Philosophy is what philosophers do, and what philosophers do is often esoteric and highly specialized. It may have no obvious application beyond the scope of a handful of other philosophers working in the same area, and maybe some interested amateurs.
I'm not sure how I personally feel about that, but I only wanted to post this to temper some of the "grander" claims about the goal of philosophy. In a 2001 interview, Saul Kripke, one of the biggest names in contemporary analytic philosophy, seems to think that being a philosopher isn't really that different from any other job.
Kripke does not care much about providing a
justification for doing philosophy. When I asked him why he
investigates the philosophy of language, he said he works on this
topic simply because he finds it interesting. Pure intellectual
curiosity drives him.
“The idea that philosophy should be relevant to life is a modern idea.
A lot of philosophy does not have relevance to life,” said Kripke. He
is clearly somewhat different from American philosophers such as
Martha Nussbaum or Cornel West, who both argue that philosophy is more
than a career, it’s wisdom, an art of living, and may have a very
Kripke claims both Plato and Aristotle did philosophy because of its
intrinsic value. But he adds: “Ethics and political philosophy are
relevant to life. The intention of philosophy was never to be relevant
to life. But ethics and political philosophy can be relevant.
Philosophy is a career like other things, but must not necessarily be
related to that outside philosophy.”
Later on in the interview:
Q: Is it negative that philosophy now is connected to a professional
career and not the unconditional search for truth it once was?
A: Perhaps it never was an unconditional search for truth. The great
philosophers did it as a professional career. The Medieval
philosophers were monks, but also professors. Descartes was not a
professor, but he did a lot of teaching.
Q: Michael Dummett claims that academics don’t have any special duty
to be engaged in social questions, but he claims that academics can
make their own schedules and may use this privilege. Do you agree with
A: I don’t think there is anything special academics can do.
I don't have any data to support this, but I have a hunch that many philosophy professors in the analytic tradition share Kripke's sentiment that they do philosophy mainly out of intellectual curiosity. The tools they use depend on the area of philosophy they are working in. They typically do use logic in a broad sense, though not just formal logic. And they also use informal reasoning, intuition, thought experiments, scientific theories and data, and make inferences to the best explanation.