Responding to some of a commenter's points

But is it necessary for numbers to exist for me to be able to use them in my explanations of the world? In physics, we talk about the world as if there were a big three-dimensional grid running through it, but it doesn't actually exist.

It's absolutely necessary for numbers to exist in order to use them in my explanations of the world...unless it's not. What I mean is that the burden of proof is on the "fictionalist" to show that belief in the existence of numbers isn't necessary for their use in science. This is because it kinda seems that mathematical truths make explanations better--our explanations of the world would be worse if we didn't have math and didn't think that numbers existed. But, hey, if you can give a convincing account of how science uses math in a way that doesn't commit you to their existence, power to you. Hell, you might even think of calling your book "Science Without Numbers."

I find your examples somewhat problematic, in that leaky pipes and protons are both objects in the physical world, which numbers clearly are not. I think part of the issue is figuring out what it means for mathematical or ethical things to exist, but I don't know if thinking about pipes will really help with that. You mentioned gravity in a previous post, and that's closer, but maybe something like color or the principles of musical harmony would work better? (Depends what parallels you want to draw.)

This argument doesn't follow through; it stops before finishing. Because it's obvious that there are differences between protons and numbers. Sure, protons are physical objects, and (according to most) numbers are not. But so what? Do only physical things exist? Can you argue that, or do we just assume that from the start?

Asking what it means for non-physical objects to exist is a fair point. Here's the way the indispensability argument for mathematical objects works: Whatever it means for something to exist, we do know that being an indispensable part of our best explanation is sufficient for us to say that something exists. And numbers pass that test. You still probably need some sort of account of what existence means (does it just mean that the facts are true independent of human thinkers? does it mean that we can disagree? does it mean that we can know facts about them? etc.), but that's not essential to the argument. Of course, you could come back and counter "Well then, I have a different principle for how to determine what things exist" and we'll have to see how that one fares.


The question is, would it matter if you actually observed a cat burning in the real world? If I made an animation of children burning a cat (even a really crude one), or just talked about burning a cat, you would have the ethical observation that burning cats is bad. It seems then more like a making aware of something that you already know, rather than something you learn from observation (it crucially doesn't matter whether or not anybody has ever burned a cat). In science, on the other hand, I can talk about flying pigs as much as I want, but you won't get any biological insight out of it. Ethics seems to only require thought experiments, which makes it much easier to claim that it is simply an analysis of human thought processes, rather than of the world "out there".

...unless that's not true. I think we should distinguish between intuitions and observations, both in science and in ethics. A physicist might perform a thought experiment and come to some conclusion about what is possible or not possible. A biologist could do that too. So could an ethicist, reasoning out what situations were bad. But what your claim depends on is that there is no role for observation in ethics--that's exactly what's at issue here. And I do recognize that observation doesn't play the role in ethics that it does in science. Like I've said, there are no ethics laboratories, and it doesn't make sense for a guy in a lab coat to run a few tests to figure out if something is ethical or not. At the same time, it does seem possible to me that through observing the world one would reach ethical conclusions that one wouldn't reach from the armchair.

For example, suppose that you've never seen a guy rip off a customer in business. You think about it, imagine it, and say "Hmm, that doesn't seem SO bad." And that's fine, until you witness some guy get ripped off. When you observe him getting cheated, you realize that there was cruelty where you didn't expect it, and you conclude that the action was unethical. Now, why doesn't this count as observation? "Well, if you had thought through everything carefully enough, you could've reached that conclusion from the armchair. You just needed to think a little bit more clearly, and then you would've realized that it's cruel." But that seems like an unfair standard to hold ethics to for a couple of reasons. First of all, maybe the cruelty was extremely non-obvious, and needed observation to show it to you. Maybe the cruelty comes from the knowledge the businessman has that through some complex transaction this will ruin his customer's financial life. Second, it seems that there are scientific observations where you COULD'VE figured it out from the armchair in a similar way. Maybe we should be told that if we thought carefully enough about our own way of learning language we should be able to figure out a perfectly good psychological or linguistic theory. But that seems unfair. But isn't that what we're asking of ethics--to rely only on intuitions and never on observational insight? But observation is helpful, just as helpful as it is in the sciences (well that's an exageration, but at least observation doesn't seem totally irrelevant).


