"Scientism" is the idea that all real knowledge is scientific knowledge, subject to experiments, empirical verification, and so on. It is "the view that all answerable questions are empirical."
Lawrence Krauss, a theoretical physicist and the author of A Universe from Nothing, recently argued for (and, more, from) this position in The Guardian. He argued that philosophy should be replaced by science, since answers, to count as answers, have to be science's answers. What some might see as science's "imperialism," he said, is actually "merely distinguishing between questions that are answerable and those that aren't. To first approximation, all the answerable ones end up moving into the domain of empirical knowledge, aka science."
The standard challenge for scientism -- dealt with, kind of, in the interview -- is about ethics. How can a statement about what one ought to do be proven empirically? How could an injunction against, say, cannibalism, be verified by observation? What would "verification" in such a case even mean?
Another issue with this idea that all answerable questions are empirical is raised by Mark de Silva at the New York Times' philosophy blog. Math, de Silva says, is generally not considered to be empirical. The answer to the square root of negative one can't be found in experience, but that doesn't mean there's not an answer.
There's an even more fundamental problem with this idea, though.
The claim is nonsense by its own standards of nonsense.
If it's the case that "all answerable questions are empirical," what empirical evidence could be proffered to answer the question of whether all answerable questions are empirical? There's an induction problem here, and also a self-referential coherence problem. What possible scientifically acceptable test could there be to prove that scientific tests offer the only real form of knowledge? What observable fact can be cited to support the claim that questions have answers if and only if such answers are observable facts?
The claim can't logically be grounded in empirical evidence. Which means, it itself isn't grounded in itself at the very moment it claims to arbitrate the only available ground of reason. If it's true that "all answerable questions are empirical," then the question "are all answerable questions empirical?" is not an answerable question.
This is not a novel argument I am making. In the history of philosophy, the above issue is most directly associated with the critique of the logical positivists of the Vienna Circle. I make no claim to originality on this point. It would be helpful, though, if those claiming science has or can or should replace philosophy knew enough philosophy and history of philosophy to at least recognized the very well established problems with their overly simplistic claims for science.
Scientism -- or at least this version of it -- has a problem with morals, and it has a problem with math. It also especially has a very very basic problem of making its own claims meet the standards those claims set for legitimate claims.