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.

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 reconstructs Heidegger’s interpretation of Kant’s Metaphysical Deduction and Schematism. In Heidegger’s view, these two sections inquire into the source of the categories that human understanding possesses a priori. Heidegger’s reading of both sections exhibits a characteristic move of his interpretive method, where he sees an innovative line of argument prioritizing the imagination emerge from a more traditional setup. The reconstruction also reveals some variety in how one can apply Heidegger’s interpretive method to the different parts of a text. Heidegger suggests that the traditional strand of argument is more prominent in the Metaphysical Deduction; while Kant attempts to derive the categories from the atemporal logic of the understanding, his references to the faculty of imagination at certain critical junctures reveal the breakdown of those attempts. By contrast, the emerging, innovative line of argument is more prominent in the Schematism, which quickly surpasses its traditional framing in order to offer a phenomenologically compelling account of how the categories, as ways of interpreting time (as constant, unidirectional, and so forth), inform our perceptual experience.

Chapter 6 is dedicated to reconstructing how Kant sets limits to the validity of the categories. In my reading, the argument that establishes these limits belongs to the negative part of the critique of pure reason. I first find confirmation that it is correct to distinguish between a positive and a negative argument concerning the validity of the categories, the former belonging to transcendental philosophy and the latter to the critique of pure reason, in three different texts by Kant: the transcendental deduction of the categories, the Metaphysical Foundations of Natural Science and On the Use of Teleological Principles in Philosophy. However, since these texts provide different pictures concerning how the two arguments are related to one another, I analyze in which sense the negative argument depends on the positive one by reconstructing relevant passages in the B-deduction.

In this chapter, I reconstruct the metaphysical deductions that, in my account, Kant presents in the Aesthetic, Analytic and Dialectic, respectively. I read metaphysical deductions as accomplishing the first task of transcendental philosophy as it is established in the Critique of Pure Reason, namely the task of cataloguing pure root concepts (Stammbegriffe) for the cognition of objects and to track their origin. I argue that the metaphysical deductions do not simply assume a distinction between different faculties. Rather, they contribute to establishing this distinction by identifying the origin of the root concepts they clarify and catalogue. Moreover, I show that Kant does not follow a univocal model in the different deductions. Rather, his approach is pluralistic.

While Chapter 3 was dedicated to metaphysical deductions, this chapter reconstructs transcendental deductions, which I take to accomplish the second task of transcendental philosophy as it is established in the Critique of Pure Reason. Transcendental deductions are tasked with determining that root concepts (Stammbegriffe) have objective validity. In a way similar to my analysis of metaphysical deductions, I identify a transcendental deduction of space and time in the Aesthetic, a transcendental deduction of the categories in the Analytic and a transcendental deduction of ideas in the Dialectic. However, objective validity does not mean the same in all these cases. I take it that the main sense in which Kant uses the term is the following: concepts have objective validity when through them we cognize something that really pertains to objects. This is not the sense of objective validity that Kant uses with respect to ideas. In this case, claiming that ideas are objectively valid means attributing to them what I call the ‘practical’ and the ‘indirect’ validity of ideas. I argue that transcendental deductions only establish positive results regarding the validity of the root concepts and are not tasked with determining limits of this validity.

This chapter explains the council and king’s ratification of hundreds of thousands of royal decrees, and the unique categories that these edicts contained, such as mestizo and mulato. It outlines the pathways through which vassals of all social backgrounds suggested new laws to the ruling Council of the Indies. Pressed for time, the council’s overwhelmed ministers often transplanted petitions’ vocabulary verbatim into decrees. This meant that subjects often phrased imperial laws minor and major, regional and Indies-wide. Using a multistep archival methodology, this chapter demonstrates how scholars can match vassals’ petitions to decrees, then shows how legal categories such as mestizo and mulato came about through the petitions of not only Spaniards but also Indians, mestizos, and mulatos themselves. Subjects of any social background could therefore introduce and shape Indies legal constructs, and the empire’s agenda from the ground up. It considers the lawmaking royal signature, as well as some vassals’ dangerous decision to attempt its forgery. Lastly, it reflects on the nature of the de partes/de oficio divide in decree production, the number of gobierno royal decrees, and the costs of their production for vassals.

