Craig’s Anti–Platonism, Lowe’s Universals, and Christ’s Penal Substitutionary Atonement

William Lane Craig has defended nominalism as a kind of “anti–Platonism.” To him, Platonism is inimical to God’s aseity. More recently, he also has defended the penal substitution of Christ. However, he has not brought the two subjects into dialogue with each other. In this essay, I will attempt to do that by exploring the implications of two major types of nominalism, austere nominalism and trope theory, for the penal substitution. I will argue that nominalism will undermine the penal substitution of Christ. Instead, to try to preserve both his anti–Platonism and the penal substitution, a better alternative for Craig is to embrace E. J. Lowe’s immanent universals.

Nominalism

This chapter is a critical discussion of nominalist accounts of the ontology of the basic properties and relations present in our experience. Predicate nominalism, concept nominalism, class nominalism, resemblance nominalism, and trope theory are discussed. Several novel objections to forms of nominalism and trope theory, in other words to accounts of properties that deny they are universals, are developed. These include a series of objections that such accounts are not able to plausibly account for the essential features of specific basic properties that appear in our experience, such as colors, in other words that they misrepresent the modal structure of those properties.

A Heretic in the Schoenberg Circle: Roberto Gerhard's First Engagement with Twelve-Tone Procedures in Andantino

Shortly before finishing his studies with Arnold Schoenberg, Roberto Gerhard composed Andantino, a short piece in which he used for the first time a compositional technique for the systematic circulation of all pitch classes in both the melodic and the harmonic dimensions of the music. He modelled this technique on the tri-tetrachordal procedure in Schoenberg's Prelude from the Suite for Piano, Op. 25 but, unlike his teacher, Gerhard treated the tetrachords as internally unordered pitch-class collections. This decision was possibly encouraged by his exposure from the mid-1920s onwards to Josef Matthias Hauer's writings on ‘trope theory’. Although rarely discussed by scholars, Andantino occupies a special place in Gerhard's creative output for being his first attempt at ‘twelve-tone composition’ and foreshadowing the permutation techniques that would become a distinctive feature of his later serial compositions. This article analyses Andantino within the context of the early history of twelve-tone music and theory.

Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory

A standard interpretation of Plato’s metaphysics holds that sensible particulars are images of Forms. Such particulars are fairly independent, like Aristotelian substances. I argue that this is incorrect: Platonic particulars are not Form images but aggregates of Form images, which are property-instances (tropes). Timaeus 49e-50a focuses on “this-suches” (toiauta) and even goes so far as to claim that they compose other things. I argue that Form images are this-suches, which are tropes. I also examine the geometrical account, showing that the geometrical constituents of the elements are also Form images. Thus everything in the sensible world is composed of tropes.

Abundant Properties

On an abundant conception of properties, properties serve as semantic values for most predicates and property names. Abundance is central to Dispositional Pluralism. Dispositional Pluralism is compatible with different theories of the metaphysics of properties. According to universalism (realism) properties are universals that are wholly present wherever they are instantiated. According to extensionalism (class nominalism) properties are sets of objects. According to trope theory, properties are sets of particular property instances, or tropes. In any case, properties correspond to sets of objects. Abundance is preferable to sparsity—the view that only an elite minority of sets of particulars correspond to properties. On most sparse views, the “real” properties are largely unknown. Consequently, sparse properties are unfit for the roles properties are posited to play: They rarely serve as the semantic values of predicates; they do not explain familiar causal powers; and it is not clear how they explain apparent similarities.