Determinable Nominalism

• Published in: Philosophical studies 2001-02, Vol.102 (3), p.297-327
• Main Author: DENBY, D. A
• Format: Article
• Language: English
• Subjects: Actualism; Armstrong, David; Epistemology. Philosophy of science. Theory of knowledge; Intrinsic properties; Intuition; Lewis, David K (1941- ); Mathematical relations; Mathematical set theory; Metaphysics; Naturalness; Nominalism; Ontology; Philosophical analysis; Philosophical axioms; Philosophy; Redundancy; Theory
• ISSN: 0031-8116; 1573-0883
• DOI: 10.1023/A:1010314926955

[...]the [abundant] properties are as abundant as the sets themselves, because for any set whatever, there is the property of belonging to that set.2Properties in the sparse sense of property (sparse properties) are required as that which makes for genuine, objective, qualitative similarity among their instances.3 Sparse properties are said to carve up reality at the joints and it is their inter-relations that natural science aims to codify.4Lewis points out that if our ontology already includes all the properties in the abundant sense, there will be one for each property in the sparse sense. According to Lewis, all the sparse properties are intrinsic.12Second, it is intended to cover only those sparse properties that are basic in the sense that there are just enough of them to characterize things without redundancy.13 This restriction is supposed to exclude disjunctive properties like the property of being either round or red, conjunctive properties like the property of being both round and red, structural properties like the property of consisting of a proton and an electron a certain distance apart, and so on.Finally, it is intended to cover only properties capable of instantiation by simple concrete particulars (whether or not these properties could also be instantiated by complex or abstract particulars). [...]as far as the base facts are concerned, DN entails that the alternative possibilities in our scope correspond oneone with the possible distributions of naturalness among actually existent abundant determinables, the possible ways that nature could be articulated at the joints.This suggests the following definitions:w is a world =df. w is a function that assigns to each actually existent abundant determinable D, a degree of naturalness w(D) (Ds degree of naturalness at w).38A world w represents that a simple concrete particular a has a basic intrinsic property F =df. a is in the extension of some property F* that belongs to w and F* is a counterpart of F.The idea here is simple. [...]if DN is correct, the definitions seem to be good candidates for converting the quantificational schema into an adequate and genuinely actualist analysis of modality (albeit a very limited one).This account is recombinatorialist: it identifies alternative possibilities with recombinations of various elements that actually exist and are actually combined in a certain way, viz. abundant properties and degrees of naturalness.