Rational inquiry is great when done with earnestness of purpose.  that would require 'following the evidence wherever it leads'.  Or, as Neil deGrasse Tyson says 'science is true whether one believes it or not'.  The only objective method available to us to learn, to know, to discover and to make predictions is the 'method' of science.  You might wish to slur the 'social sciences', but that is not because of the 'method' of science, or how it is used, but the difficulty of measurement.  What you do in the last sentence is to introduce a truism that science does not dispute.  But then, add this caveat, if science can't help neither can you or anyone else including religion.  What you are capable of doing is to make stuff up.  'Immaterial' is nothing, and that is what you have;  nothing...you cannot even say;  "then there IS the whole immaterial world", that statement defies 'rational inquiry'.