My temptation as a non-philosopher is to view this as a psychological question--different people are satisfied with different levels of proof. I believe, for example, that Neil Armstrong walked on the moon in 1969. I also know people (otherwise normal and intelligent) who believe this is not the case. Clearly, we each believe ourselves to apply reasonable standards of proof in determining what is in fact the case. I don't know that this really transfers to math and ethics, but it might. (For example, in people's different reactions to the idea of triage in epidemics--some people can't get past the gut reaction, while others are willing to entertain the idea of trade-offs. There was a NYT article about triage today, which made me think of this.)

But there is a wholly separate question from the psychological one, which is the question of justification. We might be interested in human reasoning as something to understand and explain, but what about understanding what human claims and principles of reasoning are justified? That's the philosophical question. (I might as well copy and paste the opening paragraphs from Frege's "Foundations of Arithmetic," because I'm trying to make exactly the same point.)

Two questions

1) Are we able to give a good justification for inference to the best explanation (or any other principle that justifies our inductive inferences)? If we're not able to give a good justification, then how do we defend our choice to believe in inference to the best explanation? If we simply have to shrug our shoulders and take some things as primitive and given, then can we also take something else as primitive that would give us ethical facts? How can we do this while not also allowing facts about sorcery to gain validity?

(Note: what Enoch did was try to justify inference to the best explanation, and it turned out that his justification of inference to the best explanation also plausibly would include inference to what's necessary for deliberation, and this included some normative/ethical facts. So this question could be restated in the following way: is Enoch's the best justification for inference to the best explanation? It doesn't seem very good. If we can provide a better one, will it also justify ethics? If there is no good justification (which could be OK) then how do we prevent anarchy?)

2) What is the strength of the following argument: in order to believe in inference to the best explanation you have to believe that some explanations are better than others. This means that you have some criteria for what makes an argument best. But why should you believe in the best explanation? Implicit in inference to the best explanation is that you ought to believe in the best...nevermind, this isn't going anywhere. I'll come back to number 2 later.

What I'm reading about now

So there are three choices you can make when it comes to something like inference to the best explanation.

1) You can give a good justification for the principle: I'm still looking to find one. The problem with justifying inference to the best explanation is that it's pretty much trying to justify inductive inference (meaning, trying to justify my belief that since the sun rises everyday it's also going to rise tomorrow). Hume provided arguments that make it difficult to justify inductive inference, though we can do our best to describe our practice. Then you can check to see if your justification justifies anything else by the way, such as inference to things that are necessary for ethical reasoning.

2) You can give an unconvincing justification: One could complain that this is what Enoch does. I tend to agree.

3) You can refuse to give a justification: after all, justification has to end somewhere. You (probably) can't have everything justified. The chain has to run out somewhere (probably). But then the challenge is, how do you avoid mayhem? If inference to the best explanation is unjustifiable, then is there anything wrong with us taking other wild and crazy principles as primitives?

Sorting this out is one of the current challenges I'm trying to learn more about.

Another related challenge is trying to figure out whether one implicitly assumes some normative stuff when you accept inference to the best explanation. After all, aren't we presupposing certain values when we talk about the 'best' explanation? Aren't we presupposing our ability to deliberate and come to conclusions? Doesn't this mean that there are "oughts" hidden in our scientific talk, and if those "oughts" are OK and in our ontology, then does it help out for believing in moral "oughts"?

And how the hell can I bring math back into this (after all, my primary goal starting off wasn't to defend moral realism or to explore scentific anti-realism, but to understand math and ethics better through close analysis of realism/anti-realism debate. Is that goal still possible?)

Handed into Nickel about a week ago

I'll begin with a quick summary of Enoch's argument. Enoch is sympathetic to Harman's challenge to the normative realist. Harman argues that one only needs physical and psychological facts in order to explain normative observations. Normative facts play no (indispensable) role in explaining these observations. So normative facts are irrelevant for explanations of non-normative facts. Harman considers this a strong argument against the view that there are objective normative facts.

Although Enoch agrees with Harman that normative facts play no indispensable role in explanations, he argues that there are other ways to justify belief in facts besides indispensability to explanation. After all, what justifies inference to the best explanation (IBE) in the first place? According to Enoch's analysis, IBE is justified because of the "intrinsic indispensability" of the explanatory project. For a project to be intrinsically indispensable to me means that "I have no option of stopping (or not starting) to engage in it" (Enoch 34).

