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.

Cuneo on what makes ethics and epistemology similar

Cuneo spends some time drawing out the similarities between ethics and epistemology. Here are the similarities that he points to:

1) Moral and epistemic reasons are categorical
2) Moral and epistemic facts are structurally isomorphic
3) Moral and epistemic facts normatively appraise objects of the same type
4) It's often the case that it's difficult to disentangle the moral and epistemic parts.

1) means that both epistemic and ethical facts "are, imply, or indicate reasons for agents to behave in certain ways regardless of whether these agents care about conducting their behavior in a rational/moral way, whether they belong to a social group of a certain kind, of whether they have entered into social agreements with others." (59) I take it that this is an explication of what it means to say that epistemology is a normative domain.

2) means that facts of both kinds come in the same kinds. Some ethical statements are evaluative ("Xing is good"), while others are deontic ("You ought to perform X"). Likewise epistemic statements are either evaluative ("Believing X is rational") or deontic ("You ought to believe X"). Further, ethical facts are either particular ("That deed is evil") or general ("Murder is wrong"), and the same can be said for epistemic facts which are either particular or general.

3) expresses the idea that "institutions, persons, intentions, actions, propositional attitudes (beliefs, acceptances, inquiries and hopes), character traits, emotions, policies, ways of viewing things, ways of finding things out, and so forth, are all plausibly thought to be subject to moral and epistemic norms."

4) means that "in some cases there is no obvious way to disentangle (ontologically at least) their moral and epistemic dimensions; some failing...appear to be both moral and epistemic failings." For example, "failing to treat the testimony of another with sufficient care and attention."

Are these similarities impressive? Certainly I find the first impressive, but I consider it just an explication of what it means to say that ethics and epistemology are both normative discourses. The second doesn't seem so exciting to me, though I'm having trouble picking out exactly why. I think because it seems to me (WARNING: not an argument) very difficult to imagine a normative domain that could be either deontic but not evaluative, or the other way around. The fourth way I find very impressive, though I'm not sure what to make of it if moral and epistemic domains are quite distinct. After all, it's often difficult to separate the normative and descriptive dimensions of a term. For example, take the word "murder." It doesn't seem to be murder if you kill during war, or kill an evil perpetrator, etc. So part of what it means to murder someone is to do something wrong. So there is significant entanglement between the normative and descriptive domains in these terms. Nevertheless, it's unclear to me what this goes to show.

Let's look at the third similarity. Cuneo writes "it would be incorrect to say that moral and epistemic facts are interestingly disanalogous because epistemic facts concern only 'theoretical' reasons, while moral ones concern only 'practical' reasons." He argues, and I'm convinced, that some moral reasons are theoretical and some epistemic reasons are practical.

I might be missing something, but can there be epistemic evaluations of states of affairs beyond actors? Because there can be moral evaluations not just of actors, but of situations and states of affairs. Is it obvious that the same can be done in epistemology? What is an epistemically good outcome that doesn't have to do with the actor? We can morally evaluate, for example, the goodness of evil of a war. A tax can be bad. Can epistemology evaluate anything outside of an actor? Cuneo says that institutions and policies can be epistemically and morally evaluated. But these are tangled up with actors--institutions, such as countries, companies, boards or clubs, can work together and reach decisions and act as a corporate. And policies can be morally evaluated epistemically because they are the decisions of actors. But what about plain-old boring states of affairs. I think they can be morally evaluated but not epistemically evaluated (what would that even mean?).

Is this important at all? I'll see if I can make the case for this doing some work in the next post, unless I change my mind about the previous few paragraphs.

What is non-naturalism?

I really don't have a firm grasp of this concept.

