When people ask me what philosophy is, I usually get extremely uncomfortable and want to go hide.
I. One reason it's hard to say what philosophy is
Here is one reason why it is difficult to offer a short, pithy description of what philosophy is. In ancient Greece, the term "philosophy" was used extremely broadly. Consider, for instance, the writings of Aristotle (384 - 322 B.C.). These include not only all the topics we now think of as philosophical (for example logic, metaphysics, epistemology, ethics, social and political philosophy, and aesthetics) but also a great many subjects that we would not now regard as part of philosophy (notably biology and physics). One, perhaps biased, way to look at the history of philosophy is to see it as a history in which one scientific discipline after another branches off from philosophy: physics in the seventeenth century, biology in the nineteenth, psychology around the beginning of the twentieth, linguistics in the mid-twentieth century, and so on. Philosophy as we now understand it is roughly what is left of the collection of things Aristotle was interested in after the various sciences branch off!
II. Some Areas of Philosophy
Here is a quick inventory of some philosophical topics, some of the issues that are still thought of as philosophical more than two thousand years after Aristotle.
"Epistemology" means "theory of knowledge" (from episteme, knowledge, and logos, which can mean reason or rational investigation, among other things). Epistemology considers questions such as: what is knowledge? How do we acquire knowledge? How much knowledge do we have?
Etymology isn't all that helpful here. We know what "physics" means (from "physis" or nature). "Meta" can mean "above," and maybe that's not a bad way of thinking of what metaphysics is: a set of issues that are "above" physics in the sense that they are more abstract or general. But historically the term seems to originate with the editors who collected and organized Aristotle's writings. "Meta" can also mean "after," and apparently they used the term "metaphysics" as a title for the material they put after Aristotle's book on physics, meaning just "after the physics."
To put it as cosmically as possible, a metaphysical issue is a highly general or abstract issue about the nature of reality. A main subdivision of metaphysics is ontology, which concerns what sorts of things exist. Ontological issues include whether God exists, whether numbers exist, whether nonphysical minds exist. In addition to ontology, there are other general issues about the nature of reality, including whether human beings do or do not have free will.
C. Value Theory (Axiology)
"Value theory" is a label for issues about, well, values. It includes ethics, which is concerned with moral and ethical values, and aesthetics, which is concerned with artistic value.
III. One attempt at a definition
In one way this understates the unity of philosophy, however. For if we look at what remains, we see, not only great diversity, but also some resemblances among the subjects that remain. Most notably, philosophy concerns issues which for one reason or another have not lent themselves to scientific investigation. In some cases this may only be that we haven't developed the right scientific techniques. For instance, issues in cosmology (such as whether the universe has a beginning in time and whether it is infinite in extent) used to be regarded as philosophical because there didn't seem to be any way to settle them empirically; now, however, they are thought of more as belonging to physics, and empirically supported answers have been offered. In other cases, however, such as ethics, it seems plausible that the issues are not even in principle empirical ones.
We can use this insight to construct an attempt at a definition of philosophy. Beware: this is not a standard definition of philosophy, and probably would not meet with wide agreement! It is just my own attempt, perhaps idiosyncratic, to indicate the kinds of issues with which philosophy is concerned. I invite you to attempt to construct your own definition!
So here it is:
(a) the attempt to acquire knowledge
(b) by rational means
(c) about topics that do not seem amenable to empirical investigation.
Condition (a) distinguishes philosophy from creative disciplines such as literature or music. Condition (b) distinguishes philosophy from mysticism and some varieties of religion. Condition (c) distinguishes philosophy from the empirical sciences.
IV. Is this definition adequate?
There are two questions to ask about any definition: does it include all the cases it should, and does it exclude all the cases it should? Let us consider first whether the definition includes everything it should. Condition (a) may rule out some writings that are often treated as philosophy. For instance, it rules out activism, writing or speech whose goal is to effect change rather than to acquire knowledge. But Marx famously wrote, "The philosophers have attempted to understand the world. The point, however, is to change it." And some other philosophers may have had goals other than knowledge. Kierkegaard seems to have as a goal to help his readers become religious. Still, both of these writers also were concerned with acquiring knowledge, and I would argue that it is only this aspect of their writing that is philosophical.
Condition (b) is rather vague. It is intended to rule out attempts to gain knowledge about reality by mystical insight rather than by rational inquiry. This may rule out some Eastern thought (though certainly much of Asian philosophy is eminently rational).
Condition (c) certainly rules out some topics that have traditionally been thought of as part of philosophy, such as whether the universe is deterministic, whether it has a beginning in time, whether it is infinite in extent, and so on. In my opinion this is as it should be: these issues, although they were once thought to be suitable topics for philosophy, have turned out to be part of physics. However, it is an interesting question whether condition (c) rules out some topics that are still widely held to be part of philosophy -- for instance, whether there is a nonphysical mind, and whether people have free will. I am inclined to think that, while philosophy can contribute to these issues by clarifying the issues and the concepts involved, the issues are ultimately empirical and not philosophical.
So overall, although these conditions rule out some writings that have been called philosophical, I don't think they leave out anything that should properly be thought of as part of philosophy.
The second question is whether these conditions exclude what they should. That is, are there issues or writings that are not philosophical that nevertheless satisfy these conditions?
At the moment I can only think of one example that might be a problem here, but it's a very significant one, namely mathematics. Mathematics is not an empirical discipline (well, this would not be universally accepted, but I think it's the most common view). But it is certainly an attempt to acquire knowledge by rational means. So it looks as though my definition includes at least one subject it shouldn't. Perhaps the definition should be revised? (For instance, by replacing "empirical" by "scientific"?) On the other hand, the boundary between mathematics and philosophy is anything but clear. Plato thought of mathematics as the paradigm of philosophy, and there is a large overlap between logic, usually thought of as part of philosophy, and mathematics.
Why are philosophical issues not amenable to straightforward empirical investigation? The answer may be different in different areas of philosophy.