Some unclear explorations on indispensability

This post is exploratory, not expository. It makes less sense as it goes on.

I'm starting to dig a bit deeper into discussions of indispensability arguments. I'll do a longer exposition of these types of arguments at some point soon, but here's the short version: you need to refer to math and things like numbers in order to even express scientific theorems, and you should certainly believe in things that are necessary to express your best scientific theory. That's a LOT to unpack in such a short space, and all in good time.

The goal, at least in the short term (and hopefully in the long term as well) will be seeing how this argument can apply to ethics. Just to spell it out a bit: in the realm of philosophy of math this argument is believed by some to show that we should believe that numbers exist (and, correspondingly, that mathematical statements should be taken as true at face value). The question is, can the argument be fitted for ethics, to argue that we have a good reason to believe in the existence of ethical objects or concepts (such as "X is good")?

I just want to express two possible routes. There might be more, this is what occurs to me right now.

1) The easiest route is probably to analyze the math argument, and see what we "really" care about. That is, the argument says that because we care about scientific explanation we should believe the things that are necessary for scientific explanation. But maybe there are other things that we care about just as much as scientific explanation. Though I haven't read him carefully, DE makes this kind of argument. The idea is to find a parallel to scientific explanation in ethics that we can use to leverage an indispensability argument with.

2) You could argue that ethics is part of science. Now, this is probably impossible. But it's a fun idea for me to toy around with. After all, what is science? Is it just the investigation of the nature of the universe? Then we have to beg the question against ethics to get the discussion started, I could argue. After all, the form of argument for the existence of electrons has to be something like this: there is a fact of the matter, an objective truth about the nature of matter in the universe. The best explanation of the phenomenon of matter requires reference to electrons, so we should believe in the existence of electrons. So in order to exclude ethics we have to assume that ethical knowledge doesn't count as knowledge about the universe, such that the burden of proof is on ethics to show that it's objective. That is, if we start with the premise that ethical knowledge isn't very different from physical knowledge then ethical knowledge will be part of scientific explanation and the most common indispensability argument would have us believing in ethical concepts and objects.

Let me summarize this another way: standing behind the application of the indispensability argument seems to be an implicit acceptance that the other arguments for mathematical realism put mathematical realism in doubt. If mathematical realism weren't in doubt, then mathematical statements would be assumed to be true/false, just as scientific statements are. Then math would be part of the explanation and the leverage, not that which is dragged along by the certainty of physics. It's the same with ethics: you have to assume that ethics isn't part of proper knowledge in order to use the argument to who that it is part of proper knowledge.

Let me make the point one last way. Suppose that I presented you with the following argument: we should believe in the existence of those things, reference to which is necessary for our best scientific explanation of the world. Reference to trees is necessary for our best scientific explanation of the world, so we should believe in trees. This doesn't seem quite right to me--trees are part of the core scientific explanation, it's the secure rock that we can use to leverage other knowledge that is less sure along.

But maybe this entire analysis is wrong. I've been looking at the indispensability argument in the wrong way, perhaps. I've been looking at is as if it can take objects whose existence was previously in doubt, and then through the argument, makes belief in those objects' existence more secure. But maybe I shouldn't look at it this way. Maybe the better way to look at the indispensability argument is just as an observation of the theory, to see what is referred to in our explanation of the world.

So does that explain anything for ethics? I'm totally lost now. Need to try this again tomorrow or later. Ech.