If one is a non-naturalist about ethics, then this means that one thinks that ethical properties are not natural ones. Well, what's a natural property? Attempt one: it's a property in the universe. Well that's not helpful! That just means that a non-natural property is one that doesn't exist (because I assume that the universe is just the class of all things that exist). OK, so maybe the natural properties are the ones studied by scientists. By that definition I suppose that a lot of properties that are physical could be non-natural ones. So maybe the natural properties are the ones that could be studied by scientists. What's the point of this definition; is the point just that scientists are able to study properties that can be found in space, are physical? So then all it means to be non-natural is to be an abstract object? That could be, but that doesn't pick out anything but abstract objects, obviously, so it's superfluous terminology.

I can think of two other definitions of non-natural properties. I need to read more so that I have a firmer idea of what it means. One definition would be that it is relevant for scientific explanations, or indispensable to explanations. This merges the natural properties with the ones that are derived from IBE, obviously. Again, not so interesting, but possible. The second definition is that the non-natural properties are those that we have to take as primitive. This won't quite do because then you'll have some physical properties that are non-natural. Grr. Not really sure what to do here.

Philosophical Progress

Since philosophy folks are always feeling defensive about philosophical progress, lemme say something concerning that. I remember in the introduction to "Realism with a human face" that there was a quote from Putnam. It went along the lines of: "There are almost never answers to philosophical questions, but there are better and worse ways to think about the questions." This is one way that philosophical progress occurs: there are some deep questions that might ultimately be unresolvable, but there are better and worse ways of struggling with these issues.

For example, you might wonder whether God exists. And so you might start looking into believing in things that you can't see or directly observe, that kind of inference, etc. And then you can have a whole long debate about that. But along might come some philosophers and say "You're thinking about belief in God all wrong, because what it means to believe in God isn't what you guys have been assuming it means, and so your debate has been misdirected." In this sorta-inspired-by-maybe-real-philosophy scenario, there has been philosophical progress through a clarification of what is worth debating.

To ethics: I get the feeling that the philosophical community has been moving, for a while now, towards a broadening of debates about ethics that have lasted a couple hundred years. I don't have the kind of knowledge to really defend this, but one gets the sense that at a certain point folks realized that what ethics distinctive and queer--it's normative properties--could be found in lots of other things. It's routine to point out that this is true about epistemology and what justifies are beliefs and makes some better than the others. But it's also been recognized in philosophy of perception too.

So the sense I get is that progress has been made on problems of ethics, insofar as we've recognized that the queerness of ethics is really just it's membership in a larger domain, that of the normative. And now there's focus on the normative, and people tending to deal with the normative all at once. This seems to me a better way of thinking about ethics, as part of the normative realm, and an example of philosophical progress and an insight that the rest of the world is going to owe philosophers who spend years sludging through, trying to figure out what's going on. We'll end up with a much better understanding of what it means to be moral, and we'll have a better understanding of what obligates us, and this will lead to different ways of thinking about how we treat each other.

And we've moved on to another area of research!

Again with the shifting from area of philosophy to area of philosophy...but this shift is more natural than the previous ones, and it's been coming on for a while.

http://philpapers.org/browse/epistemic-normativity-misc

But this page seems like a potential gold mine of things to read and ponder about. In short, the questions I'm thinking about now are about the differences and similarities and interconnectedness of statements such as "you morally ought to do X" and "you epistemic ally ought to believe X". Right now I'm feeling out arguments that try to blur these, not sure how I feel about it yet.

Ah, philosophy of math! How I miss you so. Hopefully there will be a way to bring it back in.

Writer's block. OK, let's try this on the blog before trying to write it down again.

I have a draft due sometime before I go to sleep tonight, and I'm having trouble getting the ideas clear enough to write down. So here's a first draft of my first draft.

Moral realism is the view that morality is factual, sometimes true, and not fake (like, it's not mind-dependent, or it's not like we're just identifying morality with social norms and peer pressure). How can one argue for this view? One way is to try, somehow, to latch moral realism onto some other discourse that we feel much more comfortable about.

