Much too simplistic.  Modern science does not now or ever depend upon philosophy.  Philosophy served a purpose in its day, and today is obsolete replaced by physics.  Superstition, magic, had their day too.  Reason is not the issue...as since the beginning of time man was discovering and inventing.  The issue is that man has continually filled the god of the gaps argument, replacing ignorance with knowing.  Modern science began in the 16th and 17th centuries as we know it.