What is a theory? I define it to be a system of ideas that are intended to explain something. Theories usually have some kind of more universal property: whilst we might use theory to explain practical phenomena, theories have a level of abstraction above the immediate phenomena. As a basic example, we might wonder why it is wrong to kill a woman. Our theory of morality would provide an explanation, perhaps in terms of rights, utility or what not. Our theory however seems to tell us more: the fact that it is a woman seems irrelevant, in fact our moral theory might explain that it is wrong to kill any human.
Explanation is a non trivial topic. What counts as an explanation? Well on some level we would expect an explanation to be something that offers value in our thinking: it helps us understand things and perhaps helps us decide how to behave. On another level, we expect an explanation to reveal the true nature of things: it lets us perceive the objective reality. In an ideal world these would coincide: all theories would purport to refer to the objective reality, and our theory helps our perception of it, thus providing us with action guidance and understanding. Unfortunately this does not seem to be the case: a literary analysis whilst illuminating may not refer to the objective reality. We might think this is the case because there is no inherent object being referred to by the analysis, we can not pick out a real thing to say that the analysis is about. Instead the analysis or theory is there to present an interesting idea; to give us insight and understand perhaps what the author was thinking.
Other times, our theories generally do try and explain the world. Our theories of atoms purport that reality is really such that it has atoms, even if we cannot perceive them. Our theories of natural selection claims that the process of biological change is governed by an overarching principle, and that this is the way the world behaves.
The important thing here seems to be the difference between the mind independent and the mind dependent. Theories are of value for both, but it is important to establish the distinction. If a theory is mind independent that the theory is in some sense externally valuable because it attempting to access reality. If a theory is mind dependent then the value is entirely internal, it depends on us being able to think and understand.
I've suggested here that mind independent theories have some kind of special status. I want to explicate what I mean here. If a theory is mind independent and purporting to reflect reality then this provides us with some kind of ontology of theories. These theories actually are trying to grab hold of the world. These theories are especially important because assuming the world exists, the development of these theories genuinely allow us more and more access to the world. Because the world is a specific system with rules and laws, we expect a degree of logical consistency. Thus if a theory is viewed as correct and / or as of value, it can be in some sense easily measured against the other mind independent theories.
The mind dependent theories have a weaker ontology since they don't have the objective reality to connect themselves to. Instead they operate inside our mind. They offer ways for us to think about things without necessarily purporting that reality is as they say. This lack of committment is inherently weaker, because our ability to evaluate these theories are in some sense limited to other mind dependent arguments.
Now it is very important for people to clarify the ontology of their theories. The example that I am quite interested in is questions about gender. For example suppose we have a theory of gender in which transexual people exist. Perhaps our theory tells us that one's assigned gender can be distinct from one's actual gender. This is characterised by the idea that you are a woman in a man's body. Now we have an important question: what is the ontology of this theory?
If the theory is meant to the mind independent ontology then we expect that there is this genuine concept of gender somewhere in reality. That is that there is some kind of switch or indicator (perhaps that we cannot epistemically access) that says whether a person has gender male or gender female or neither. Because we think the world is logically consistent, we think that there must be a true theory of gender out there; some objective and decisive way of understand these concepts. If you're telling me that people's real gender is what they identify with, then you'd be saying that there actually exists some kind of mechanism in reality (even if we cannot access) that takes self identification as a means to establish the switch.
If in comparison the theory has the mind dependent ontology, then it is saying something rather different. The theory of gender is then just a way for us to understand society, to understand certain phenomena. For practical purposes, this might not be so bad, in fact perhaps this is enough. However one might think we lose some element of justification. The mind dependent ontology just seems to lack the concreteness of the mind independent ontology since we don't purport there to be any objective tests of validation. That is, there would be no way for anyone to really prove it wrong, even in principle.
Now I'm sure we will face some confusion here so I want to emphasise two points.
First, the ontology is distinct from the theoretical provability. I can have a theory of mathematics that says there are abstract objects that I cannot access. I couldn't prove their existence, yet my theory still claims that they are there. It claims that the things we talk about genuinely refer to an objective reality. Thus philosophical and non empirical arguments can very much have mind independent ontologies. It's not necessarily about the ability to verify, its about whether the theory is purporting to describe the objective reality.
The second point is in terms of normativity. Suppose I say something like 'killing is wrong'. This is a normative claim because I am assessing what is good or what is bad. Now what is important here is what my 'good' or 'badness' is in reference to. If I am a moral realist I might think that the use of 'wrong' here is because I purport that reality genuinely has concepts of right and wrong, and that killing has the property of wrongness. Good and bad exists in our objective reality, and I have access to it.
Compare this to a claim like 'You should call people by their preferred pronoun'. We can identify here another sense of morality, that it would be wrong not to do so. However we can do this whilst remaining agnostic about the ontology of the theory of gender. That is, we can accept it because we think its nice to do what people ask of us, without having to accept some underlying theory that people have the gender of their preferred pronoun. Consider the example 'you should think 2 +2 =4'. Perhaps I think the theory of number does not refer to actual reality, but instead is mind dependent - it just offers a good and valuable way to think about plurality. In that case, I should still think that 2+2=4, but my reason to do so is not because 2 exists in our objective reality, but instead dependent us valuing concepts such as rationality. Whether or not a theory of rationality has a mind independent ontology is another interesting question. I'm inclined to think not, but that doesn't mean it lacks value.
So when people come up with theories about the world, ask them what the ontology of their theory is. Is their theory genuinely trying to purport that the world is a certain way, in a mind independent sense? Or are they just offering a useful way to think about reality?