Disentangling Leibniz's Views on Relations and Extrinsic Denominations

1. Introduction

Most commentators agree that Leibniz advocates some version of a doctrine of the ideality or reducibility of relations, but there is considerable disagreement on the question of what exactly this doctrine is supposed to amount to. This question is pressing because of the central place that Leibniz's theory of relations occupies in his philosophy. How one understands Leibniz's views on relations will influence how one understands Leibniz's complete concept doctrine, his (super)essentialism, the principle of the identity of indiscernibles, his account of compossibility, and his theory of space and time, to name just a few examples.¹

The most divisive question in this context is whether Leibniz is what I will call a "reductionist," i.e., whether he advocates some form of "reductionism" about relations. There are several ways in which this question could be understood, depending on how the term 'reductionism' is explicated. A reductionist about relations could be said to hold that all there is in the world are individuals and their intrinsic properties, or that a complete description of the world is possible in purely non-relational terms, or that all relations and extrinsic properties (strongly) supervene on intrinsic properties—which are popular ways in which Leibniz's views on relations and extrinsic denominations have been interpreted. The question of whether Leibniz is a reductionist splits commentators into two camps: those who answer the question in the affirmative,² and those who answer it in the negative.³

Despite much good work on this topic, the proponents of the two camps have been talking past each other to a considerable extent. One of the main factors hampering the discussion is the widespread, if only implicit, assumption that there must be one unified thesis, or, at most, a small number of closely related theses, that Leibniz is trying to articulate in his various pronouncements on relations and extrinsic denominations. On my view, this assumption is clearly false.⁴ Another obstacle to exegetical progress is the frequent inadequate appreciation of Leibniz's division of reality into different ontological levels. The failure to take this level distinction into account tends to obscure the complex and multi-faceted nature of Leibniz's views on relations and extrinsic denominations. Once Leibniz's various theses about relations and extrinsic properties have been sorted out, it becomes clear that both camps of commentators are correct about some aspects of Leibniz's views, even though the overall flavor of Leibniz's position on relations remains non-reductionist.

The argument of this paper will proceed as follows. Section 2 covers some preliminaries and background material, including a sketch of Leibniz's tiered ontology. In section 3, I discuss Leibniz's thesis of the ideality of abstract relations. Section 4 explicates the sense in which all phenomenal extrinsic properties can be reduced to the perceptions of monads, and addresses the question of whether monads have irreducibly extrinsic properties. In section 5, I analyze Leibniz's notorious claims that there are no purely extrinsic denominations and that every extrinsic denomination has a foundation in the thing denominated, which I take to be concerned primarily with the phenomenal level of reality. I argue that these claims do not commit Leibniz to reductionism, but they warrant ascribing to him five other weaker theses about extrinsic denominations and their relation to intrinsic denominations. In the sixth and final section, I revisit Leibniz's much discussed project of reformulating relational sentences into non-relational ones, and identify two more Leibnizian theses about relations and extrinsic properties.

2. Preliminaries and Background

The main focus of this paper is on Leibniz's views on relations and extrinsic properties in his mature philosophy, which I take to have been in place by the mid-1680s, at least as far as its main doctrines and principles are concerned, several changes in emphasis and presentation style notwithstanding.⁵

An important step toward disentangling these views is a careful appreciation of Leibniz's division of reality into several ontological levels. This level-distinction is widely acknowledged in the literature, but there are different views...