From pre-theoretical ideas about paradox, truth, fallacy and contradiction to the systematic study of logic and innovations in logical theory like syllogistic and propositional logic, the ancient period in the Western tradition was both enormously productive and hugely influential. This volume, which aims to give both student and expert readers insight into the development, richness, reception and significance of ancient logic in the Western tradition, is therefore a welcome addition to the Cambridge Companion series.
Edited by Castagnoli and Fait, the Companion is divided into three sections. The first section explicitly concerns the chronological and philosophical development of ancient Greek logic. N. Denyer deals with the period before Aristotle (Chapter 1). He gives readers a sense of the agonistic context of argument in ancient Greece and points to some of the interesting and important pre-theoretical ideas that this motivated. Fait explores the extent to which Aristotle's work marked an important break with that of his predecessors and discusses Theophrastus’ development of Aristotle's thought (Chapter 2). K. Hülser casts light on the historical and logical connections between the Megarian and the Stoic schools (Chapter 3). B. Morison's nuanced chapter about logic in late antiquity (Chapter 4) is one of the strongest in the volume and makes a crucial contribution in addressing the question (in the context of late antiquity) that readers will find themselves asking, namely ‘what the discipline of logic is trying to achieve and what role it has within philosophy as a whole’ (p. 82).
Unfortunately, the burden of discussion of the development of logic before Aristotle in this section falls to Denyer. Whilst Castagnoli and Fait fill in resulting gaps concerning Plato in their introduction, it is disappointing not to find more about the Presocratics, whose contributions seem to be worth far more discussion and which extend beyond the obvious. For example, it seems to me that it is with the Presocratics that we find the beginnings of particular kinds of arguments that were later developed and criticised. Xenophanes’ B15–B16, which show that the anthropomorphic way in which the gods tend to be conceived of leads to absurdity, are, I take it, intended to lend support to Xenophanes’ view that the highest god is not anthropomorphic. This seems to be something approaching a reductio ad absurdum (since p leads to absurdity, not-p). Similarly, Zeno's paradox of place seems to be an infinite regress: if everything that exists has a place, every place will have a place, which will have a place and so on ad infinitum.
The second section makes up the majority of the volume and concerns the defining problems and features of Western ancient logic. W. Cavini, taking the concept of logical truth in Aristotelian and Stoic logic to be a kind of alethic realism, examines the nature and role of the semantic predicates ‘true’ and ‘false’ as well as logical principles within this framework (Chapter 5). M. Ferejohn tackles definition, focusing particularly on the texts of the late Plato and on Aristotle's Categories, Topics and Posterior Analytics (Chapter 6). P. Crivelli explores issues concerning terms and propositions in Plato, Aristotle and the Stoics (Chapter 7). Castagnoli and Fait compare syllogism in Aristotelian, Stoic and contemporary logic (Chapter 8). A. Bown looks at demonstration in Aristotle, the Stoics and the Epicureans (Chapter 9). M. Malink focuses on modality and its role in Aristotle's logic as well as Theophrastus’ and Eudemus’ criticisms of Aristotle's modal syllogistic and ideas about the nature of modalities in the Megarics and the Stoics (Chapter 10). Castagnoli outlines some of the theories of and responses to fallacy in Plato, Aristotle and others, notably Sextus Empiricus, Chrysippus and Cicero (Chapter 11). C. Rapp's chapter concerns logic as a tool in rhetoric pre-Aristotle and post-Aristotle as well as in Aristotle himself (Chapter 12). R. Netz examines the relationship between ancient Greek logic and mathematics (Chapter 13).
The chapters in the second section are mainly appropriate for students. (One wonders if this is in part because Castagnoli and Fait anticipate that another volume co-edited by them, Ancient Logic [2024], will deal with similar issues, but for a solely expert audience.) Nonetheless, the Companion certainly delivers on its promise to cover key themes – and in fact goes beyond what one might expect with Rapp's and Netz's treatments of rhetoric and mathematics (Chapters 12 and 13). Every chapter is of high quality, and none could be substituted with material published elsewhere; even Crivelli, who incorporates some of the material on Aristotle previously used in his ‘Aristotle's Logic’ (in: The Oxford Handbook to Aristotle [2012]), offers a far more detailed treatment of Aristotle here and also notes interesting contrasts between Plato, Aristotle and the Stoics. Moreover, the authors focus on a theme in the context of multiple individuals or schools, which yields further insight into the development of logic and an appreciation of the complex ways in which philosophers in antiquity engaged with one another.
