There are some who think of philosophy not as a search for truth in some unique range of topics (distinguishing it from various sciences and math, which have their own topics). Some of these people see philosophy as an art form, or as entertainment, or as guidance in life. It is hard to see how one could even begin to refute such a view (what would you say if someone said the same thing about math or science?), but I will do my best.
Let us consider the existence of absolute ethical facts. If we were working with a classical logical system we could say that the claim that there are absolute ethical facts or there are no absolute ethical facts must be true, but to satisfy certain alternate views on the subject I will instead say that the claim that that there are absolute ethical facts or there are no absolute ethical facts or to speak of absolute ethical facts is meaningless is always true. But if that claim is true then one of the following possibilities must be true: there are absolute ethical facts, or there are no absolute ethical facts, or to speak of absolute ethical facts is meaningless, or that the disjunction is somehow true without any of the individual claims being true (a very odd possibility), or it cannot be discovered which possibility is true. What then is the discipline that investigates which of these possibilities is true (and one of them surely must be)? Neither math nor science can, even though, as I have shown above, there is some fact of the matter. And certainly these topics fall under what is usually considered philosophy (ethics and epistemology). So it seems logical to conclude that philosophy is the discipline that searches for the truth in certain areas that are outside the scope of science and mathematics, since there exist truths in these areas to be discovered.
Of course it could be the case that philosophy is an attempt to discover certain truths as well as fulfill some other function (such as being art). However, we already have disciplines that cover that ground, namely art, entertainment, and religion. Thus to require that philosophy do those things would be redundant, not to mention interfere with its function of discovering certain truths. In contrast there is no other discipline that investigates quite the same topics as philosophy does, and certainly there are some truths to be found there (as demonstrated above), so it seems logical to conclude that philosophy should be the discipline that investigates them, and that this is the only thing philosophy should do. (If it isn’t sign me up for the discipline that does.)
But some would still object to this, arguing that philosophy can’t be concerned with discovering truths since it doesn’t have a specific area of investigation. I don’t see how not having a specially designated area affects the issue, but it is easy to delimit such an area if it makes you feel more comfortable. Simply take the set of all areas in which truths can be discovered. Then subtract out the areas covered by science and mathematics, and what you have left is the area of study for philosophy. Admittedly this region changes over time, as science expands there is less and less that is considered the domain of philosophy, but, as shown by the fact that it can expand, the area that is the domain of science isn’t fixed either.
It is because I view philosophy in this way (as a search for truth in a unique subject area) that I am not a continental philosopher. The difference between analytic and continental philosophy can be seen as primarily one of method. Analytic philosophers focus on making progress by argument about the issues. Continental philosophers make “progress” by reinterpreting philosophical texts. The method of continental philosophy is often “philosophy via oracle”, where a work of philosophy is considered good because it says things that seem plausible, and not because its theses are well supported by argument and evidence. This is unlikely to lead to the truth, because what seems plausible depends more on out intuition than what is really the case. And certainly one cannot expect to proceed by pronouncements and get closer to the truth. And thus I consider myself to be an analytic philosopher, and am continually amazed that anyone can consider the continental tradition, which produces people such as Heidegger, good philosophy.