Jason Stanley has a post on the Leiter Reports discussing the problem of “Chmess”. As he puts it,
Chmess, for those of you who haven’t heard, is just like chess – except the king can move two squares in either direction. As Daniel Dennett has pointed out, Chmess provides a rich source of a priori truths to explore. However, the a priori truths of chmess are not particularly worthy of exploration. Dennett’s challenge of Chmess is to explain the difference between describing the a priori truths of Chmess and practicing philosophy.
He says that the sciences don’t face the problem of Chmess because they are clearly investigating an independently existing body of truths. He suggests that for the humanities, the problem doesn’t even arise, because they don’t see themselves as investigating a body of truths, but rather as changing people’s lives. I think he suggests that something like the latter is the right way to avoid the problem for philosophy as well:
In philosophy, as much as any other discipline, one engages in the practice of investigating alternative conceptual structures, be they systems of value or systems of belief. Such investigations may seem like theorising about Chmess, if we conceive of philosophy as a science. But [if] we regard philosophy instead as an activity intended to help those who learn it acquire the resources to lead a dignified life, it quite clearly does not.
However, I’m not convinced that this is the right way for philosophers to avoid the problem. (Admittedly, I don’t know what Dennett’s preferred solution is – he must disagree with Stanley here because of his scientific picture of philosophy.) To see that another solution must clearly be available, consider the case of mathematics. Working on Chmess problems bears only a very distant resemblance to working on science or the humanities, and a somewhat closer relationship to philosophy (especially when characterized as the study of a priori truths). However, many mathematicians explicitly claim that mathematics is just the study of what can be proven in arbitrary abstract formal systems, and many further claim (echoing G. H. Hardy’s famous A Mathematician’s Apology) that there is absolutely no use to any of their work and they only do it for their own amusement.
If that were really the case about mathematics, then the problem of Chmess would be extreme. Why shouldn’t a top university hire someone who was an incredible genius and had made all sorts of deep and subtle discoveries about Chmess?
My thought is that all mathematics is applied – if not to the physical world, then at least to other mathematics. There is a deep sort of interconnectedness between all the disciplines of mathematics. Chmess is unlikely to have these connections, just like almost any other arbitrary formal system, including Chess (though Go may have helped lead Conway to the surreal numbers). Mathematicians only work on problems that are relevant to other problems that already have established interest. If a certain formal system arises in multiple contexts, then that system will become of interest in its own right.
In philosophy, if one wants to take a “scientific” sort of view, one can see the point similarly. Unlike the other sciences, philosophy encourages discussion of non-actual systems in order to uncover their structure. However, these systems will ideally have some connection to actual systems, and hopefully will illuminate some of the relevant issues. And although philosophy very often deals with non-actual circumstances (twin earth, Gettier, trolley problems, etc.) the only cases I can think of where people really deal with formal systems that are not intended to describe something actual are in analytic metaphysics, or when they are specifically trying to disprove someone else’s theories.
So I think Jason Stanley’s argument is far from conclusive in establishing that philosophy should not be thought of as a science, but rather as something like a therapeutic activity. (I know that’s not what he said, but I can’t resist comparing him to Wittgenstein.)