What is there? This is the ontological question. To ask the ontological question is to engage in ontology. One’s views about what the question means and how to go about answering it is one’s meta-ontology. In this dissertation a particular meta-ontology will be in view: Quine’s. Call it `Quinean meta-ontology.‘ But there is confusion over how Quine intended ontology to be done, enough confusion to warrant a very close look at his meta-ontology.
One of the primary goals of this dissertation then is to clearly present Quinean meta-ontology, showing just what it is—and isn’t. Another goal is to show how Quinean meta-ontology is used, particularly in arguments for the existence of abstract objects.
So after carefully presenting Quinean meta-ontology in a way that shows it’s key features as well as merely putative features, I provide evidence that the arguments for platonism which use Quinean meta-ontology are really indispensability-style arguments. I do this by showing how both Peter van Inwagen’s argument for properties and Hilary Putnam’s argument for mathematical objects are species of the same genus.
Once this is done, the philosophical geography surrounding Quinean meta-ontology (the meta-ontology proper as well as its use in arguments for platonism) should be apparent. Given this better view, I will then address four important objections to both Quinean meta-ontology and the indispensability-style argument for abstracta. Most of these objections, it turns out, focus on the uniquely Quinean views of existence and quantification. And all of them focus on particularly subtle aspects of language and so suggest that Quinean meta-ontology may just be too heavy-handed when it comes to interpreting our sentences.
In the last chapter, I make a proposal for future work, work for a nominalism that takes the subtleties of natural language quite seriously. I propose that a type of fictionalism might be the answer. Such a view needs a lot of attention though and so I point out four of the most salient problems for fictionalism, also alluding to where the solutions to these problems lay.