Quick thoughts on why ethics and math would be difficult

I started this project looking at similarities between ethics and math, and now I'm looking at similarities between ethics and epistemology. Why the switch? I think I'm able to explain more clearly why I shifted focus.

Let's say you have some problematic discourse, X. It has problematic features and properties, and these problematic features have lead some folks to suggest that this discourse X is not real--doesn't describe or pick out anything out in the world. How can one respond to these concerns?

I can think of at least two ways (I'd be really excited if I could think of more). One way is to directly engage with the "problematic features" and attempt to show that they are not problematic, or that they are not features of X. For the latter you have to argue that X doesn't have the features ("There's no widespread disagreement in ethics"). For the former you could directly argue that these properties are simply unproblematic ("So what if there's widespread disagreement in ethics?! Who cares?"). But another way to answer in the former way is to cheat a bit. You can cheat by finding companions in guilt: "X may contain these features, but so do a bunch of other unproblematic, real discourses, and so these features are not problematic." Companion in guilt arguments can be convincing, but in order to be convincing eventually they have to come around to explaining why the features are not problematic. It's insufficient to simply find a companion in guilt--because maybe what we've learned is that this other discourse Y really should be problematic, just as X is. True, we're more confident in Y than we are in X, but in order to be really convincing we need to learn how come these features aren't problematic.

I want to make one more distinction. The following distinction isn't a really tight one, because you can easily collapse it, but I think what I mean will be clear. There's a distinction between finding a companion in guilt between two objects that shares a problematic feature, and two arguments that share a problematic feature. On the one hand we can try to find other objects that are queer in the sense that ethical objects are, but we can also try to find arguments that are problematic in the same way that arguments that justify ethics are problematic.

When I started, I was looking at math, and specifically the Quine-Putnam indispensability argument for mathematical realism. I was, essentially, doing the second of these two options, looking for a companion in guilt for an ethical argument in a mathematical argument. I wasn't looking for a companion in guilt for ethical objects in mathematical objects. I think the search for an analog of the indispensability argument for ethics didn't really go anywhere, and here's why. The indispensability argument in math is strong, if it is strong, because it stays close to something like IBE. The argument, in other words, is strong because it doesn't invoke much beyond IBE. This, however, means that if I'm looking for an argument in ethics that I can find a companion in guilt in math for, I need to restrict myself to IBE and not much more. This lead me to Sturgeon and Ethical Naturalism at first. That didn't seem interesting to me. Then it lead me to Enoch.

Another way that I could've gone was to look at mathematical facts or statements and attempt to show that these objects are themselves companions in guilt to ethical statements. Justin Clarke-Doane has been working on this for disagreement, arguing that if disagreement is problematic than it's not just ethics, but (perhaps even more so) math that is problematic.

So how would I continue if I thought more about math? First would be to try to pivot off of IBE in some other way. Note, however, that thinking about IBE is no longer really thinking about math. But maybe IBE is rich enough a principle that it actually justifies ethics somehow, either directly or by some sort of reflection through what justifies IBE itself. So Enoch and Sturgeon are still possibilities, but they have nothing to do with math (not that there's anything wrong with that! but I'm explaining my change in focus). Rather, IBE is an epistemological principle and that means that if I'm going to evaluate these arguments I need to learn about epistemology.

I could also reexamine the Quine-Putnam argument and try to see if it reaches beyond IBE. Maybe the resources that it needs to justify the reality of mathematical discourse goes beyond IBE? The problem is that to argue in this way is actually to substantially weaken the indispensability argument. What makes the argument strong is that it doesn't reach beyond IBE, that someone who believes in electrons should believe in numbers. Of course, it's possible that belief in electrons reaches beyond IBE, but then this is to weaken scientific realism in order to find a companion in guilt for ethics. Possible, but not what I was trying to do, and not something I think would go over very well (but maybe necessary to try at some point, of course!).

Finally, I could try to look for problematic features that math shares with ethics. Disagreement was mentioned. What else? The thing is that mathematical statements and her putative facts are not normative, at least I don't think that they are. If they were, then that would be a significant insight and would make for interesting analogies with ethics. But that's certainly not obvious. Is math queer? Maybe, but not in the sense that ethics is, because the queerness of ethics comes from normativity. Is ethics irrelevant for explanations? Harman argues "no," and maybe we could contend with that. Does math supervene on natural facts, or any other facts? Presumably not. What ethics and math definitely have in common is that they are not traditionally empirical domains. That may or may not be a helpful connection. I need to think about this some more, maybe there are some similarities that I didn't think of, but I don't think that they share a lot of the problematic features.

Ethics and epistemology, on the other hand, share normativity, and that's really special and important, since a lot of the arguments against ethics become much weaker if there's nothing wrong wit normativity (Blackburn's supervenience argument, I think, takes advantage of a special feature of normativity, queerness more or less trades on that, etc.) This is why I shifted focus--becuase epistemology seems more promising than math in this regard. It's not an excuse for stopping to think about math, but it is an excuse for putting it on the back burner.