If this analysis is correct, however, deliberation seems to be just as intrinsically indispensable as explanation. Just as we have no option of generally stopping to explain what we observe, we have no option of generally stopping to deliberate when faced with decisions. Finally, Enoch argues that normative truths are indispensable for this deliberative project. Hence, we are as justified in believing in normative truths as we believe in protons, numbers, or anything else that whose existence we inferred from our best explanations. So, Enoch concludes that if IBE is a valid principle, then we are likewise justified in believing in normative truths.

Actually, Enoch believes something stronger than this conditional claim--he believes that we are unconditionally justified in believing in normative truths. But this claim depends on his thesis that he can ground "epistemic justification in pragmatic utility" (42), and he defends that claim in an unpublished manuscript. So I'll limit myself to the conditional conclusion (presented on p.43) that "the price one has to pay in order to reject normative facts is a denial...of the validity of IBE."

In the following analysis I'll raise and begin to develop two challenges to Enoch's argument.

II. Is the deliberative project in tension with the explanatory project?

According to Harman, normative facts neither harm nor help us in our explanatory project--normative facts are irrelevant to explanation. Enoch largely accepts Harman's analysis, but he counters that even if normative facts are irrelevant to explanation, their indispensability to deliberation justifies our belief in them. These normative facts are still irrelevant to explanation, but we have some other justification for introducing them into our ontology.

I am concerned that once these normative facts are introduced into our ontology for the sake of our deliberative project, they cause problems for our explanatory project. In other words, once we accept Enoch's argument we end up with a less-than-best explanation of the world. Our explanation of the world was better before we accepted the existence of normative facts.

If this concern is justified, then there would be a conflict between our deliberative and our explanatory projects. On the one hand, deliberation would be urging us to accept the existence of normative facts, and on the other hand explanation would urge us not accept their existence. We would then need to find a way to reconcile these claims on our ontology, and we might decide that the explanatory concerns override the deliberative ones, in which case we would no longer be justified in believing in normative facts.

Why am I concerned that these normative facts cause explanatory problems? After all, didn't Harman show that normative facts are irrelevant to explanations? This would mean that normative facts do not (help or) harm our explanations. So how can normative facts cause problems for our explanatory project? Harman's claim was actually more limited. He argued that normative facts do not help or harm our explanations of non-normative facts. But once we introduce normative facts into our ontology, they are part of the universe and might have features that need to be explained, just like any other fact might.

Once normative facts are introduced into our ontology, our explanatory project has expanded. We now will seek explanations of any peculiar features of these normative facts. Some of these explanations are easy to supply. For example, "How do we explain our knowledge that these normative facts exist?" has a known explanation; the explanation is that the argument that led us to believe in these facts is valid. But there are other features of these normative facts that will require difficult, hard-to-come-by explanations. For example, it's often observed that normative facts are queer, in the sense that they have motivation built into them, such that if they are true they are sufficient to motivate an agent to act. This makes normative facts quite different from non-normative facts. What explains the queerness of normative facts?

Note that I'm not claiming that entities with these strange features can not exist. That would be rehearsing Mackie's argument from queerness. Rather, I'm making a more modest claim, that these strange features require some sort of explanation. What's the difference between the arguments? An acceptable response to Mackie's argument would be that many of the objects that we normally believe to exist are metaphysically queer, and so queerness is not an obstacle to existence. But that response would be insufficient for my objection. My argument still requires an explanation of this queerness. If there is no explanation for this queerness, then there is something additional in the world that I am unable to explain, and so my explanatory project is worse off than it was before I believed in normative facts.

But isn't my objection based on a confusion? The discovery of the existence of any new object inevitably leads to more questions. This doesn't mean that, somehow, our explanation of the world is worse. Rather, we judge how strong or poor our explanations of the world are given the objects that we believe to exist. For example, suppose that we directly observed a new planet in between Jupiter and Saturn. This would mean that we would have to throw out a lot of our astronomy--all of our laws of gravitation would be wrong. So, in a sense, our explanation of the world is worse off once we know that there is this tenth planet. But this is clearly no reason to reject a planet that we've directly observed. So why isn't it the same when it comes to normative facts? We've recently discovered, thanks to Enoch, that normative facts exist. Once they exist, there are features of these facts that need to be explained.

