Empiricism, the epistemological foundation for science, is the theory that knowledge is only derived from empirical/physical phenomena.  However, empiricism carries non-empirical assumptions, e.g. observation has no causal effect on physical reality.

The problem with an empirical methodology wielding non-empirical assumptions is that this means the assumptions are derived elsewhere.  In this case, that "elsewhere" is philosophical.  But, if we assume this non-empirical assumption to be valid, then we concede that knowledge must also derive from outside empiricism, i.e. outside science.

Yes, science works, and yes it produces technology that improves convenience and quality of life.  That, however, does not mean it is the best source of knowledge in all cases, and we know this especially because science doesn't work without its philosophical and mathematical underpinnings.