The philosophers I study under criticise the sciences for not being rigorous enough. The problem goes both ways. The sciences often do not understand the basic concepts from which they are functioning. A good scientist will also have a rudimentary understanding of philosophy, in order to fiddle with the background epistemology of their work.
You are correct in thinking that Continental philosophy is not continuous with the sciences, because it is the core of the humanities and as such being continuous with the sciences would be unnatural for it. I still think that asking questions about our connection to existence is interesting and important, although I personally do not find Continental philosophy as potentially fruitful as Analytic.
Intuitions are by no means accepted within the discipline as a whole, and are also an interesting topic of debate within it. Because philosophy is a highly speculative discipline it isn’t going to be following a normal scientific model, but instead will model constant discovery. If you want to see where science connects up with philosophy what you should look at is the disciplines that end up coming out of philosophy as questions that can be answered scientifically. This is what we produce with regard to science.
Philosophy is the core of the academic disciplines. It isn’t in the business of scientific inquiry and it should not be. Some philosophers are still looking for universal truths after all. Simply disagreeing with the idea of a priori does not make it go away.
It is good that you recognise there are problems in philosophy. Too many people take it as dogma and do not question the area they have explored. My advice is to take what you can from the discipline well keeping in mind that every piece you take comes with a centuries long dialogue.
First, I think you do very well in capturing that sort of giddy excitement in having a belief undermined and the world turned upside down. I find it a rather addictive experience.
“It will touch each and every idea, and change it, and move on.”
Not necessarily.
Sometimes I am having a conversation and I say something like ‘we should stop dumping garbage.’ There are ways that I can believe this validly. I could mean that we should start a better recycling program. We should change the sort of consumer goods are available. We should make people more conscious of what sort of place they are creating. But I don’t know any of these arguments because this belief comes from the time before I learned to analyse and challenge beliefs, before I learned that I could fight back if a belief is challenged. Before I learned that I can see my belief in even the material world temporarily vanish without breaking. (It came back, which is nice because I like the material world.)
So there are residual beliefs, unless you systematically change all your beliefs at once only some will be changed. It is possible to have obsolete beliefs, which is really weird.