The difference is that this tenth planet, if it were to exist, pulls its explanatory weight. An explanation of the world that didn't suppose that this tenth planet existed would be a worse explanation than one that did assert its existence, because the former fails to explain our direct observation of the planet. But in the case of normative facts, the facts do not pull any explanatory weight. And so explanation only suffers from their presence.

(There are other ways to respond. Is explanation really needed? What sorts of things need to be explained?)

If my argument works, then Enoch's argument becomes more complicated. In order to reach his conclusion he has to show that the deliberative benefits somehow outweigh the explanatory costs.

III. Does IBE need a justification?

According to Enoch, the proponent of IBE needs to provide "a reason for taking explanatory indispensability to justify ontological commitment" (29). Further, he suggests that any such reason will be unable to justify explanatory indispensability without also justifying deliberative indispensability.

But one may reasonably wonder whether justification might run out at IBE itself. Enoch recognizes that "justifications come to an end somewhere" (42). There are some things that we must accept without justification (unless we’re conformational holists, I suppose, in which case every belief gains has some justification in merit of being part of the overall theory). These primitive beliefs we will hold as true, yet we will be unable to justify them. Supposing we take IBE as such a primitive belief, one that we hold as true but have no justification for. This would seem to undermine Enoch’s argument. He argued that the justification for IBE is the same as the justification for inference to deliberative indispensability—IBE is justified if and only if inference to deliberative indispensability is justified. But if IBE is not justified, then deliberative indispensability is also unjustified.

The question then becomes, is there any reason to take IBE as a primitive belief that is not a reason to take inference to deliberative indispensability as a primitive belief? Now, since we’re refusing to justify IBE, reasons for taking IBE as a primitive are not reasons for thinking IBE is true. We will not be justified, in any sense of the word, when we believe IBE (but since we take IBE to be true, we will be justified when we employ IBE). Rather, we’re looking for a principle that guides our choice of where to stop seeking justification. I will not pretend to have such a principle. However, I can think of plausible candidates that would include IBE but exclude inference to deliberative indispensability in the set of primitive beliefs. For example, perhaps our principle will advise us to take as primitive only those beliefs that have some broad agreement already. We wouldn’t want our most basic beliefs to be too controversial. This is a bit dangerous as a principle, since IBE is itself somewhat controversial. But Enoch’s inference to deliberative indispensability is far more controversial than IBE. It wouldn’t seem prudent to take it as a primitive belief.

Enoch might respond that we are acting arbitrarily here, and that we are simply stacking the deck against his robust meta-normative realism, and that we are unjustified in distinguishing between IBE and Enoch’s own principle. And that is exactly right. The reason why this is a response to Enoch is because he claimed that he could force the proponent of IBE to accept a further principle of belief-formation, inference to those things that are indispensable to deliberation. But the proponent of IBE only needs to do that if he has a justification of IBE; if he has no such justification, because he’s taken IBE as a primitive belief, then there is nothing to justify Enoch’s principle. Then the question is whether Enoch’s principle is attractive as a primitive belief. Plausibly, it is not.

Explaining why Enoch’s principle shouldn’t be taken as a primitive belief is difficult; any principle for choosing primitive beliefs must either be justified or itself taken as a primitive. Eventually justification for these principles guiding the choice of beliefs to be primitive will run out as well, and we’ll be forced to take something as primitive again. At some point we will need to make some arbitrary choices. If Enoch’s argument is “Since we have to make some arbitrary choices eventually, why not arbitrarily choose to include inference to deliberative indispensability?” then I don’t think the argument is very convincing. Of course, since I’ve run out of justification, what I mean is that I don’t like such an argument, though I can’t justify my dislike of the argument. Perhaps I prefer to play things safe and not make arbitrary choices that will expand my ontology. Perhaps I am biased against arguments that would easily allow for principles that would force me to include sorcery into my ontology. One way or another, though, I don’t like this argument, though I can’t justify it.

The point of this line of argument, though, is that the anti-realist can avoid Enoch’s conditional conclusion by moving the discussion into the realm of the arbitrary, as opposed to the realm of the justified. By refusing to justify IBE, the anti-realist forces the burden of proof back on Enoch. Enoch must provide a way to add inference to deliberative indispensability to our set of primitive beliefs without opening the door to any old belief—even one that could justify sorcery—being included in the set of primitive beliefs.

Inference to the best explanation and skepticism

Inference to the best explanation is a really interesting philosophical topic.

