When it comes to philosopshy it feels to me a bit like astrology, where there are some things that can work, but mostly because of auto-suggestion, or any other kind of suggestions. So, I wonder if philosopshy is a science and why so many people rely on it.
Philosophy is not a science; rather, science is a philosophy. More specifically, science is applied logical positivism, structuralized for us to better understand our universe. Philosophy is not a science, but it is a starting point for us to build upon science. It's the initial foundation with which we can build upon. It is however an academic discipline in its own right, just as the other humanities are generally known to be.
No, philosophy is not a science. Science uses the scientific method to form hypotheses and then test them by gathering or generating empirical evidence. Most of the issues in philosophy are currently beyond the scope of those addressed by science - issues such as "what is knowable", "what is right and wrong", and "what is the nature of time".
Philosophy is the science that tries to formulate a deeper coherence of the wealth of experiences of both human/social existence and physical reality. — But, like science, philosophy has since ever been essentially censored (by religious and governmental authority; it is an error to think that the religious influence no longer continues in the underground today), with the consequence that philosophers and scientists are recording since ever solely their own projections, as already explained in several of my posts.
You do not believe that? Liebig, the most distinguished and versatile German chemist in the 19th century complained that modern philosophers (hence also Kant) “completely failed to provide assistance to scientists to broaden their insight into the nature of things and to justify it more deeply”.
You can joke around saying that 'philosophy is similar to astrology' but sooner or later you will get stuck on some kind of philosophical problem. I believe that philosophical problems are not problems that only professional philosophers deal with. They are general problems that arise within our language. Sometimes we don't even know that we have to deal with some kind of philosophical problem. For example, our children dies and we ask if there's justice on this world, we ask what is the nature of consciousness, what is the best politics, what it means to think correctly, etc.
There is no way that science alone can answer on above questions for they are pseudo questions in some way - they rest on misunderstanding of the grammar of our language. Besides that they are linked to our subjective values and beliefs - whether we believe in god, freedom, equality, etc.
Therefore, when we are trying to answer some philosophical problem, we have to take into account this complex and overlapping web of different fields and acknowledge differences between them. For example, you can't ask the same kind of questions and expect the same kind of answers in science or in ethics. Science discovers new and interesting facts that can be confirmed or refuted through experience. Ethics doesn't work that way. You can't 'look into' the world and discover 'good'. Philosophical problem arises when we try to answer what is the nature of good on the model of empirical sciences.
That was trivial example, so let's consider another one. What if I ask, what is the nature of mind and body? Are these two different substances or one? How do they relate to each other? Is mind open to empirical investigations of natural sciences or is it strictly domain of philosophy, maybe even religion?
I believe that philosophy can give us an overview of specific area of language that troubles us. It directs thinking and prevents us to fall into traps of our language. In this way it is far far away from astrology and even astronomy. It is more close to mathematics and logic because of it's a priori structure - they are also in the same way independent from empirical facts.
In my experience, math is not exactly science. I'm a set-theorist so it's very philosophical. Science is an approximation and math (some philosophy) is about pure reality.