Ideally I would like to simply discuss what a philosophical theory is, and how it can be evaluated, but to do that we need to have a theory about theories in general first. And the best place to start thinking about theories in general is with scientific theories, since their success at explaining the world is partly because we have a clearer understanding of what makes one scientific theory better than another.
The whole point of a theory is to explain the world. Well, perhaps that is too hasty, because the existence of a world is really only part of a particular theory about reality, one that is so good that questioning it seems like madness. Perhaps more fundamentally then the point of a theory is to explain our observations. And because the existence of a world containing us in it is a great explanation for our observations the job of a theory then become to explain this world, or at least part of it, which is how I will describe the job of a theory from now on.
In order to explain the world a theory must do two things. It must convert ostensive definitions to categorical ones*. And it must provide rules describing how the entities postulated by the theory are related to each other (usually relations in space are taken for granted, and the explanation is cast in terms of how some configuration of entities at one time gives rise to the configuration at subsequent times). Roughly, an ostensive definition is one that picks something out by describing it as that thing which bears some specific connection to us. For example, a particular chair might be defined as “that thing over there which seems chair-like”. Such a definition doesn’t presuppose anything about what the chair really is, it only says that whatever is going on needs to explain how it seems to me, in a way consistent over time and over numerous senses, that there is a chair over there. So explaining that there is a collection of particles over there which reflects light, ect is one way of explaining it. But an explanation which makes the claim that I and everyone else who thinks that there is a chair over there is hallucinating could be equally successful.
Thus it seems natural to say that what a theory (or the creation of a theory) does is convert ostensive definitions into categorical definitions. Categorical definitions, in contrast to ostensive definitions, say what something is by describing it as having various properties. Saying that the chair is a collection of particles is a categorical definition, which is especially obvious when we provide more details, about how they are arranged, how they interact with the environment, ect. And so is the explanation in terms of hallucination, except this time it is the hallucination that is given various properties (such as being a similar defect in all of our mental capacities, ect). Of course this hallucination might in turn be reduced to an explanation in terms of the particles that make up the brain, but the fact that a theory can be explained in terms of another theory does not make that first theory wrong, assuming that it is in perfect agreement with the theory that explains it. The conversion of ostensive definitions into categorical ones is necessary because of the second task of the theory, to provide rules for the relations between the various entities it deals with. Obviously to express these relations, especially the rules that govern how they change over time, we need to be dealing with objects that have various properties, in order to formulate those rules and those relation in terms of those properties.
As a side note then let me say a few words about terminological borrowing. Terminological borrowing is when we have a word to describe a particular kind of entity in one theory and later borrow it to describe an entity in another theory. Used responsibly terminological borrowing can be helpful. For example, when we made the move from classical atomic physics to quantum physics we retained things like “electrons”. This is because there was a strong correspondence between the two theories; even though they ascribed different properties to the fundamental objects they talked about those objects behaved in many of the same ways, were observed through the same experiments, ect. Thus it was useful to carry over the same language, especially since the classical atomic theory was still occasionally useful for roughly describing systems, or explaining them to other people. And because this is physics, and the word electron is not really understood by many non-physicists (they know roughly what an electron is, but don’t have a detailed theory of what exactly it is), this isn’t a problem. No one is mislead by the use of the word electron in quantum physics into thinking that they are by definition point particles that orbit the nucleus. However, terminological borrowings can be hazardous when the entitles in the two theories do not play basically the same role, or when most people already have a categorical description in mind of what that entity is, because the theory involving it has become part of common thought. In such a situation to use a word describing an entity in one theory to describe a different entity in another theory is at best misleading, and at worst lying. An example of this problem is Spinoza’s use of “god”. By god Spinoza means only the totality of everything. And so his use of god is very misleading, because god is part of a primitive theory about the way the world works, which contains a special entity or entities that have extraordinary powers which in turn explain certain mystifying features of the world (such as why it is the way it is), and which have a human-like mind, such that they take an active interest in the affairs of the world. This is obviously not what Spinoza means by the term; if he had really needed a new word to describe the totality of everything he should have invested one, instead of dragging along the connotations of the old usage of god.
But back to the main topic. Understanding what a theory is is only part of the problem. The other part is determining what makes one theory better than other. We can begin by evaluating the success of the theory in isolation. Of course a successful theory is one that is consistent and correct. Consistent meaning that it doesn’t explain the same event in two different ways, and correct meaning that as far as we can tell the theory is in agreement with reality (meaning that the theory can provide an explanation of all the observed phenomena that it is supposed to, and that the rules of the theory predict correctly what will happen before it happens). Given those initial considerations if we are left with multiple theories that are about equally good by those standards then we must compare them to each other directly. Such comparisons are relatively straightforward; the theory which is better is simply the one which explains more of the world. If two theories deal with different subjects obviously then there can be no comparison, which is why the superiority of physics to psychology in terms of predictive and explanatory power does not motivate us to discard psychology; they explain different things. But if they overlap and one theory explains everything the other theory does and more than it is the better theory.