Let's start the story with Descartes. Skepticism becomes an option--what if we're all being deceived? What if our eyes and ears are lying to us? Descartes tried to answer this question by starting with some firm knowledge and slowly justifying almost all of our knowledge from a few secure facts. In this way all our purported knowledge would be justified, and we would be allowed our confidence again.

As the story goes, not everyone agreed with Descartes secure truths. So other attempts at justifying our knowledge, at securing epistemology, began. Locke and Hume tried to justify human knowledge by matching all knowledge with observation. But, famously, this only gets you so far. So empiricism doesn't work to give us complete, skeptic-free confidence in our beliefs.

(Here I fudge the story a bit.) So what do you do now? Is it a free for all just because we don't have an answer to the skeptic? No, it's not. What we do is acknowledge that justification needs to end somewhere, and as it turns out justification for our beliefs ends before the point where we would feel totally secure in our beliefs. So there isn't any answer to the absolute skeptic. But that means we need to figure out where to stop.

So the game becomes trying to build your house as close to the cliff as possible. You lose if your house falls off the cliff, and you also lose if your house ends up looking like a mess. That is, the game is to find a starting point with as few assumptions as possible (satisfying a general desire for parsimony in the absence of justification) and building and justifying as much of our common-sense and scientific beliefs as possible. You lose if you end up with skepticism, and you also lose if you end up justifying silly beliefs, like beliefs in fairies or witches.

Right now I'm reading a paper where someone tries to say "We don't have to stop the trail of justification at inference to the best explanation. We have a way to justify inference to the best explanation that makes sense." As it turns out, that way of justifying inference to the best explanation is designed to allow for other kind of "inferences" besides inference to the best explanation. Specifically, it wants to allow for inference to the only things that make deliberation possible, which would include normative facts.

As far as I can tell, the debate about this paper has to be (obviously about the details of his argument, he needs to show lots of little points in order to get his big points into play) about whether he tried to go too far back. If his stopping point is no better than Inference to the Best Explanation, I think he'll find many people saying "Hmm, yeah that's interesting. I'm going to build my house right over here on ground that's a bit more secure, right here with Inference to the Best Explanation."

[His response will be, but building your house over there you still haven't made deliberation possible, but that's the second half of his debate. If the first point is dependent on the second, then he's got a very different argument on his hands.]

There's also a debate (that I know nothing about) where people wonder if inference to the best explanation is the right place to stop for reasons that have nothing to do with ethics.

Also, an observation: there are no arguments for mathematical or ethical realism that are particular to math or ethics. That's because realism itself isn't restricted to math or ethics. You win the realist game if you define plausible methods for coming to physical truths, and then use those same methods for reaching mathematical or ethical truths. This is exactly what inference to the best explanation/indispensability arguments do.

A weird idea about reductionism

What is reductionism? Here's an example of a reductionist approach--a reductionist approach to metaphor. You start with a sentence that seems kinda weird: "The city is a jungle; you've got to take care of yourself." So, on the surface this sentence seems to be quite similar to sentences where you identify two things, or at least apply some property to some subject, EX: "Michael is that guy" or "The eagle is a giant bird." If you classify "The city is a jungle" with those sorts of sentences you get really screwed up results. What I mean is, if you take "The city is a jungle" literally you'll either think that I'm classifying the city in the category of jungles--cities are jungles--which is just stupid. Obviously, that's not how you're supposed to read "The city is a jungle."

Quite clearly, what we need is to analyze what "The city is a jungle" means. What it really means is "The city is similar to the jungle in certain ways [e.g. it's dangerous and complex]." The point is that you start with some weird way of speaking that we don't think that we should take literally, and we reduce it to a level of discourse that we're more comfortable taking literally. This is what I just did with metaphor.

A more philosophical example: We start with the notion of causation, and we think that it's mysterious and confusing (Hume thought this). He doesn't think that a literal understanding of causation makes much sense, so he reduces it to a more down-to-Earth notion. So he takes a sentence "A causes B" and translates it as "Whenever B happens, A happens too." He's reduced discussion of causation to a discussion of correlation, the occurrence of two events at the same moment.