For example, here's a recap of Sturgeon's argument: if you're a scientific realist, you think that our scientific views are largely true. And so you probably think that inference to the best explanation, or something awfully close to it, is true. This tells us that unobservables like protons or electrons exist, and it might also tell us that numbers exist. Sturgeon argues that ethical beliefs are necessary for making our explanations better, and so inference to the best explanation should tell us that there are moral facts. Of course, one could just say "Feh, I don't like science either" but we're not taking up that argument. We're just trying to argue for the conditional, "If you accept science (then you accept inference to the best explanation, and if you accept inference to the best explanation) then you accept moral facts.

Let's say that fails. What other ways are there to approach an argument for moral realism?

In Enoch we saw another way. But what he's still doing, the rock of his argument, is scientific realism. Put it like this: inference to the best explanation is true, we know that from scientific realism. If you think that inference to the best explanation is true, then you believe that it is justified. Then Enoch provides a justification for IBE. Then he says that the justification he provided also justifies some new principle--inferring that what is necessary for deliberation is true.

I've spent time trying to argue that this approach is misguided. First, I think that it's easy to see how you could have conflicts between what's necessary for deliberation and what's necessary for explanation. What this comes down to is there being a problem with creating something like two epistemic realms--they're going to interact and cause problems (though maybe make things better too). Also, the argument gets off the ground by demanding that a basic belief, such as IBE, give itself a justification, but maybe that's an unfair requirement. Maybe we need to simply take some principles as primitive and unjustified, or maybe we need to be coherentists and not ask for a single justification for every belief. So Enoch's argument is sensitive to alternatives that seem more attractive than his account.

There's another account that came before Enoch's, but it's vague and not fully worked out (as far as I can tell). S-M suggests the following:

Still another reply, compatible with the first two but relying specifically on neither, shifts attention from science and from mathematics and logic, to epistemology itself. To think of any set of considerations that they justify some conclusion is to make a claim concerning the value (albeit the epistemic as opposed to moral value) of a conclusion. To hold of science, or mathematics, or logic, that there is a difference between good evidence or good arguments and bad ones is again to commit oneself evaluatively. This raises an obvious question: under what conditions, and why, are epistemic claims reasonably thought justified? Whatever answer one might begin to offer will immediately provide a model for an answer to the parallel question raised about moral judgments. There is no guarantee, of course, that our moral judgments will then end up being justified. The epistemic standards epistemology meets might well not be met by moral theory. But there is good reason to think the kinds of consideration that are appropriate to judging epistemic principles will be appropriate too when it comes to judging other normative principles, including those that we might recognize as moral. This means that any quick dismissal of moral theory as obviously not the sort of thing that could really be justified are almost surely too quick.

In other words, the epistemic realm is another normative realm. The question S-M is asking is what justifies our justifications? What's the second-order justification of justifications? Now, if we're just asking for more justifications, why do we think that we'll get anywhere new? Put another way, we're asking for normativity to provide the basis for normativity. I think the idea is that we'll get somewhere, and that since we're providing justifications of something normative, that will also provide a model of how to deal with a different normative realm, such as ethics. In his longer essay S-M suggests that it's conceivable that maybe there would even be something that justifies both our epistemic beliefs and our ethical ones. His example is a long shot, but it's possible, I guess. Enoch really seems to me to be operating in that model: trying to find what justifies our epistemology, and then reflecting that back on ethics.

There's another thing S-M wants to say, which is that if some argument would conclude that normative stuff isn't good in general it would be too strong. But there's a natural weakening of these arguments to give a prima facie reason not to believe in the existence of something. We can allow stuff into our ontology, even if it's problematic to do so.

OK, one thing out of the way: this probably gives a good argument against a specific interpretation of the argument from queerness. Specifically, if the argument from queerness gives us a reason not to believe in ethical stuff, it should also give us a reason not to believe in epistemic stuff. But queerness says "There's nothing else like it," but here we went and found something else like it.

