Thesis Proposal

Debates about realism in ontology and realism in truth-value are central to both metaethics and philosophy of mathematics. In both fields the existence of objects and concepts central to the field’s practice are debated. But more seems to be at stake when it is questioned whether ethical or mathematical statements have truth-value at all. After all, if ethical statements are neither true nor false, then it would seem that I’m unjustified in criticizing someone else’s moral practice. Likewise, if mathematical statements cannot be false, how can I be justified in criticizing someone for embracing the law of non-contradiction, or other seemingly false claims?

So philosophers of math and ethics share similar concerns; the connections between the two subjects run deeper, though. It is plausible to suppose, for example, that the shared concern of these philosophers stems from a shared set problems facing both math and ethics. For example, it has seemed for many that neither math nor ethics is able to bring empirical justification for their claims. This seems to be a challenge to the objectivity of mathematical and ethical discourse. How can a philosopher of math or ethics respond to such a challenge? A defender of realism could suggest that humans have some way of mathematical or ethical intuition that gives them access to the truth, in a way that is analogous to sensual perception. Another choice is to challenge the premise itself, arguing that math and ethics really can be justified empirically. On the other hand, perhaps the lack of empirical justification suggests that our discourse is actually subjective, not objective. Then either math and ethics are false, or they lack truth-value (then the challenge is to explain why our discourse sounds so objective, and projectivist accounts begin to enter the picture).

What is fascinating, yet predictable, is that all of these positions have been staked out in both philosophy of math and in metaethics. Despite this broad similarity in the landscape of both subjects, there are still some arguments that are particular to either math or ethics. Consider, for example, one of J.L. Mackie’s arguments from “The Subjectivity of Values”: the “argument from relativity.” Stated sloppily, this argument states that the best explanation of widespread, deep and irresolvable disagreements in ethics is that ethical statements are subjective rather than objective. This is a powerful challenge in metaethics, but is not often brought in philosophy of mathematics. Likewise, in philosophy of math a powerful argument for realism is the Quine-Putnam indispensability argument, which argues that we are justified in believing in the existence of some mathematical objects (and therefore given a better chance at maintaining truth-value realism in math) due to their indispensability in expressing our best scientific theory. This is an argument that seems peculiar to math and versions of it are less often brought in ethics.

Given the great deal of overlap between the two subjects, arguments that seem peculiar to either math or ethics provide an important opportunity to explore the relationship between math and ethics. First, is it possible to map one argument into the other’s field? For example, can a plausible version of Mackie’s argument from relativity be made with regards to math? Can some kind indispensability argument be made in ethics? If the answer is “yes,” then we have made some progress to showing some stronger connection between math and ethics. If the answer is “no” then we also have an important opportunity: to investigate closely to determine why the argument failed to be plausible when translated into the other subject. For example, if study shows that the argument from relativity fails to be plausible in math, we should be able to isolate why the argument failed. Whatever the reason for this failure is, it should be a very important difference between the two subjects. In other words, failure for the argument to map between the subjects should isolate an important difference between math and ethics.

My initial investigations have shown me that there are some philosophers engaged in this sort of project. For example, there is a dissertation in NYU being written on ethics and mathematics by Justin Clarke-Doane (Hartry Field, Thomas Nagel, Derek Parfit and Stephen Schiffer are on his committee). Clarke-Doane has argued that Mackie’s argument from relativity applies just as strongly to mathematics than it does to ethics. Another NYU-educated philosopher, David Enoch, wrote his dissertation defending a version of the indispensability argument for metaethics (again, Field, Nagel and Parfit were on the committee).

I propose to write a thesis that continues this line of thought. In order to focus the project, I will pick one argument for or against realism in truth-value that is made either solely in philosophy of math or metaethics. Then I will, following the procedure that I laid out above, see how plausibly the argument translates into the other subject. After I determine how plausible translation is I will be able to make (only modestly, given the scope of the project) some observations concerning the similarities and differences between math and ethics that make translation either plausible or implausible. My continued research on this topic will determine which argument I choose to focus on—my research so far has looked at Mackie’s argument from relativity and the Quine-Putnam indispensability thesis (my interest in these arguments led to the discovery that Clarke-Doane and Enoch had also done work on them, not the other way around), but as I continue this project better candidates for arguments to focus on will emerge (analyzing the argument from queerness or the attempt to identify mathematical with logical truths might yield interesting insights).


Preliminary Bibliography:

Introductory textbooks:

“Thinking about Mathematics” by Stewart Shapiro
“An Introduction to Contemporary Metaethics” by Andrew Miller

Collections:

“Philosophy of Mathematics: Selected readings” edited by Paul Benacerraf and Hilary Putnam
“Essays on Moral Realism” edited by Geoffrey Sayre-McCord

Articles and books:

“Philosophy of Logic” by Hilary Putnam
“Realsim, Mathematics and Modality” by Hartry Field
“Mathematics in Philosophy” by Charles Parsons

“Essays in Quasi-Realism” by Simon Blackburn
“Moral Realism and the Argument from Disagreement” by D. Loeb
“How is Moral Disagreement a problem for realism” by David Enoch
“Moral Realism and the Foundation of Ethics” by David O. Brink