This was the basic motivation of Edmund Husserl when he developed his phenomenology. He wanted to know what a number was, or a logical judgement, and to do that he started developing a way of talking about how these things appear in consciousness itself, which is their natural ecology. In other words he wanted a way to understand what the basic constructs in our mind were that Science was based upon. That turned out to be complicated as any reading of Logical Investigations will show. In the end however in Krisis he talks about the problems that occur as science becomes estranged from the common lifeworld in which we live. That estrangement was from his point of view the fundamental crisis of our worldview.
Quora answer: How can we successfully integrate science with philosophy?
So phenomenology is a basic attempt to build that bridge between science and the everyday lifeworld by understanding better the nature of our consciousness that generates both. Philosophy from his standpoint could be that bridge between science and the lifeworld. But unfortunately it is a gulf that becomes greater all the time.