Syllabus: Abstract Entities


This course will be concerned with the ontological status of abstract entities. As in: are there any? Are there any such things as numbers, or sets, or propositions, or properties?

We will start with the classic problem of universals, then move to contemporary literature on the existence of properties and relations, in particular the work of D. M. Armstrong. Our concern will mostly be the foundational issue of whether properties or relations exist at all, and less with related debates over the nature of properties and relations, universals vs. tropes, the bundle theory, etc.

Then we will discuss ontological commitment and the nature of existence. We will begin with the contemporary paradigm, due to Quine, which requires nominalists to engage in the familiar project of paraphrasing sentences that appear to carry commitments to abstracta. We will then consider alternate conceptions of existence and/or ontological commitment that would eliminate the need for this project of paraphrase.

Finally we will turn to mathematical entities. After a review of the nature of the problem of mathematical existence, we will discuss several arguments for the existence of mathematical entities. First we will discuss the Fregean argument for the existence of numbers, as defended by Crispin Wright. Second we will discuss the Quinean indispensability argument, and the extended response to that argument due to Hartry Field. Finally we will discuss the philosophy of mathematics known as "if-then-ism".


Abstract entities: Tentative Schedule

"M&O" indicates the reading is in Mellor and Oliver, Properties (available at Folletts Orange Bookstore) otherwise the reading will be on reserve in the grad TA room.

  1. Introductory stuff
  2. The problem of ontology
  3. The problem of universals (old stuff)
  4. Armstrong against nominalism
  5. Ostrich Nominalism
  6. Nominalism and paraphrase
  7. Traditional problems with realism
  8. Nominalism and intensional logic
  9. Quine on existence and ontological commitment
  10. Non-Quinean views of existence and ontological commitment
  11. The problem of abstracta in mathematics
  12. The Fregean argument for abstracta
  13. The indispensability argument
  14. Field
  15. If-then-ism