Of course it seems natural to say that this understanding of what a theory is, and how one theory can be compared to another, fits scientific theories. But it seems less natural to apply it to philosophical theories. I claim though that this problem is one of our own making, coming from some of the high expectations we have come to have of theories. When we require that a theory explain phenomena and make predictions we are used to the theory doing so in a precisely quantified way. The theory predicts a specific measurement, we make the measurement, and then we compare the two. I claim that this is a requirement only if the theory in question is to be considered a scientific theory. What makes a scientific theory distinct from a theory in general is the close coupling between results and the theory itself, specifically you can only have a scientific theory when the object of your study can be measured in some way in a controlled fashion. If you are studying something that can be measured in this way then it is in some ways easier to know when you have a good theory, because it is easy for you to test that theory. But restricting theories in general to studying only these things is too much of a restriction. There is plenty we want to study, such as ethics, and knowledge, and truth, and aesthetics that we don’t have a way to precisely measure. Indeed finding a way to measure them would turn the study of them into a science, and that would be easier on everyone. They can’t be easily measured not because they aren’t real, but because they are too abstract; they supervene, so to speak, on the simpler phenomena that are measurable, but because they supervene on these phenomena it is hard to make measurements of them and not that which they supervene on. In fact to make such measurements requires a theory about how they supervene on the more easily measurable parts of the world. Which in turn requires some kind of theory about them. So this then is the work of a philosophical theory, theorizing about the parts of the world that we can’t form scientific theories about. Thus philosophical theories are in a sense necessary precursors to any scientific theory, by spelling out connections between things and measurements, although most of them are so obvious that we never give them any consideration. For example, a simplistic theory about length requires a theory that states that the property of having the same length is transitive, that the property of being longer than is transitive, and that if the object isn’t changing in some way that length is constant. This pre-theory about length is not scientific, it is not open to testing; it is philosophical. Given that we accept that not all theories have to be in terms of measurements the outline of how a philosophical theory is constructed is actually rather simple. You start with a term or a concept (or a family of concepts) that seem like they could benefit from investigation (those we don’t have a satisfactory theory about). Then an ostensive definition of the term is developed. After thinking about the best explanation for what is really going on (this is the hard part) we develop a theory involving categorical definitions. We also explain how the objects in our theory fit into the ostensive definition, either by saying that they (or some arrangement of them) are what it is that is related to us in that way, or how they cause us, falsely, to believe that there is such a thing. Then we test our theory by considering cases in which the ostensive definition applies and then seeing whether our theory satisfactorily explains them (explains why the ostensive definition applies). This very post is an example of such a process. I began with an ostensive definition of what a theory was “those things that explain the world or our observations to us”. Then by understanding how something could explain things to us a hypothesis was developed about what a theory was. And then that definition is applied to various cases, that of science and that of philosophy, to see how well it deals with them.
As a way of a final note let me apply this theory about theories to make a point about a particular method of philosophy, and about math. There is a way of doing philosophy in which we simply begin with definitions and then use those definitions to derive further statements. And, unlike the theories we have been considering, the philosophers who work in this way don’t judge their theories by how well they explain the world, but rather on the basis of internal consistency. And they don’t expect their definitions to match up with how we use the words, as they work on the premise that language is flawed, and thus not a suitable basis for an investigation. Rather their work is more like a mathematical derivation, in which terms are defined solely by reference to other terms in the work. Such philosophers include the rationalists and some of the post-modernists and their precursors, people such as Heidegger. The problem with philosophy done in this way is two-fold. First no philosopher can ever shown to be really wrong, and so no progress can be made. Even if they give attributes to something, say X, from which a contradiction can be derived they are free to respond to this simply by modifying their theory by breaking X into two things, Y and Z, one of which has one of the attributes and one the other, so that they are not in contradiction. Since the objects of their theories aren’t tracking the world there can be no objection to this fix. Secondly this method makes the philosophy developed in this way totally useless. Since the theory doesn’t track reality it can’t be of any use to us, except possibly as a very strange form of art. Of course such philosophers are likely to respond by comparing their philosophy to math, which seems to work by a method like this. But that is no defense, because math isn’t a theory. Math is simply an abstract system. Math does become useful as part of a theory; when we connect numbers to the counting of things then arithmetic is useful. But the fact that math can be useful is because it is so formally spelled out, so that it is clear when the objects of a theory can or can’t be described by a particular system of mathematical theorems. It is not so with philosophy developed in this way; while math is useful as a tool in the construction of theories (especially calculus and linear algebra for physics, and logic for philosophy) philosophy done in this way never is. And thus I see this approach to philosophy as flawed, and best replaced by an approach that treats philosophy as just another kind of theorizing about the world.
* For more on what I mean by these terms see here.