In ‘Early Learning in Plato’s Republic 7’, James Warren provides an analysis of Socrates’ account of the sort of early learning needed to produce philosopher-rulers in Republic 7 (521c–525a), namely a passage describing a very early encounter with questions that provoke thoughts about intelligible objects and stir up concepts in the soul. Warren explains how concepts of number, more specifically the concepts ‘one’, ‘two’, ‘a pair’, and so on, play an essential role in these very early stages of the ascent towards knowledge, and he stresses the continuity between the initial and very basic arithmetical concepts and the concepts involved in more demanding subjects taught in later stages of the educational curriculum. On this account, Socrates is prepared to ascribe to more or less everyone an acquaintance with some, albeit elementary, intelligible objects. This, in turn, can shed some light on broader debates in Platonic epistemology about the extent to which all people – not just those whom Socrates calls philosophers – have some conceptual grasp of intelligibles.

Engaging directly with the question whether Platonic Forms are concepts, David Sedley’s chapter ’Are Platonic Forms Concepts?’ takes its start from the Parmenides 132b–c, where Socrates and Parmenides briefly examine the hypothesis that Forms are ‘thoughts’ (noēmata). Sedley asks what ‘thoughts’ are in that context, and argues that they are not thought contents, but acts of thinking. The chapter offers an ambitious and comprehensive analysis of the classical theory of Forms as showcased in the Phaedo, Republic, Parmenides, and Timaeus, in terms that clarify why Plato was bound to reject the hypothesis considered in the Parmenides (132b–c), namely that Forms are thoughts.

In ‘Doing Things with Concepts in Sextus Empiricus’, Richard Bett examines Sextus’ terminology in connection to his use of such strategies and highlights their inventiveness and sophistication. On the one hand, Sextus appears to agree with his dogmatic opponents insofar as he says that we need to get our concepts clear before investigating any topic. On the other hand, he often raises objections against dogmatic concepts, arguing, for instance, that they are inherently inconsistent and therefore there are no objects corresponding to such concepts or, alternatively, that even if we accept these concepts, there exists nothing real corresponding to them. It is not clear whether or how these two lines of approach can be coherently combined. Nonetheless, Sextus frequently runs the two together, and Bett enquires into his reasons for doing so. An important upshot of this study is that it leads us to consider what kinds of concepts and what sort of reflection about concepts are available to a sceptic of Sextus’ variety.

The chapter ‘Alexander of Aphrodisias on Concepts’ by Frans A. J. de Haas takes up another aspect of concept theory, that is, the endeavour to define what a concept is. Furthermore, he explores the interactions between the Peripatetics and the Stoics, as they are evidenced by Alexander, on ontological as well as psychological and epistemological issues. De Haas also offers a systematic study of part of Alexander’s rich vocabulary denoting concepts, thoughts, and universals, and of a correspondingly rich collection of verbs referring to the human activities of abstracting or constructing concepts. Importantly, this analysis sheds light on Alexander’s understanding of ennoia and noêma, and on Alexander’s views concerning the epistemic reliability of concepts and the unity of concepts in the human soul.

Problematisation about concepts and related notions in Aristotle greatly depends on the particular work or works under consideration. Richard McKirahan’s contribution ‘Concepts and Concept Formation in Aristotle’s Logical Works’ argues that an account of how concepts are formed may be extracted from passages of the Organon, on topics relating to the problem of how we gain knowledge of scientific principles, in combination with Aristotle’s statements on the relations among objects in the world, affections in the soul, and language. Aristotle’s view is pieced together on the basis of the account in Posterior Analytics 2.19, supplemented by the parallel account in Metaph. A.1, as well as Aristotle’s remarks on the utility of dialectic for the sciences in Top. 1.2 and the brief discussions of epagōgē (frequently and controversially rendered by ‘induction’: An. Post. 1.18 and 1.31). The chapter also addresses questions about the nature of perception as conceived in the Organon, the epistemic status of experience, the transition from the awareness of individuals to the grasp of universals, the status of nous, and the relation between universals and concepts.

‘Concepts and Universals in Aristotle’s Metaphysical Thought’ by Christof Rapp starts with the recognition that Aristotle does not have a general term for ‘concept’ and examines which entities in his metaphysical theory might play the role of concepts. According to Rapp, many of Aristotle’s discussions focus on the meaning of general terms and whether they signify something real and existing independently in its own right. Aristotle remains committed to the view that universals as captured by genuine definitions are crucial for human knowledge and understanding. Insofar as Aristotle resists a conception of universals as existing in the way that particular substances do, he can be taken to intimate that universals are ‘merely conceptual’. In the Metaphysics, he distances himself from the view that universals such as genera and species qualify as substances. His main contribution to our thinking about concepts consists in the view that both universals and embodied substantial forms have mental counterparts, by which we grasp and understand the things falling under the conceived form or essential definition.