People do this to ethics too (Harman recommends that one has to do this in order to maintain ethical realism). "Saving lives is good" sounds a bit spooky, and it's not clear what things in the universe ethics is talking about, and if it's anything it would seem that it would have to be abstract objects or properties that you can't see, smell, touch, etc.... There's a bunch of problems. So people say, "Well, let's take a reductionist approach to ethics; we'll translate ethical statements into normal ones that we feel more comfortable with." So this, for example, can mean that ethics gets translated into the language of emotions--after all, we all agree that people's emotional reactions exist, and so everyone should feel comfortable talking about that. For example, you might reduce/translate "X is good" or "Y is bad" into "I like X" or "I don't approve of Y." (That would be called "emotivism", and it's a reductionist approach to ethics). If you're willing to translate everything into the language of emotional responses, then you no longer have to say that there's anything special about the language of ethics; truth in ethics is just truth about evaluating the way you feel. There are no ethical facts, only physical facts, and in particular, physical facts about emotional responses to situations and actions.

I wonder, though, what if we were to try to reduce physical facts into ethical ones? That's a bit of a loony idea. But suppose that we felt comfortable with ethical facts and uncomfortable with physical ones. What's stopping us from trying to reduce physical facts to ethical ones? If it works in one direction, it should be possible to do it in the other.

How would that project go, though? We would need to find an ethical translation of all statements that refer to physical objects of properties! Let's take an example, "There is a zebra eating grass behind the barn." Now, could we simply translate this as "It's good that zebras eat grass behind barns"? Of course not, for a bunch of reasons. First, because it's not really a translation--we're still referring to zebras, grass, and barns, and this means that I'm still committed to the truth of some physical facts. Second, because a reductionist approach works when you can capture what is meant by the original sentence (for the most part) in the translation. There will be lots of situations when we would want to say, intuitively, that there is a zebra is eating grass, but we wouldn't always want to say that that's a good thing. Come to think of it, while the second is true, the first problem I mentioned is the real problem.

So, what's the reason behind this failure? Part of the problem is that there aren't any particular ethical objects that we can employ. The language of physical objects is very rich, and the language of ethical objects is quite poor. So what could we do to correct this? Maybe expand our circle out from ethics, and let's employ all talk of values (this will include discussions of beauty, simplicity, etc.). It's still no good, I think, and I'm willing to diagnose the problem in the following way: value language has a lot of predicates, concepts, properties, but very few objects.

(So there's a few complications to what I wrote. First, for naturalists there are only scientific facts, so to ask whether I can translate physical facts into ethical ones is a question that wouldn't make sufficient sense. Also, I'd have to show how this argument works in math. Could we begin to talk about reducing physical concepts to mathematical ones? Probably not, but why? Is it because the language is so sparse. So then what's my point here?)

The absence of ethical objects in our everday ethical manner of speaking is a complication that I run into in my research. The indispensability argument in math concludes that mathematical entities exist; it's not clear that anybody really wants such an argument to work in ethics. We want the objectivity of ethics, but ethics-talk usually involves applying predicates/concepts/properties to physical things--acts, deeds, states of the world, rules, whatever.

I think that this is a more precise way of saying Harman's argument. The reason why ethics seems to be dispensable, the reason why our best explanation of the world doesn't need it, is because it doesn't make reference to any ethical objects, just ethical concepts/predicates. And part of the reason why math seems indispensable is because we're making reference to mathematical entities.

Earlier I posted about why existence--ontology--should matter to us. After all, even if we have an argument that concludes that numbers exist we won't start suddenly bumping into numbers on our way to the library, work or school. Our lives will be the same; it's our perspective on the world that is liable to change. And I put out the following idea: the reason why existence is interesting is because ontology seems to secure semantics. We know that some sentence can be true or false if it refers to objects that actually exist--if it's actually talking ABOUT something in the world. So ontology becomes a handmaiden of semantics. Some philosophers disagree with this; they think that it's interesting to investigate the world to settle the question of what exists and what doesn't. I'm not sympathetic to that view. We know what it's like to live in the world, and if we're positing the existence of acausal, abstract objects that shouldn't really change my life. But it still seems to matter whether stuff exists or not, and I argued that the only reason that I knew of was because if X exists it seems that it could be true or false to say stuff about X.

If what I've posted is right, then there might be very different problems facing philosophers of math and metaethicists. Philosophers of math need to secure the objectivity of math by saying that mathematical objects exist. But ethics doesn't really make reference, in general, to ethical objects. They just apply ethical predicates to regular, normal physical objects. So the question of objectivity in ethics might be the kind that our form of the indispensability argument can't really touch.

