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.