified thing that is the substantial form of a human being, whose true nature we are largely ignorant of. Aquinas, to be sure, is quite different from Hobbes, in that for Aquinas it is crucially important that human beings have a substantial form, which is their immortal soul. But in terms of their scientific methodologies, the difference is less than one might expect, since Hobbes too thinks, as Anstey puts it in his chapter, that “all scientific knowledge is demonstrated from definitions” (196).

There is, however, something deeper that divides the camp of Aquinas and his nominalist critics from the camp of Hobbes and his contemporaries. For when medieval Aristotelians endorse essences, they commit themselves not just to the idea that every substance within a species shares a cluster of properties that are necessary and jointly sufficient for membership within that species. More than that, they endorse the causal thesis that substances have an inner explanatory principle that accounts for all of the intrinsic features of the thing. (Anstey and Bronstein, in their introduction on p. 2, refer to this as the explanation condition.) For Aristotelians, the object of definitions is that inner principle, and definitions are meaningful within science precisely insofar as they capture these explanatory structures. Aquinas may not have thought that we can succeed in fully understanding the essences of things, but he did think we could frame definitions that track these structures well enough to be useful. In contrast, once the project of real definition falls entirely out of favor, the whole Aristotelian theory of demonstration starts to look misguided.

The volume’s later chapters offer various illustrations of this transformation. For Descartes, as Deborah Brown understands him, definitions play a role “that is more pedagogical than epistemic’ (171). For Arnauld and Nicole, in the Port-Royal Logic, only nominal definitions can serve as principles in demonstrations, with the result, as Anstey puts it, that “real definitions have little or no role in the discovery of scientific knowledge” (205). Laura Kotevska’s chapter on the Port-Royal Logic shows that its focus on nominal definitions comes with a deemphasis of the syllogism, and a concern for using definitions to make sure of the connection between words and ideas. John Locke, similarly, takes the role of definitions to be “making another understand by Words, what Idea, the term defined stands for” (Essay III.3.10). Anstey quotes this passage, remarking that Locke “does not accept the view that definitions function as principles in demonstrative sciences” (209). These developments are put most vividly on display in Kirsten Walsh’s chapter on “proof by experiments in Newton’s Opticks”. In a sense, this chapter has little to do with the other chapters in the volume, but that is part of the point. Walsh shows that Newton’s famous series of experiments with a prism offers a “proof” that relies only marginally on definitions and axioms, and instead attempts to construct “a new kind of proof” (245), one based not on indemonstrable premises but instead on experiment. With this, we have left the domain of Aristotelian definition entirely.

I hope the preceding remarks provide a sense of how much there is to be learned from this volume. Let me close with two brief remarks on the book’s production. First, as one expects from Routledge, each chapter has its own bibliography, and endnotes rather than footnotes. The former practice makes good sense in an era where these chapters will circulate mainly as separate files. Perhaps Routledge regards the latter practice as expressing a distinctive style, but to the reader, it comes off simply as cheap. Second, an impressive amount of attention has been given to copy editing and proofreading. I could find only three minor blemishes of this kind across the whole volume. In an era where publishers have largely stopped caring about such matters, the participants here are to be congratulated for taking the time to get this right.

ACKNOWLEDGMENTS

Thanks for their advice to Jacob Calhoun and Matthew Wennemann.