Summing up the way I've been thinking so far

I'm about to dig into a more substantial phase of research now. Over the next few weeks I'm going to be trying to understand what an explanation of the world is, and what the differences are between science, math, and ethics in this regard. So before I do, I want to clarify what I'm going into this research with, what my hypothesis (of sorts) is. I can't really defend this view; it's just a starting point, a bunch of suspicions that I have.

Without a doubt there is something that is quite different about ethics, science and math. Pinning down exactly what is really the challenge, and the next challenge is trying to figure out what those differences should mean--why the differences matter.

My general hypothesis is that hard, strong, epistemological lines tend to break down under stress. For example, Quine convinced most of the philosophical world that there is no strong, philosophically useful distinction between the meaning of words in a sentence and the substance of those sentences; there's no strong dichotomy between analytic sentences and synthetic ones. The argument comes down to just applying a great deal of stress to the dichotomy, and watching it collapse under investigation. I expect, coming into a philosophical investigation, a similar thing to happen when we've set up boundaries between realms of knowledge. Facts/values, empirical/non-empirical, a priori/a posteriori, history/science, objective/subjective and of course science/math/ethics are all ways that people have tried to divide up realms of knowledge. The problem is not dividing up realms of knowledge itself--everyone does that because there are real differences between the areas--but when it comes to epistemology, how we know what we know about these realms, I expect the dichotomies to break down. I expect that the way we gain historical knowledge isn't very different from the way we gain scientific knowledge. I expect that the way we gain mathematical knowledge isn't so different from the way we gain scientific or ethical knowledge. That's my hypothesis, in general. It's heavily influenced by Quine and Putnam (and Dewey, through Putnam), I think. At the very least, it's influenced by a misinterpretation of Quine and Putnam.

So, in particular, I expect that the distinctions between how we gain ethical knowledge and how we gain scientific knowledge break down under pressure. I expect that all knowledge is more or less in the same boat. I suspect that the differences are all of quantity, and not quality of knowledge. So I suspect that any attempt to explain why scientific stuff is objective and ethical or mathematical stuff is not eventually breaks down. I think that the indispensability argument goes a good way towards showing how the distinction breaks down between math and science, and I suspect that something similar can be adapted for ethics. I think that there are at least two good, promising ways of doing this, but in the end every way of making the argument does it by trying to make science a little bit more modest.

But I started by saying that there are real differences between math and ethics and science? It's just a fact that there are no ethics laboratories in universities, and it doesn't strike us as a very good idea to start such labs. Why is that? An analogy from math is useful in clarifying the question. Once Quine/Putnam argue that math is actually empirical knowledge and as objectively known as science, they need to answer the question: what fooled people for so long? Why did people think that math was a priori and divorced from experience? So, if you argue that ethics is on the same par as science, you have to explain why ethics strikes people as being the sort of thing that it doesn't make sense to start a lab for.

Of course, you could say that people are wrong, and that we really should be building ethics labs of some sort. Some people--I think that I heard this in the name of Nagel or Parfit--think that ethics is just a young science, one that's bound to develop the way that other sciences have. So maybe these people think that opening ethics labs makes sense. But I'm more sympathetic to the position that there is something about ethics that makes such a notion strange. I guess this could be consistent with the view that we should open labs, but I guess the view I find most attractive is that ethics is really really really hard. (This is also the reason why I'm not swayed by an argument from disagreement that ethics is subjective. Disagreement is consistent not only with subjective views, but also with really really really hard ones.) I bet that I could even show that some things that eventually fell into the realm of science were considered subjective problems, ones that it wouldn't make sense for a lab to study. For example, I bet a lot of brain stuff fits this pattern.

How does this relate to the original program of contrasting math with ethics? Well, the idea is that by taking an argument that's found in the math literature, and seeing how it holds up under ethics we'll be able to see what math and ethics have in common. And my guess is that math and ethics can be both shown to be close to science when it comes to epistemology. And that the differences in the way they have been considered have to do with how hard/easy studying the subject is (math is more objective cuz we're able to isolate variables, ethics is REALLY hard cuz there are so many variables, math is a priori because it's an essential part of the web of beleif, ethics barely seems like knowledge because it's so hard to get secure on it, etc.).