Two ways to make an indispensability argument in ethics

In this post I'll quickly go over the Quine-Putnam indispensability argument in math, and describe two ways that I can think of applying this argument to ethics.

Here's a version of the indispensability argument (and it's sorta sloppy with the ideas, but hopefully clear)

(1) We should believe that something exists if, when we describe the world with our best scientific theories we are forced to speak as if that something exists.
(2) When we describe the world with our best scientific theories we are forced to speak as if mathematical entities exist.

Therefore:
(3) We ought to believe that mathematical entities exist.

Now, how could we apply this argument to ethics? In short, we can change premise (1) above, or we can change premise (2). Here's how.

Version #1:

(1) We should believe that something exists if, when we describe the world with our best scientific theories we are forced to speak as if that something exists.
(2) When we describe the world with our best scientific theories we are forced to speak as if ethical entities exist.

Therefore:
(3) We ought to believe that ethical entities exist.

Would it shock you to learn that such arguments have been made? I'm still at a very low level of familiarity with this kind of argument, but it's my impression that Sturgeon makes an argument very similar to this one. He argues that we should believe that ethics is objective, because if we don't believe that ethical statements are literally true and objective we are at an explanatory loss! I need to read more about this, and I also need to read about the relationship between the indispensability argument and inference to the best explanation.

Here's the second, less audacious version of the argument applied to ethics:

Version #2

(1) We should believe that something exists if, when we do something that we are really committed to taking seriously we are forced to speak as if that something exists.
(2) When we do that something that we are really committed to taking seriously we are forced to speak as if ethical entities exist.

Therefore:
(3) We ought to believe that ethical entities exist.

In short, this version can get off the ground by asking why, in the original Quine-Putnam version of the argument, we let science decide what we're committed to existing? Then you say, "the reason we give science such a privileged position is because X". The next step is to argue that there is something else that is X, and that something else makes us committed to ethical entities.

Just to make something up that sounds the tiniest bit plausible: Why do we say that science has the ability to determine what we're committed to? Because science helps us live our lives in safety. If we weren't to take science seriously then our lives would be unsafe! But that means that anything else that is indispensable for living our lives in safety should have the same status as science, with respect to its ability to determine what we believe in. Perhaps we believe that ethics is necessary for living our lives in safety--otherwise chaos in society would break out!--so we need to take ethics as seriously as science. And then you argue that you can't talk about ethics without believing in ethical entities, so you're justified in believing in ethical entities. This argument isn't sustainable, but it's the form of the argument, the move that's made, that I want to draw out.

As it happens, David Enoch takes an approach that resembles this one. I need to read him more carefully, but he talks aobut non-explanatory indispensabilities.

So we're in good shape! We've recognized, abstractly, two ways that the argument could go, and we've found some names who make such arguments. Plus (and I didn't tell you this yet) I found a couple articles that review both of these strategies. One of them is by Brian Leiter. So we're making some progress here.