Chmess

8 05 2007

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.)

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11 responses

8 05 2007
Greg

I’m more sympathetic to your position than Stanley’s. One small point, though: you say “Unlike the other sciences, philosophy encourages discussion of non-actual systems.” In theoretical physics, though, the situation is exactly like this — lots of the solutions people have found to Einstein’s Field Equations (e.g. Godel’s) describe systems that are, for lack of a better term, extremely non-actual. And this sort of activity is seen as contributing to our understanding, and for the most part encouraged.

8 05 2007
Kenny

Good point.

I wasn’t sure how to properly draw the distinction I was thinking of here. But if anything, your point shows that physicists will have some version of the Chmess problem as well, as their work veers towards mathematics. So it’s not obvious that philosophy will have to follow the humanities in its solution to the problem.

I suppose I should also add at this point that I don’t object to saying that philosophy can help give people the resources to live a dignified life, but just to the conclusion that this must be the goal of philosophy in a sense that it isn’t a goal of the sciences.

8 05 2007
Jed Harris

Very interesting set of questions. I think there is a clean criterion lurking in your point about mathematics, but I think none of the criteria for philosophy that you mention are correct.

I’d agree with you that the criterion for significance in mathematics is how much a given result or set of ideas ties into a larger network — whether that network is strictly internal to math or crosses the boundary into e.g. theoretical physics.

I think philosophy can’t be judged by the criteria of science (trying to articulate accurate theories of “how the world is”) or mathematics (trying to complete significant parts of the network of formal systems).

We can see the right criterion more clearly if we consider that typically philosophical work is normative and tries to build on, reconcile and clarify our intuitions, successful theories, formal results, etc.

Philosophy is basically a design discipline, trying to grapple with the challenges raised in thinking about significant questions, and develop better guidelines, language, norms, formal procedures, etc. for us to use in thinking.

So the criterion for good philosophy is that it has to give us useful guidance in thinking better about significant questions. Pretty general, but I think this describes pretty much all good philosophy (over a very wide range of topics and styles), explains its normative force, and clearly differentiates philosophy from other disciplines — for example mathematics (philosophy isn’t formalizable, though of course it uses formal results), science (philosophy doesn’t aim at finding accurate models, though of course it uses them), the humanities (philosophy is trying to design better methods for thinking, not help people “acquire the resources to lead a dignified life”), etc.

One implication of this that many philosophers might find uncomfortable is that philosophy can’t establish “the truth”. Another implication that other philosophers might reject is that philosophical conclusions can help us judge that something is right or wrong in a largely mind and culture independent way. They do this in the same sense that civil engineering helps us judge whether a bridge design is a good fit for a given use.

12 05 2007
Jed Harris

Huh. I didn’t mean for that to be a terminal comment. I hope it wasn’t anything I said.

12 05 2007
Kenny

No, I just wasn’t sure what to say to all of that. It looks like you’re thinking of philosophy very differently than I do, but I don’t have much of an argument one way or another.

13 05 2007
Jed Harris

Well, one response that would be useful to me would examples of philosophical arguments that have significantly advanced the “state of the art” in philosophy (however you define that) and that don’t (as far as you can see) fit my description.

Good examples don’t need to be arguments you even agree with, as long as they seem pretty clearly contributions to the philosophical project. The less these are reducible to purely formal results (math) or to purely empirical results (science) the better. It would be especially interesting (but not necessary) if they have a clear normative dimension.

26 05 2007
Greg

I just found, on the web, a mathematician who appears to be studying a general theory of chmess. In this paper Doron Zeilberger talks about some of the research being conducted in his group. I quote:
Thotsaporn Thanatipanonda (a.k.a. “Aek”) teaches computers how to play Chess but, unlike Deep Blue and Deep Junior, not on an 8X8 board (this is not math!) but on an mXn board.”
I don’t know how much weight to put on Zeilberger’s ‘this is not math!’ comment (he’s very fond of saying provocative things), but it seems to me to run completely counter to the thrust of Dennett’s point.

26 05 2007
Kenny

Oh, that’s right! I even talked to Aek once, but forgot about this fact. But if Zeilberger and his students are the only counterexample to a claim about mathematics, then that’s not so bad, since he definitely has a very different perspective than most practicing mathematicians.

Although actually, even here it doesn’t look like too much of a counterexample. He seems to be saying that just teaching 8×8 chess isn’t math, but once you start considering the general case and seeing what patterns emerge, then you might be doing math. In Dennett’s example, I think he’s just talking about studying the one game, and not the general case.

26 05 2007
Greg

I certainly agree that if Zeilberger et al. are the only counterexample, then there are no real counterexamples.

I don’t have a good feel/ intuitive sympathy for the drive animating Dennett’s chmess-hating, but… it sounds like you’re saying Dennett thinks investigating the truths of chmess is a waste, but investigating which sentences are true in both chess and chmess is OK. Maybe that is his view, but it seems a bit strained to me. (In other words: in your version of Dennett’s objection, we can/should study any bizarre scenario, so long as it is understood as an instance of something more general that also includes the actual scenario as a special case.)

27 05 2007
Greg

After thinking about it some more, I rescind the previous comment. I wasn’t thinking straight.

27 05 2007
Shawn

It is too bad the original post on Leiter Reports didn’t link to Dennett’s article, as it is available a few places online, e.g. here. Glancing back at Dennett’s article, it seems like the mathematicians mentioned above don’t constitute a counterexample to Dennett’s point; rather they look like an example. The thrust of the article seemed to be this. One can always make up some a priori domain of problems that can generate truths and one can often times get others to join in the fun of playing in that domain. Not all problems are worth (in a loose sense) investigating for any number of reasons. It seemed like chmess was supposed to be ex hypothesi low worth. To avoid the low worth areas, one should try to find problems that are (loosely) worth investigating. He gave a couple of rough diagnostics for this, but, like he said, they aren’t 100%.

If the investigations of the mathematicians into generalized chess led to important discoveries, then it would no longer be a chmess example; it’d be good work. Similarly, if chmess became all the rage and, so, culturally important, Dennett would need a different example. Figuring out whether chmess leads one to a deeper understanding of anything besides chmess takes some work and, in Dennett’s phrase may “be met by stony incredulity or ridicule”. Dennett seems to think part of the job of the chmess researcher was to show why chmess is a worthwhile object of study. As advice to fresh graduate students, this doesn’t seem that bad (says the grad student who just finished his first year, so take that with appropriate amounts of salt.). The advice is really summed up in the last line: “My point is just that you should not settle complacently into a seat on the bandwagon just because you have found some brilliant fellow travelers who find your work on the issue as unignorable as you find theirs. You may all be taking each other for a ride.” While Dennett doesn’t explicitly say what his preferred solution is, it seems like he would advocate stepping back often and questioning what one is doing or trying to connect it to a bigger picture.

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