Of course, this is an approach that is difficult to pull off in such brief chapters without omitting important details. However, I found only one minor case that bears mentioning where further detail would have been beneficial. This occurs in Chapter 6. Ferejohn rightly notes that the following seem to be demands in Plato's early dialogues:
1. Co-extensionality: the definiens must be neither broader nor narrower than the definiendum (pp. 129–30);
2. Explanatory priority: that which satisfies the definiens must explain why it satisfies the definiendum and not vice versa (p. 130);
3. Non-contingency: the features mentioned in the definiens must belong necessarily to instances of the definiendum (p. 130).
However, in the Meno one of the complaints Socrates makes about Meno's definition of virtue as the ability to acquire good things with justice is that he is not keeping it whole (ὅλον); rather, the definition specifies one of its parts (μόριον) (79a9–c9). This seems to be problematic in light of 2: since justice is a part of virtue, a definition that features justice is not sufficiently explanatory. Establishing exactly how we should understand the part–whole relationship here and why it means that justice is not explanatorily prior to virtue is not straightforward. But whatever the answer is, the specific mention of parts seems to merit attention in Ferejohn's chapter since parts and wholes are clearly significant for the issue of definition in both late Plato and Aristotle, which Ferejohn goes on to discuss in detail.
The final section concerns the reception and influence of Aristotelian and Stoic logic. J. Marenbon compares the place of Aristotelian logic in the Latin and the Arabic traditions (Chapter 14), M. Capozzi and L. Haaparanta cover the period from the Renaissance to the twentieth century (Chapter 15), and J. Woods deals with Aristotle's and Stoic logic in a contemporary context (Chapter 16). This section gives readers insight into the importance and influence of logic in Aristotle and the Stoics. However, whilst Marenbon does remarkably well to cover as much about Latin and Arabic philosophy as he does, a single chapter for the reception of Aristotle in both hardly seems sufficient for this volume, given the sheer scale of engagement with Greek logic in each tradition.
There is much to be admired in this volume. It undoubtedly has student appeal. This is particularly evident in Denyer's chapter (Chapter 1), which is bound to challenge any preconceived ideas that a student might hold of all matters of logic as dull and abstract, and in the care that Crivelli takes to explain different interpretations and textual issues without pressing his own view too strongly (e.g. p. 160). The volume is also useful, albeit to a lesser extent, for the expert. For example, rather than point out better-known connections between contemporary analytic philosophy and logic in the Western tradition, such as contemporary solutions to Zeno's paradoxes or the connections between being, not-being and non-existent objects, Woods makes rather more novel points. Moreover, the volume undoubtedly provides a good overview of ancient logic in the Western tradition. It also offers insight into its development and significance.
However, there are two problems that mean that some readers will find the volume unpalatable. The first stems from the title: The Cambridge Companion to Ancient Logic. This wording suggests that ancient Western logic is ancient logic. Yet, logic was far more widespread in antiquity. The implied identity of ancient logic with ancient Western logic continues, when one opens the volume, with the short description of its contents. The introduction, which follows, begins with a substantive discussion of Plato, through which readers are given the impression that ancient logic (in the non-systematic sense) begins with him – which anyone familiar with logic of other traditions will find objectionable. It is not until p. 16 that the editors explicitly acknowledge that there are other rich logical traditions (they mention Indian and Chinese). This is not merely misleading. It also devalues philosophy of other traditions and will consequently alienate some students and experts. And whilst it is true that Castagnoli and Fait acknowledge the existence of other important logical traditions, the significance of this should have been far more carefully considered.
The second issue is the gender imbalance. Both editors are men, and fifteen of the sixteen chapters are written by men. This is surprising since many important studies on ancient Western logic, its development and reception have come from women (see e.g. S. Broadie, Passage and Possibility [1982]; V. Harte, Plato on Parts and Wholes [2002]; K. Ierodiakonou, ‘Logic and Knowledge’, in: The Routledge Companion to Ancient Philosophy [2012]; L. Jardine, ‘Logic and Language: Humanistic Logic’, in: The Cambridge History of Renaissance Philosophy [1988]; M.M. McCabe, ‘Persistent Fallacies’, Proceedings of the Aristotelian Society 94 [1994]; G. Striker, ‘Assertoric vs. Modal Syllogistic’, in: From Aristotle to Cicero: Essays in Ancient Philosophy [2022]) – and the enormous influence of S. Bobzien's prolific work on ancient Western logic on the volume is evident from a quick glance at the bibliography (pp. 374–5).
Of course, the volume is hardly exceptional in displaying these problems, and many readers will be willing to overlook them, especially given the quality of its contents. But by now we should be doing better.
