And examples of the shaky ground would be ... Quoting: Anonymous Coward 762124
I say that the scientific method cannot be tested scientifically because the foundations of the method rest upon assumptions independent from experience.
As someone has put it better than myself:
"..there are certain philosophical assumptions made at the base of the scientific method - namely, that reality is objective and consistent, that humans have the capacity to perceive reality accurately, and that rational explanations exist for elements of the real world. These assumptions are the basis of naturalism, the philosophy on which science is grounded.."
The nature of something cannot be observed independently of the observation (as it really is). There will always be "perception" of something, even if you are perceiving something through an apparatus.
Math is the only science that does not need to be based on reality. The other sciences, the natural sciences, do need to be based on reality.
Today's science does not test its core assumptions. Because that would mean the end of science as we know it. Why would it want to kill itself?