However you say it, the broad definition of the scientific way of knowing covers everything, not just physics, biology, chemistry and geology. Not only that, it appears to be the only way of knowing that has proven to be successful. Thus, I can tentatively conclude that it is the only way of knowing until someone provides an example of knowledge obtained by another way of knowing.
Alan Sokel has posted three articles on Massimo Pigliucci new blog, Scientia Salon [What is science and why should we care? — Part III].
Here's how he describes science in Part III.
We have now travelled a long way from “science,” understood narrowly as physics, chemistry, biology and the like. But the whole point is that any such narrow definition of science is misguided. We live in a single real world; the administrative divisions used for convenience in our universities do not in fact correspond to any natural philosophical boundaries. It makes no sense to use one set of standards of evidence in physics, chemistry and biology, and then suddenly relax your standards when it comes to medicine, religion or politics. Lest this sound to you like a scientist’s imperialism, I want to stress that it is exactly the contrary. As the philosopher Susan Haack lucidly observes:
“Our standards of what constitutes good, honest, thorough inquiry and what constitutes good, strong, supportive evidence are not internal to science. In judging where science has succeeded and where it has failed, in what areas and at what times it has done better and in what worse, we are appealing to the standards by which we judge the solidity of empirical beliefs, or the rigor and thoroughness of empirical inquiry, generally.” 
The bottom line is that science is not merely a bag of clever tricks that turn out to be useful in investigating some arcane questions about the inanimate and biological worlds. Rather, the natural sciences are nothing more or less than one particular application — albeit an unusually successful one — of a more general rationalist worldview, centered on the modest insistence that empirical claims must be substantiated by empirical evidence.
Conversely, the philosophical lessons learned from four centuries of work in the natural sciences can be of real value — if properly understood — in other domains of human life. Of course, I am not suggesting that historians or policy-makers should use exactly the same methods as physicists — that would be absurd. But neither do biologists use precisely the same methods as physicists; nor, for that matter, do biochemists use the same methods as ecologists, or solid-state physicists as elementary-particle physicists. The detailed methods of inquiry must of course be adapted to the subject matter at hand. What remains unchanged in all areas of life, however, is the underlying philosophy: namely, to constrain our theories as strongly as possible by empirical evidence, and to modify or reject those theories that fail to conform to the evidence. That is what I mean by the scientific worldview.
Hat Tip: Jerry Coyne: Alan Sokal highlights the incompatibility of science and religion