Chapter 2 - Abstract Entities

Annotated Bibliography

David Armstrong. 1975. Towards a Theory of Properties: Work in Progress on the Problem of Universals.

http://www.jstor.org/stable/3749504

Presents and defends an Aristotelian theory of universals

David Lewis. 1983. New Work for a Theory of Universals.

http://www.tandfonline.com/doi/pdf/

Argues that a theory of universals or nominalism supplemented with facts about which classes are natural can be used to explicate many notions of interest to philosophers including laws of nature, determinism, physicalism, and content

Frank Jackson. 1977. Statements about Universals.

http://www.jstor.org/stable/2253615

Provides of examples of statements with commitment to universals that cannot be paraphrased away

Ross Cameron. 2008. Truthmakers and Ontological Commitment: Or How to Deal with Complex Objects and Mathematical Ontology without Getting Into Trouble.

http://link.springer.com/article/10.1007/s11098-008-9223-3

A defense of truthmaker theory against the Quinean theory of evaluating ontological commitment

George Boolos. 1984. To Be is to Be a Value of a Variable (Or To Be Some Values of Some Variables).

http://www.jstor.org/stable/2026308

Defends an interpretation of second-order logic as not committing one to sets or attributes but only to first-order objects considered plurally

Michael Resnik. 1988. Second-Order Logic Still Wild.

http://www.jstor.org/stable/2026993

Defends Quine’s view that second-order logic is problematic against Boolos’s proposal to view it as committing us plurally to first-order objects

Nelson Goodman and W.V. Quine. 1947. Steps Toward a Constructive Nominalism.

http://www.jstor.org/stable/2266485

Defense and development of a nominalist view, eliminating all abstract entities

Michael Devitt. 1980. “Ostrich Nominalism” or “Mirage Realism”?

http://www.oxfordscholarship.com/view/

A defense of Quinean nominalism

D.C. Williams. 1953. On the Elements of Being.

http://www.jstor.org/stable/20123348

A defense of trope theory, including the view that tropes can provide a complete fundamental ontology

Peter Simons. 1994. Particulars in Particular Clothing: Three Trope Theories of Substance.

http://www.pdcnet.org/pdc/bvdb.nsf/

Defends a novel version of the trope theory

James Van Cleve. 1985. Three Versions of the Bundle Theory.

http://link.springer.com/article/10.1007/BF00355089?LI=true

Discusses various versions of the view that objects are bundles of properties and raises objections to them

Alan Baker. 2005. Are There Genuine Mathematical Explanations of Physical Phenomena?

http://mind.oxfordjournals.org/content/114/454/223.short

Explication and defense of the Quine-Putnam indispensability argument for Platonic realism

Penelope Maddy. 1992. Indispensability and Practice.

http://www.jstor.org/stable/2026712

Critique of the Quine-Putnam indispensability argument for Platonic realism

Jody Azzouni. 2002. On “On What There Is”

http://onlinelibrary.wiley.com/

A critique of the indispensability argument raising issues about the Quinean view about determining ontological commitment underlying it

Paul Benacerraf. 1973. Mathematical Truth.

http://www.jstor.org/stable/2025075

Argues that theories of mathematical truth have problems providing an adequate semantics at the same time as a plausible epistemology

Paul Benacerraf. 1965. What Numbers Could Not Be.

http://www.jstor.org/stable/2183530

A critique of attempts to reduce numbers to sets

Linda Wetzel. 1989. That Numbers Could Be Objects.

http://www.jstor.org/discover/

Defends a realism about numbers against Benacerraf’s objections

Annotated Weblinks

http://www.philostv.com/paul-humphreys-and-john-symons/

Paul Humphreys and John Symons debate properties and emergence at Philosophy TV.

http://www.3ammagazine.com/3am/truthmaking/

An interview with Gonzalo Rodriguez-Pereyra at 3:AM Magazine on truthmakers and other topics.

http://www.3ammagazine.com/3am/the-platonist/

An interview with Scott Berman at 3:AM Magazine on universals and other topics.

Discussion Questions

1. State in your own words what you take to be the clearest way of distinguishing abstract objects from concrete objects. Give an example to illustrate the distinction.
2. State a novel instance of the One Over Many argument.
3. In your view, is the One Over Many argument a convincing way to argue for the existence of universals? Why or why not?
4. Explain in your own words the difference between sparse and abundant theories of universals.
5. What is there to be said in defense of the view that tropes are the only fundamental entities there are? What is one reason someone might object to this view and claim there must be at least some fundamental entities beyond the tropes?
6. Many truthmaker theorists argue that all truths must have truthmakers. What would be a true sentence constituting a potential counterexample to this claim?
7. What is there to be said in defense of the Quinean response to the One Over Many?
8. What is the most plausible way of rejecting the indispensability argument? Be precise. Does this involve rejecting a particular premise or the validity of the argument?
9. What do you think is the best way of responding to Benacerraf's dilemma for theories of mathematical truth?
10. Defend your own view about whether abstract entities exist. Do any exist? If so, what kinds of abstract entities? How do we learn about their existence?