Essentially there are two kinds of investigations we can pursue in philosophy, we can inquire about specific claims, such as “should we be just?”, or we can search after general theories, trying to answer questions such as “what is justice?”. The way we investigate the two isn’t identical, but since the second kind of investigation occurs as a part of the first I will discuss only how to investigate specific claims, with the idea that it isn’t hard to simply omit certain parts of the investigation. But I guess before I get into those details I should say a few words about what an investigation is. A philosophical investigation is not the same as a philosophical theory or claim, philosophical theories and claims are the result of philosophical investigations. Nor are philosophical investigations the main component of philosophy papers, again philosophy papers are ways of expressing the results of investigations. The investigation itself then is the thinking and research we do in order to arrive at our philosophical ideas; once we have arrived at them the investigation itself withers away to some extent. Which is not to say that we abandon the work that composed the investigation, but only certain parts may provide a suitable basis for justifying our claims. And although the investigation is the process by which we come to entertain certain theories it is not necessarily the method by which they are best evaluated. But, even though the investigation doesn’t do everything we might wish, as it doesn’t necessarily produce perfect claims, it is a starting place, and we have to start somewhere.
Suppose then that we are considering whether we should be just. We probably have some existing intuitions about whether we should or shouldn’t be just (hopefully that we should be just). But these intuitions are not a suitable place to begin our investigation. Although we can produce a claim on the basis of intuition it is hard to justify that claim because we haven’t achieved any understanding about what is involved in it. We might try to back up our intuitions by arguing that they are widely shared, or that they are a simple extension of other opinions, but such arguments are rarely successful in the long run, because opinions and intuition are subject to change. And so such a defense of the claim can only stand up to scrutiny until someone who believes the opposite produces an analysis that reverses our intuitions (such as by successfully describing justice as a tool of oppression) or, worse, arguing for the opposite in a way that is completely free of intuition and opinion. To do better we must achieve some understanding of the larger issues that are involved with the claim, and then on the basis of that, arrive at a conclusion. Usually what these larger issues are is fairly apparent, they are anything that is of a debatable nature found in our original question. In our case it is fairly obvious that what we need to understand is the nature of justice and what we should do (normativity) and then, on the basis of them, try to arrive at a conclusion about whether we should be just.
In most cases understanding things such as justice and normativity will result in our ability to give what looks like definitions, claims of the form “justice is …”. And so it might seem that we are looking for our claims to be revealed as true or false on the basis of the definitions alone. But that is definitely not what we are looking for, at least in the vast majority of cases. Now this is not to say that legitimate definitions can never demonstrate certain claims. For example, when considering the claim “water contains hydrogen” we might legitimately lean on the definition “water is H2O” to simply demonstrate that the claim is true on the basis of the definition of water, assuming we have correctly defined water. The problem with such demonstrations, however, is that we can only be confident in their results to the degree that we are confident in the definitions involved. In this specific case, for example, it would be far preferable to determine the truth of the claim by testing a sample of what is considered water for the presence of hydrogen, thus bypassing completely our reliance on having a correct definition of water. But I digress, the point I am trying to make is that if the claim is really worth investigating, meaning that we aren’t completely sure whether it is true or false, then demonstrating it on the basis of definitions will not be satisfactory. Because if we are unsure of its truth and it is entailed by the definitions this means we aren’t sure of the definitions, and hence that we haven’t made any real progress. For example, we could answer our original question if we simply defined justice as the things we should do, but then, since we clearly are unsure whether we should be just, we must thus be uncertain about whether justice really is the things we should do. But, on the other hand, it is pretty clear that our question can only be answered by an appeal to the nature of justice and normativity, since, unlike the example with water, there is no way to test the claim by itself.
