It seems to me that philosophy is distinguished from other endeavors by the method that it adopts. This is not unusual, as science is usually identified by the scientific method. But what is the philosophical method? This question is obviously controversial but I think a good case can be made that the philosophical method involves a commitment to reason and argument as a source of knowledge.
In its earliest form it was often argued that reason could discern facts about reality that were in opposition to the way that the sense revealed reality to be. This was taken as evidence that only reason was a source of knowledge (this is rationalism). So Parmenides argued that though reality appeared as a plurality that was in constant change in actuality it was a static unity that never changed. The reason that we are supposed to adopt this radical position is that positing the reality leads to a contradiction (that of something coming from nothing or opposites existing in the same place at the same time).
This may make it seem as though empiricists who see philosophy as continuous with the sciences (or as I prefer, see science as natural philosophy) are not really doing philosophy anymore. They are doing science, or at least advocating that they should be doing science. But this is wrong. The empiricist is using the philosophical method because their belief in empiricism is based on reasoned argument. Hume’s arguments are just as good as any rationalists; perhaps better!
The philosophical method then involves a commitment to the following:
A good argument with the conclusion that p is a reason to believe p
What counts as a good argument (or even an argument at all) will be debated but everyone agrees that if there is a good argument with the conclusion that p then there is a reason to believe that p. This also lets us see how it is that science is a type of philosophy. The scientific method presupposes the philosophical method with the restriction that good arguments come from empirical testing of theory. So though Einstein used thought experiments to come up with relativity no one believe it until there was empirical confirmation.
Even this doesn’t preclude the rationalist from agreeing that the scientific method presupposes the philosophical method. They may hold that we have to do science because we are not omnicient. But a purely rational being that new every physical fact (i.e. the position of every fundamental unit of physics and the laws that govern them) that being could deduce what was possible and actual a priori.
So the identification of the philosophical method with a commitment to reason and argument as a source of knowledge (or at least justification for people to believe) seems reasonably viable.