The Continuum of Knowledge: Philosophy and the Sciences

There are many ways in which phillsophy is connected to the sciences.
(1) There is no line separating philosophy and any of these disciplines: sociology, literature, political science, economics, mathematics and computer science. For example: Take computer science. In the undergrad program eventually the courses get quite theoretical and difficult and there is no way to manage then execpt through the realization that most of the founders of the field were philosopher-mathematicians, and it was through studying their works that one could really understand what computer science was all about. For example you have to understand the work of Godel. Now Godel is taught in mathematics department, in computer science department and of course in the philosophy department. But Godel's proof is so crucial that even sociologists and anthropologists use the ideas (but without understanding the full-blown proof).
(2) It is evident from the history of philosophy, that many of the other subjects which have become independent fields at university were first studied and written about by philosophers, and because of the practical success of those writings that subject became independent, and took a life of its own. But the core principles of these sciences continue to be studied in philosophy department. For example take economics. The only way to understand the core of economics is to understand the history of economics, and that cannot be done without reading through those who are counted among the philosophers. (For example a recent work, a very good one, on economists was called "Worldly Philosophers").
(3) There is no line (not even a vague one) that separates philosophy and science. There were physicists who wrote philosophy, and vice versa. In fact the development of Relativity Theory was motivated by Ernst Mach, a philosopher whose writings inspired Einstein on the lines of his Relativity Theory. And those at the core such as Dirac and Bohr continued to contribute to the philosophical understanding of Relativity Theory and Special Relativity, and they quite naturally wrote in both philosophy and science journals.
(4) Any scholar of any of the western sciences has to study philosophy. For that matter any conscientious student has to do the same. My friends who did their undergraduate studies from McGill were forced to study philosophy and logic, because that was the only way they could really understand their field because most of the leading writers in any field are eventually philosophers (or are versed in philosophy and inevitably their writing assumes that background).
(5) My view is that only mathematics (applied mathematics leads to most of the ideas in the hard sciences) and philosophy are two pure fields, in the sense, that all other fields are derived from these two (mostly a combination of the two). For example: computer Science is a branch of number theory, and the theory turns on Godel's Proof and other results that were arrived at in 1936. The theory has remained the same, and the founders of this field were for example Alonzo Church, Alan Turing, Kurt Godel, all of them philosopher-mathematicians and wrote in philosophy journals.
These are among the many arguments that lead to the position that philosophy is not a well-defined core of ideas. In fact, it straddles every field and the only way to understand any field is to go to its philosophical and historical roots. Newton was called a natural philosopher, because there was no physics at his time. Just because physics is an independent field taught outside the philosophy department does not imply it does not have philosophical ideologies hiding beneath it.