Is there another way to go? I want to throw out the possibility that maybe the game's over once we have some normative beliefs, specifically epistemological beliefs. Here's one argument: being justified in something, we'll assume, has some aspect of normativity to it. And so here's one possibility. Let's say that we analyze justification as, "X is justified in believing Y" as "X ought to believe Y." And so epistemology is full of ought-statements about belief. Then the only thing that distinguishes ethics from epistemology is that ethics deals with a lot more actions that belief (assumption: belief is an action). But it's not just justification that's normative, because there are some actions that involve being justified. You know something only if you're justified in believing it.

Another way for the game to be over is if we showed that ethics was doing nothing more than justifying beliefs. "You ought to do X" could be reinterpreted as "You ought to believe that you ought to do X." And what would be wrong with that? Plenty. It's actually a remarkably bad argument. Moving on...

A third option is that ethics and epistemological norms are just quite different things. As different as ethics and etiquette. Well, then what? Then I guess we're back to Enoch and S-M's efforts. Which isn't necessarily a bad thing. It's just that Enoch is problematic (and I think the problems come from pushing epistemology too hard and by carving up our knowledge) and S-M doesn't really offer anything. So if there's anywhere to go, maybe it's by just saying "belief is an action, so why not?" but that's a pretty rotten argument too, because you could just as easily say "picking up your fork is an action, so why not?" Oy, still not getting anywhere.

Enoch on S-M

1.A.8 Sayre-McCord
In the last section of his (1988a) Sayre McCord presents – in just four pages – what is by far the most detailed and careful attempt at the second strategy I know of. Despite its lack of crucial details, this section clearly anticipates my line of argument for Robust Realism.
Sayre-McCord starts by noticing that the explanatory project – indeed, the explanatory requirement itself – is normative through and through, for it requires, at the very least, that we evaluate explanations, and choose the best one. He notes that there is little to recommend a view that is realist about some normative facts but not about moral ones, and so he concludes that our engagement in the explanatory project already commits us to evaluative, and so to moral, facts. There is just no way of engaging in explanation without relying on normative facts.
Sayre-McCord goes even further than that. He argues that the respectability of normative (and in particular moral) facts and properties does not depend on their indispensability to the explanatory project:
The legitimacy of moral theory does not require any special link between explanatory and moral justification. (280)

Instead, what guarantees the respectability of moral and other normative facts are their justificatory, not their explanatory, role:
Just as we take the explanatory role of certain hypotheses as grounds for believing the hypotheses, we must, I suggest, take the justificatory role of certain evaluative principles as grounds for believing the principles. (278)

This is, I take it, an explicit rejection of the first strategy of Harman’s Challenge, a rejection of the explanatory requirement, and the beginning of an argument for normative realism from a different kind of indispensability. Though Sayre-McCord does not use the term “indispensability argument”, he does often say that evaluative facts are indispensable (e.g., 279). And he suggests that we talk in this context, instead of an inference to the best explanation, of an inference to the best justification (ibid.).
Now, Sayre-McCord does not give some crucial details here (details which I try to give in this chapter and in the rest of this essay): What exactly does indispensability amount to? Why does indispensability to the explanatory and the justificatory projects justify ontological commitment? Why is there a justification-related need to invoke irreducibly evaluative facts and not just, say, psychological ones about one’s brute desires or preferences? Furthermore, in some important respects the line he seems to suggest is different from mine: For one thing, I cannot see how anything like inference to the best justification can be made to work . More generally, it seems to me the justificatory work normative facts do matters to us because of the deliberative indispensability of justification. What is intrinsically indispensable, in other words, is the deliberative project, not the justificatory one. The latter only matters because the former does. This is why I think the argument for Robust Realism is better put in terms of deliberative rather than justificatory indispensability.
Despite the lack of details and these differences, and despite Sayre-McCord’s commitment to Metaphysical Naturalism, it is clear, I think, that his suggestions anticipate – in broad outline, at least – my indispensability argument for Robust Realism.