Scientism is the view that we should believe only what can be proven scientifically. In other words, science is the sole source of knowledge and the sole arbiter of truth.1
Many of the modern, secular epistemologies fall short in providing a logical basis for truth. These theories are usually way too restrictive, to the point of being self-refuting. We see this with moral relativism, empiricism, materialism, and many others.
Scientism falls into this category of being a self-refuting epistemology also. It fails to account for itself as being true. Once again, scientism is the belief that everything must be proven by the scientific method to know if it is true. The problem is that this very proposition itself cannot be proven using the scientific method. This being the case, we cannot know if scientism is true. Based on the restrictive definition of scientism, it is an illogical epistemology.
Since scientism cannot be proved empirically by the scientific method, to hold to it as a theory of knowledge is to have faith in scientism.