What we must do then is investigate the philosophical ideas themselves in such a way that doesn’t presuppose a particular definition, at least in any way that matters. To do that we need to begin with essentially ostensive definitions of the terms involved, meaning that we begin with definitions that in some way point out the things we are interested in, but don’t presuppose that they have any particular properties (or if we must presuppose that they have some properties then they must be properties that will be irrelevant to the later theory we develop about them). For example, we might ostensively define water as “the kind of stuff that makes up lakes, rivers, rain, and so on”. By picking out water in this way the only things we presuppose about it are that it must be able to appear to us in certain ways (because our ostensive definition picks it out essentially by what it looks like), and that is safe because we aren’t attempting to define water in terms of its appearance. Naturally such definitions are much harder to provide for philosophical terms, but it is essential that we start with them because otherwise our investigation will include a kind of logical circle. Unfortunately I can’t give an example of this for justice, as I myself have only been able to define justice as part of a larger theory, and never by itself. I suppose that if you wished to embrace some form of ordinary language premise you could always begin with the ostensive definition “that kind of thing that is called ‘justice’”, because certainly what it is called has no impact on what justice is. But this is not the only way to construct an ostensive definition of philosophical terms, just a very lazy way.
Of course that is only half of the investigation, and the easier half at that. Once we have some way of picking out what we want to investigate in a neutral way the next step is to actually create a theory about it. This means first seeing whether there is actually some kind of thing that our ostensive definition connects to. For example, we can’t construct a theory about leprechauns because there are no actual leprechauns for our ostensive definition to really point at. Nor would we be able to successfully theorize about water if every example of water was chemically distinct, because there would then be no kind of thing that united all our samples. Having established that our ostensive definition actually connects with something the next step is to examine what makes it distinct from the rest of the world. What properties does it have and which does it lack that distinguish it? Note that these properties do not have to appear in absolutely every case, it is enough that they appear in most cases, as we can allow that our ostensive definition is occasionally in error. And this gives us the theory we were after. Of course this process doesn’t produce a defense of the theory. We might have to argue that our theory is the correct theory about justice because it largely conforms to certain strong intuitions about justice (possibly captured in our original ostensive definition) or we may simply stipulate it as what we mean by justice in this context, under the assumption that what we have defined as justice is an interesting enough category that our claims about it will be worthy of consideration in their own right, even if not everyone agrees with us that what we have defined is “really” justice.
With these various theories in hand we can now return to the original topic of our investigation. And it may be that we can deduce a relevant claim directly from our theories. But this won’t always be the case. If we have defined justice, for example, as a category of laws defined by property A, and we have defined what we should do as things that are good for us, then it isn’t immediately clear whether we should be just unless A happens to be the property of being good for us. However, in this case it is probably easy for us to work with the theories and arrive at what we want to know, specifically by considering the effects of acting in accordance with the laws having property A. If doing so turns out to be always good for us then we should be just, under these definitions. Or it may turn out that such laws are always harmful to us, in which case we shouldn’t be just. Or, finally, it may turn out that sometimes those laws are good for us and sometimes they are bad for us, so that our answer will have to be qualified by reference to the relevant situational facts that make the difference, or we may even concede that there is simply no relationship between the two.
Unfortunately, even given well-developed theories of all the philosophically interesting terms involved in the specific question we are tackling there may be no obvious way to apply the theories to arrive at the answer, meaning that we simply can’t see how the theories connect at all on this issue. For example, if we were attempting to determine how words refer we could have suitable theories about words (as certain patterns of sound or shape) and suitable theories about reference (such as some kind of correspondence between assertion and states of affairs), but these theories simply don’t seem to shed any light on our question. What is missing might be called “middle terms”, things that have some relationship to both of the theories, such that through the theories about the middle terms the two can be connected. The problem is, naturally, determining what the middle terms are, and this can be a process that sends us down a number of dead ends, because the way to proceed is simply to try different possibilities, developing theories about each, and then seeing whether those theories can make the necessary connections. A good place to start is often with how the objects of the theories that we can’t connect yet are actually related. In our case that would be individual words and the actual objects they refer to. And such considerations would lead us to try middle terms either involving the causal relationship between naming events and individual words or the mind of the users of those words (assuming that the speaker is able to think about those objects). But this is just a place to start, it isn’t guaranteed to produce the desired middle terms.
With this process complete your investigation is at an end, you have reached a conclusion about what you set our to consider that is grounded in an understanding of what is involved in that claim. But of course that doesn’t guarantee that you are correct, and considering the merits of this claim may necessitate investigating it again, but this time beginning with different ostensive definitions, relying on different common properties to define the term, or taking additional factors into account when deriving conclusions on the basis of those properties. A topic for another time.