This dissertation asks and discusses answers to the question: how can we refer to abstract objects? The question is interesting because, like the question of how we know about abstract objects, the radically different nature of abstract objects seems to defy our ordinary theories of reference. In the first chapter I argue that if abstract objects are abundant and non-causal, we cannot refer to them. The non-causality entails that in order to establish reference, we must single them out by definite description, and the abundance prevents those descriptions from being definite. I further argue that this problem is not solved by reference magnetism. The remainder of the dissertation examines how one could solve this problem by denying either abundance or non-causality. In chapter 2 I examine solutions which attempt to only deny abundance and argue that most are either ad hoc, too abundant (and so still have the reference problem), or too sparse (and so have the problems of nominalism), though there is one sparse solution which could work, but comes with serious costs. In chapter 3 I argue that once we distinguish truth or instantiation in a world or time from truth or instantiation at a world or time, we can see that there is nothing absurd about abstract objects being contingent or temporal (since we will still be able to say all the same true things about other worlds and times). The purpose of this discussion is to pave the way for a causal theory of properties. Chapter 4 offers a causal theory of properties, namely the view that all abstract objects are created by human mental activities. I argue that this is not only a good solution to the reference problem, but an attractive ontology in general.
Reference and Ontology: How Can We Refer to Abstract Objects?Doctoral Dissertation
|Author||David J. Pattillo|
|Contributor||Peter van Inwagen, Research Director|
|Degree Level||Doctoral Dissertation|
|Record Visibility and Access||Public|
|Departments and Units|