The Introduction by Gabor Betegh and Voula Tsouna outlines the historical and philosophical objectives of the volume, identifies principal questions and challenges that the authors are invited to address, gives summaries of the individual chapters, and specifies the contribution of the volume to the history of scholarship and to contemporary philosophical thinking about concepts. Especially useful is the survey of the technical or quasi-technical terminology used by the ancient authors in order to talk about concepts and related notions. This terminology is rich and nuanced and, as the editors point out, sorting it out is not merely a lexical matter but an inextricable part of the analysis of substantive philosophical questions.

Matthew Duncombe’s chapter ‘Relative Concepts’ asks: what are relative concepts according to ancient philosophers? Duncombe argues that Plato, Aristotle, and the Stoics have a clear concept of relatives, distinct from incompleteness approaches, which he calls ‘constitutive relativity’. The core idea of constitutive relativity is that a relative is constituted precisely by the relation it bears to an exclusive correlative. Duncombe discusses particular philosophers and schools in detail. The examination of Agathon’s speech in Plato’s Symposium illustrates that Socrates understands relative concepts in general and love in particular, on the constitutive model. Aristotle’s concept of relatives in Categories 7 draws on Plato, but Aristotle addresses a worry that relative concepts might be vacuous. Duncombe argues that a Stoic relative concept is the concept of a relative that relates exclusively to a correlative. He examines Sextus’ sceptical argument, which raises a worry about any conception of relativity where relatives relate exclusively to their correlatives.

In ‘The Place of Concepts in Socratic Inquiry’, Terence Irwin examines Socrates’ question ‘What is F?’, which is often taken to be a request for some sort of definition or account of what F is. When Socrates asks, ‘What is courage?’, ‘What is piety?’, ‘What is temperance?’, does his discovery that everyone, including himself, cannot answer such questions in a satisfactory manner imply that these answerers do not know what the words mean? If one cannot answer the ‘What is F?’ question, does it follow that one lacks the concept of F? Irwin argues that conceptual argument has an indispensable role in the arguments that lead to Socratic definitions, but it will not take us all the way to them. To understand Socratic definitions, Irwin compares them with Aristotelian real definitions, and with Epictetus’ views on the articulation of preconceptions.

Plotinus’ views on concepts have so far received little attention, whereas his views on ennoiai, conceptions, have been more widely discussed. This is partly due to the varied vocabulary that Plotinus uses to refer to what we might call concepts, assuming that the latter are understood as mental items distinct from thoughts. Sara Magrin’s chapter ‘Plotinus on Concepts’ focuses on one important passage of the Enneads (Ennead 6.6.12–14) which offers a critical discussion of an account of the concepts (ennoēmata) of one and numbers commonly attributed to the Stoics. The chapter pursues the twofold aim of reconstructing the account in question and of interpreting and assessing Plotinus’ criticism of it. This has scarcely, if ever, been attempted in the scholarship, both because the evidential value of that passage in respect of the Stoics has been deemed questionable and because Plotinus’ criticism of the Stoic concept of number is extremely compact and difficult to articulate. The main contribution of Magrin’s analysis consists in her use of Plotinus’ criticism of the Stoics as evidence, on the basis of which she pieces together Plotinus’ views on concepts.

‘Early Christian Philosophers on Concepts’ by George Karamanolis integrates some of the themes encountered in previous chapters into the broad theological perspective of the early Christian thinkers, according to which explorations in every area of philosophy are ultimately intended to reveal aspects of God’s relation to His creation. It is argued that the position of the early Christian philosophers on concepts is part of their perceptual realism and their stance against scepticism. Karamanolis examines three case studies: the theories of Clement of Alexandria, Origen, and Gregory of Nyssa. In all three cases, he maintains, concepts are treated both as mental representations and semantic/linguistic items through which we grasp reality. Clement develops his view on concepts in the context of an anti-sceptical elaboration of his thesis that knowledge of the world is propositional and attainable by humans, while Origen and Gregory of Nyssa defend more sophisticated theories of concepts in connection with their respective epistemologies. In every case a theological question motivates the Christian author’s stance with regard to the nature and formation of concepts.

This chapter sums up the main argument of the book and offers a brief overview of the reception of the Epicurean theory of justice.