In ‘The Stoics on Conceptions and Concepts’, Katerina Ierodiakonou offers an account of the Stoics’ distinction between ennoiai and ennoēmata (‘conceptions’ and ‘concepts’), and also of the distinctions suggested by the standard Stoic terminology of concepts also mentioned above: notably, prolēpseis (‘preconceptions’), phusikai ennoiai (‘natural conceptions’), and koinai ennoiai (‘common conceptions’). All these terms appear intended to point to general notions that play a central role in the acquisition of human knowledge, but it remains puzzling how exactly the Stoics understood them or why they introduced them into their doctrine in the first place. Ierodiakonou addresses these issues, as well as further questions debated in the secondary literature. These include whether all human beings necessarily possess concepts or just have the ability to possess them, what is the content of conceptions and how it is determined, what is the ontological status of conceptions and concepts, and what are their epistemological functions.

Chapter 2 explores the right to make use of medically assisted procreation to conceive a child, upheld by the Strasbourg Court as an expression of private and family life. It discusses limitations based on ‘the rights of others’ (e.g. the other gamete provider in disputes over embryos) and ‘morals’ (e.g. public policy objections to heterologous fertilisation, surrogacy and the posthumous use of cryopreserved gametes/embryos). The chapter argues that the refusal to treat couples with donated gametes imposes a choice between genetic parenthood and the continuance of marriage to an infertile spouse, affecting both prospective and existing family life. It further maintains that reproductive autonomy should extend to posthumous reproduction where the deceased left advance directions and there are no overriding child welfare concerns. The chapter notes the recognition of legal ties between children and genetic parents in foreign surrogacy cases, albeit exclusively through the lens of children’s privacy (identity) rights.

Chapter 4 argues that there is a (limited) human right to a healthy child, to the extent that medical technologies are available to detect and prevent disease in the future offspring at the conception or gestation stage. It considers two claims arising in Strasbourg litigation: access to timely, accurate prenatal testing and to the termination of pregnancy on grounds of foetal abnormality, and the selection of healthy embryos through pre-implantation genetic diagnosis by aspiring parents afflicted by serious hereditary illnesses. While many judgments are country-specific and regard the failure to correctly implement existing laws or the adequacy of remedies in case of errors, the chapter also questions the legitimacy of total bans on embryo/foetal selection against disability; it maintains that, notwithstanding possible objections based on, inter alia, the message sent by permissive laws to existing disabled people and the human dignity rhetoric, they fail to satisfy the principle of proportionality.

Experience is the cornerstone of Epicurean philosophy and nowhere is this more apparent than in the Epicurean views about the nature, formation, and application of concepts. ‘The Epicureans on Preconceptions and Other Concepts’ by Gábor Betegh and Voula Tsouna aims to piece together the approach to concepts suggested by Epicurus and his early associates, trace its historical development over a period of approximately five centuries, compare it with competing views, and highlight the philosophical value of the Epicurean account on that subject. It is not clear whether, properly speaking, the Epicureans can be claimed to have a theory about concepts. However, an in-depth discussion of the relevant questions will show that the Epicureans advance a coherent if elliptical explanation of the nature and formation of concepts and of their epistemological and ethical role. Also, the chapter establishes that, although the core of the Epicurean account remains fundamentally unaffected, there are shifts of emphasis and new developments marking the passage from one generation of Epicureans to another and from one era to the next.

The chapter ‘Concepts in Greek Mathematics’ by Reviel Netz problematises a set of assumptions commonly encountered in the literature on Greek mathematics, which typically derive from a supposedly objective, a-historical conception of mathematical theory and practice. In sharp opposition to that tradition, Netz raises the possibility that the purpose of engaging with mathematical concepts may have been different in antiquity than what it has been taken to be. He asks central questions afresh, for instance: why do mathematical texts begin with definitions, and what is the purpose of mathematical definitions and of axioms. In connection to these issues, he highlights new aspects of the relationship between Greek mathematics and Greek philosophy, between engaging with mathematical concepts and philosophical thinking. He also advances the thesis that the relations between mathematics and philosophy changed through the various eras of antiquity, as did mathematical concepts and the role of mathematical definitions. We should seriously entertain the idea that even mathematical concepts need to be viewed within a given historical and cultural context.

In ‘The Emergence of the Concept in Early Greek philosophy’, André Laks argues that we can trace the first inklings of thinking about concepts by paying close attention to early Greek answers to the following three questions: how is perceptual information reached and processed by the mind, what is the relationship between perception and thinking, and how do the early Greek philosophers account for name-giving? First, Laks discusses whether the explanations of sensory mechanisms offered by the early Greek philosophers as well as by the medical authors might have prepared the ground for later theories of concept formation. Second, he argues that we should resist the Aristotelian report according to which the early Greek philosophers identified thinking with perceiving. In fact, we have good reasons to assume that early Greek philosophers attempted to offer an account of the process of thinking. The final section of the chapter turns to the question of the relationship between giving names to things, and forming and grasping the corresponding concept.