Moving beyond Hegel's critique of Kantian general logic and the logic of the Aristotelian tradition, this chapter considers his critique of Kant's transcendental logic: specifically, the Analytic of the Critique of Pure Reason. It offers an account of Hegel's famed swimming objection, going beyond previous ones by arguing that the objection has a more specific target than is often realized: the Metaphysical Deduction of the Categories. It further explains Hegel's dissatisfaction of the efforts of two of Kant's successors (Reinhold and Fichte) to overcome the dilemma the swimming objection presents. Some attention is given here to Fichte's project of deriving the categories from a version of the cogito, that is post-Kantian rather than the one familiar from Cartesian rational psychology. In my view, it is Jacobi and Romanticism who furnish Hegel with the possibility of deriving the categories from a post-Kantian version of the ontological proof – though he rejects their irrationalism. This explains Hegel's provocative claim that the ontological argument, and its rigorous distinction between the modes of thinking appropriate to finite and infinite entities, constitutes the true self-critique of reason.

Categorization – assimilating objects to psychological equivalence classes – is a crucial cognitive capacity that has always enhanced vertebrate fitness. This chapter reviews from a primate perspective the state of knowledge in comparative categorization’s subdomains: prototypes, exemplars, rules, and abstractions. Primate studies have made a profound contribution to the prototype-exemplar debate – essentially resolving it. They have illuminated the evolutionary emergence of a cognitive capacity for category rules, illuminating also the emergence of humans’ explicit-declarative cognition. In this area, primates appear as a pivotal transitional form. In the literature on abstract concepts (e.g., Same-Different), primate studies highlight the differences in cognitive capacities across vertebrate lines. The review will demonstrate the crucial role of a fitness/ecological perspective in understanding categorization as an adaptive, information-processing capability. It will raise important questions about the similarity structure of natural (and unnatural) kinds and categories. It will show strong continuities between human and animal cognition, but important discontinuities as well. In all the subdomains, the primates have been extraordinary behavioral ambassadors to the broader field of categorization.

This chapter examines Aquinas’s views on the ontological status of the actualization of an agent’s active power, namely its action, and the patient’s passive power, namely its passion. Aquinas claims that one and the same motion constitutes both an agent’s action and its patient’s passion. This chapter considers Aquinas’s motivations for defending the “action-passion sameness” thesis and his responses to common objections. The chapter also includes a solution to a longstanding interpretive difficulty regarding Aquinas’s views on the ontological status of action. Aquinas claims in some texts that actions are accidents in the agent as subject. This seems to conflict with his standard view that an agent’s action is the motion which it causes in its patient. While advancing a solution to this textual difficulty, the chapter proposes a novel interpretation of Aquinas’s understanding of the relationship between forms and accidents and the metaphysics of inherence.

This chapter outlines an approach to the study of categorisation in language practice grounded in the work of American sociologist Harvey Sacks known as Membership Categorisation Analysis. MCA proposes that categories and their associated ‘normative orders’ are not simply stored in people’s heads; they are used as part of the accomplishment of practical tasks in various social settings. Thus, MCA focuses on how categories are used to do things within talk and text, such as criticising, complaining, praising, encouraging, inviting, commending, blaming, and so on. Moreover, we also propose that power relations can be central to the study of categories. We demonstrate this in a political context through analysis of a political speech made by the previous British Prime Minister, Theresa May. We show that May’s category-based reasoning about social injustice was used to appeal to a sense of social solidarity and moral responsibility of ‘the fortunate’ to help the ‘less fortunate’ in society. We conclude that MCA has value for students and practitioners of language because no other approach comes as close to the study of how categories are used in talk and text in real-life situations.