Does the umbrella of philosophical inquiry include science?
Yes. By definition, philosophy IS the pursuit of knowledge. Science is merely a systematic way of accomplishing that through observation and experimentation of physically manipulable and measurable phenomenon. The pursuit of truth outside of science comes in the form of logic, deduction, and thought experimentation. Philosophy was and is science… early science, in a true sense… a less developed and refined form of it. Early, ancient philosophers were also mathematicians, logicians, geometers, astronomers, chemists, physicists, etcetera… this is no coincidence.