Lesley Brown’s chapter ‘Do Forms Play the Role of Concepts in Late Plato?’ starts by noting a major issue of controversy concerning the Forms in the Middle Dialogues, namely whether Forms are explanatory properties whose role is to account for why things are the way they are and are therefore the objects of philosophical inquiry and knowledge, or whether Forms are concepts whose role is to explain everyday thinking and discourse. On the assumption that the former option best captures the role of Forms in Plato’s so-called Middle Dialogues, Brown addresses the question whether Plato’s later dialogues manifest a shift in emphasis such that the latter interpretation gains greater prominence. In her view, even though Plato’s later dialogues show increasing interest in matters of language and meaning, and hence may perhaps be taken to show a somewhat greater interest in the role Forms or Kinds play in our everyday thinking and discourse, nonetheless the prominence of the method of division in these works underscores that the Forms are primarily properties discoverable by philosophical inquiry, not everyday concepts or meanings.

Péter Lautner’s chapter ‘Concepts in the Neoplatonist Tradition’ expands the scope of the enquiry by discussing Platonist theories of concept formation in Late Antiquity. Generally speaking, the philosophers belonging to the so-called schools of Athens and Alexandria believe that the articulation of our rational capacity and the acquisition of knowledge somehow derives from the senses as well as the intellect, and they mostly agree that some elements of concept formation, notably generalisation, occur on the basis of sense-perception. They disagree, however, as to whether or not such generalisations are full-blown concepts. While all the philosophers under consideration endorse some version of the view that the main source of concepts is our intellect, which essentially contains fully fledged concepts, their accounts vary in respect of the intellect’s ability to project concepts onto the lower cognitive faculties. The problem of how the two kinds of concepts mentioned above are related to each other occupies the Platonists through the entire period under examination and constitutes the focus of Lautner’s analysis.

‘Contested Concepts: Plutarch’s On Common Conceptions’ by Thomas Bénatouïl addresses the question of how ordinary concepts, for instance a layman’s concept of a spider, intersect with a zoologist’s concept of that insect. While from the epistemological point of view the latter’s concept should be allowed to prevail, from the point of view of semantics and the philosophy of mind it is not at all obvious that the scientific concept of spider should be allowed to rule over the corresponding lay concept, nor is it obvious that there is only one concept of spider whose content can be fixed for every context. Clearly, the Academics and the Stoics were aware of the importance of this and related problems. Plutarch’s dialogue On Common Conceptions, subtitled Against the Stoics, is a representative text of these schools’ respective stances, and its study by Thomas Bénatouïl aims to bring out both its historical significance and systematic interest.

In ‘Aristotle on the Stages of Cognitive Development’, Thomas Kjeller Johansen examines Aristotle’s contributions to our thinking about concepts from a different perspective, namely in connection to Aristotle’s psychology. He revisits Aristotle’s account of how we acquire universal concepts mainly on the basis of Metaphysics A.1, Posterior Analytics 1.31 and 2.19, and the De Anima. The chapter begins by articulating the following puzzle. On the one hand, Aristotle points out (An. Post. 1.31, 2.19) that we perceive the universal in the particular. On the other, he suggests (Metaph. A.1) that it is only when we have craft and science that we grasp the universal, while perception, memory, and experience all are concerned with the particular. Building on the widespread view that, according to Aristotle, the universal grasped in craft and science is the universal cause, Johansen argues that we should understand perception, memory, and experience teleologically, as stages in the ordering of perceptual information that allows this causal concept to emerge.

In ‘Platonist Notions and Forms’, Mauro Bonazzi explores an aspect of the Platonists’ engagement with Stoic epistemology, namely the Platonists’ appropriation of the Stoic ennoiai, conceptions or notions, to show that Plato’s doctrine can provide a satisfactory answer to the problem of the foundation of knowledge, which Stoicism has proved unable to solve. The Stoic ennoiai, (conceptions) or phusikai ennoiai (natural conceptions) are notions naturally arising in the human mind and constituting the basic elements of human reason. They are ‘natural’ in the sense that humans are naturally disposed to acquire them, and they are koinai (common) in the sense that all humans have them or are disposed to have them. They are also invariably true and therefore can serve as criteria in order to increase knowledge, promote scientific understanding and contribute to the good life. It is these ennoiai that the Platonists integrate in their own reinvention of Plato’s epistemology and employ in their polemics against their principal rivals.

The Conclusions put forward a first catalogue of procreative rights based on the claims successfully asserted in international case law to date. Obstacles to the development of procreative rights are also considered, from jurisdictional issues (such as the recognition of the subsidiary nature of international human rights law and States’ margin of appreciation in sensitive areas) to certain underlying assumptions in the judicial analysis (e.g. the importance of marriage as a foundation for intentional non-genetic parenthood). Finally, this closing chapter examines incipient and potential rights, that is, claims which have not yet been raised in international litigation (some currently pending in Strasbourg) or which were left to the discretion of national legislatures. Although many procreative rights are still aspirational in nature, it is suggested that the continuously evolving interpretation of the ECHR, aligning its requirements with medical advances and social perceptions, will eventually expand the scope of procreative autonomy in international law.

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.