An Austere Nominalist Strategy for Paraphrasing Away Properties and Relations

Nominalism, the position that everything is concrete, is an attractive position to many philosophers. However, nominalism faces the serious problem of accounting for ordinary discourse about abstract objects. Abstract objects are referred to in all the essential domains of ordinary inquiry and practice, from natural science to the trades. Nominalism is thus in need of a novel, comprehensive strategy for nominalistically reconstructing essential ordinary inquiries and practices if it is to be a viable position. This dissertation lays the foundation for a comprehensive nominalist system. It thus significantly raises the credibility of nominalism.

The structure of the dissertation is as follows:

Chapter 1, the introduction, explains the problem that ordinary discourse poses for nominalism and the need for a new paraphrase strategy, criticizing strategies that have already been suggested.

Chapter 2 articulates a new paraphrase strategy for simple sentences about intrinsic properties of concrete objects. Speaking loosely, the paraphrases I suggest are counterfactuals concerning certain inscriptions – one-place open sentence-tokens, specifically – that would exist were there some universes so plentiful and diverse that they collectively realized every way a universe could possibly be. For example, if “pluriverses” are composites of universes that are plentiful and diverse in the way described, ‘spiders have anatomical properties’ can be replaced with ‘were there a pluriverse, spiders in our universe would satisfy one-place open anatomical sentence-tokens.

Chapter 3 summarizes and defends the assumptions on which my strategy relies. This chapter offers brief justifications of these assumptions and shows how some of them can be dropped by modifying the paraphrase strategy to fit different metaphysical visions.

Chapter 4 extends the paraphrase strategy to include more sophisticated sentences about intrinsic properties of concrete objects as well as sentences about extrinsic properties of concrete objects, higher-order properties, and dyadic and greater adicity relations.

Finally, Chapter 5, the conclusion, summarizes what has been accomplished and suggests how the paraphrase strategy might be further extended to include sentences about classes and propositions.