Relativity against dogmatism in Sextus Empiricus

Sextus often tells us that relativity underpins Pyrrhonian Scepticism. Some scholarship focuses on the role of relativity in overarching Pyrrhonist sceptical strategies. Much less scholarship addresses relativity in Sextus’ criticism of particular dogmatic concepts. This chapter argues that Sextus invokes conceptual relativity—a version of constitutive relativity—in his treatment of three dogmatic concepts: signs, causes, and demonstration. However, as a Pyrrhonist, Sextus would likely resist committing himself to a certain concept of relativity, even a conceptual one. This chapter argues that Sextus employs conceptual relativity dialectically against his dogmatic opponents. First, the chapter sets up the two readings of Sextus’ view of relativity. The chapter then presents direct and indirect evidence that the conceptual view is present in Sextus.

Stoic relativity

This chapter focuses on our most comprehensive record of Stoic relativity. In his commentary on Aristotle’s Categories, Simplicius reports two sorts of Stoic relativity, and plots them in a taxonomy. The orthodox reading of Simplicius’ report faces philosophical and textual difficulties. Moreover, Simplicius’ taxonomy appears inconsistent. This chapter reads the report in light of constitutive relativity: some Stoic relatives are directly constituted by a relation while some are indirectly constituted by a relation. The chapter goes on to show how reading Stoic relatives in this light makes better sense of Simplicius’ report and also offers a new, less puzzling, account of Simplicius’ taxonomy.

Relativity in Categories 7, Topics, and Sophistical Refutations

Aristotle discusses relatives in the Categories, Topics, and Sophistical Refutations. This chapter begins to argue that Aristotle adapted Plato’s ideas about relativity into an Aristotelian framework. In the Categories, Aristotle defines relatives (6a36–b10) then discusses four hallmarks of the class of relatives: contrariety (6b15–18), scalability (6b19–27), reciprocity (6b28–7b14), and simultaneity (7b15–8a12). This chapter clarifies what these hallmarks are and shows how constitutive relativity is involved in the hallmarks. The chapter goes on to discuss how Aristotle treats the idea that relatives can fall into genus and species structures and how Aristotle treats the definition of relatives.

Conclusion

The conclusion summarizes the results of the book, by returning to discuss three broad theses that the book has defended: that Plato, Aristotle, the Stoics, and Sextus share a broadly constitutive view of relativity; that the wider philosophical pictures of these thinkers affected how they precisely each understand constitutive relativity; and that how these thinkers viewed relativity, in turn, affects their wider philosophical positions. The conclusion also offers some reflections on the ancient and modern reception of ancient thinking about relativity. These reflections focus on relational inferences in Aristotle, Galen, De Morgan, and Russell. The conclusion briefly discusses the notorious objection that Aristotle’s logic cannot validate some obviously valid inferences involving relativity: the famous horses’ heads inference.

Relativity and partition in Republic

In Republic IV, Socrates argues that the soul has three parts. Before arguing that the soul has three parts, Socrates argues that it has at least two parts. I call this the Partition Argument. This argument crucially involves relatives, but commentators have thought the partition argument falls to one of two objections. In this chapter, I argue that, once we understand that constitutive relativity is in play, neither objection is fatal. But this approach reveals a tension within constitutive relativity: some of the formal features may turn out to form an inconsistent set. The chapter ends with some reflections on how Plato articulates this tension in the Statesman and how one might respond.

Aristotle on the distinction between substances and relatives

Aristotle worries that his first account of relativity in the Categories, relativity1, over-generates relatives. In particular, some relatives might also be substances, which he thinks absurd. Aristotle responds with a second account of relativity (relativity2, at Categories 7, 8a31–2), which he thinks avoids any relatives turning out to be substances. Recent commentators have held that Aristotle intends to solve the over-generation worry by restricting the scope of relatives. That is, relativity2 counts fewer items as relatives than relativity1. This chapter argues that this cannot explain Aristotle’s attitude. Instead, Aristotle distinguishes between two ways to understand a relative, called here the schematic and the specific. Both operate within the framework of constitutive relativity, since in both cases the question is how we understand a relative, rather than a relation, and in both cases the relative is constituted by its relationship to a correlative. With this distinction in play, Aristotle can avoid over-generating relatives.

Introduction

The introduction draws some distinctions and uses them to articulate the scope, argument, and approach of this book. First, the chapter distinguishes: relatives (things that are related); relational properties (certain properties that related things have); and relations (items which do the relating). These distinctions delineate three approaches to ancient relativity that scholars have adopted: relativity does not involve relations; relativity is a matter of incomplete relational predicates; relations constitute relatives. Since the book focuses on this latter view, the chapter describes constitutive relativity in more detail. In particular, I identify some ‘formal features’ of constitutive relativity: exclusivity, reciprocity, aliorelativity, and existential symmetry. These are features that relatives have simply in virtue of being relatives, on the constitutive view.

Relativity and independence in Aristotle’s On Ideas

According to Alexander of Aphrodisias’ report, one of Aristotle’s key criticisms of the theory of Forms revolves around relativity. Traditionally understood, Aristotle’s objection suffers from two problems: it attacks a straw target, and it strains the philosophical lexicon. With the developed understanding of relativity in Plato and Aristotle, this chapter offers a new reading. This reading shows how the criticism involves constitutive relativity and does not suffer from the problems of the traditional reading. The chapter begins by outlining the traditional reading of the Relatives Argument refutation. The chapter then argues that this reading faces two problems: one philosophical, one lexical, outlines my alternative reading, and shows that my reading faces neither problem. The chapter ends by showing how the Relatives Argument should be understood, given Aristotle’s refutation.

Relativity in Aristotle’s Metaphysics 5.15

This chapter discusses Aristotle’s other official discussion of relatives: Metaphysics 5.15. Although commentators have pointed to apparent doctrinal discrepancies, this chapter argues that the conception of relativity found in Metaphysics 5.15 is consistent with that presented in the Categories and Topics. Scholars disagree on how close the treatments of relatives are in Metaphysics 5.15 and the Categories. Some hold that the two texts agree but do not make this case in detail. Others, who you might call developmentalists, hold that there are significant philosophical differences between the two texts and that Aristotle’s view of relativity develops from that of the Categories to that of Metaphysics 5.15. I argue that what we find in Metaphysics 5.15 is consistent with the Categories, by showing that the tensions developmentalists point to are merely apparent.

Relativity and separation in the theory of Forms

At Parmenides 133c–134e, Parmenides presents what he calls the ‘Greatest Difficulty’ with Socrates’ inchoate theory of Forms. Although many scholars have recognized that Parmenides’ objection relies on relativity, they have not been able to offer a satisfactory account of the Greatest Difficulty. This chapter shows that once we understand that Plato’s constitutive understanding of relativity is in play, we can give a satisfactory reading. This adds further evidence that Plato assumes a constitutive view of relativity. Section 3.1 introduces the texts of the Greatest Difficulty. Sections 3.2–3.4 discuss the main existing approaches to the argument in the literature. Scholars generally think that the Greatest Difficulty does not pose a threat to the theory of Forms, either because it is not formally valid, or, if it is formally valid, because it begs the question against the Platonist. However, this chapter argues that the Greatest Difficulty poses a genuine challenge to the theory of Forms. Furthermore, the existing approaches assume that Plato holds an incompleteness view of relativity. The chapter argues that, in fact, the Greatest Difficulty assumes a constitutive view of relativity. Section 3.5 shows how it is possible to properly understand the Greatest Difficulty, with the constitutive view of relativity assumed in the background.