What is the fundamental principle that distinguishes science from non-science? I have been thinking about this a lot lately. I am somewhat familiar with the vast literature from the philosophy of science which speaks to this question (e.g. Popper, Kuhn, Feyerabend). Popper is best known for the "falsifiability criteria". Kuhn is famous for his "paradigm shifts". And Feyerabend insisted that science not follow any method whatsoever, lest it somehow restrict itself.
I buy into pieces of each of these philosophies but yet I feel compelled to think about a principle that would resonate with almost every practicing scientist. To me, the principle can't be as simple as "the scientific method" or the use of mathematics. Much scientific progress happens outside the confines of rigorous method and rigorous math. Scientists can't escape from the fact that they are ultimately human and as humans they succumb to emotion, prejudice, and turf wars. They use rhetoric as much as they employ differential equations and statistics.
Ultimately, despite temporary deviations from method and rigor, all true scientists buy into the principle of Occam's razor. No matter what mode a scientist is presently working, he or she is guided by a quest for simplicity. This does not mean the path to simplicity is always a straight line.
Most computer programmers, like myself, are also on a quest for simplicity. We call code "elegant" when it achieves great feats while remaining simple. However, most programmers don't regularly write elegant code; we just know that when we do it is the most satisfying experience imaginable. Likewise, most science does not start out elegant but it is constantly seeking this state. Science is looking for the simplest rules, laws and equations that explain the most observations, dispel the most mysteries and lead to the most new discoveries.
Occam's razor is the essence of Science.
This, more than anything else, is why the vast majority of practicing scientists reject pseudoscience (like Intelligent Design, Astrology, Numerology and the like). For example:
Intelligent Design: how could an explanation that requires the preexistence of a designer before the designed be the simplest explanation? Isn't simpler to assume the non-circular premise that intelligent life does not depend on the preexistence of someone more intelligent than the life whose origin requires explanation?
Astrology: how can the position of planets whose, gravity is too weak to even move a feather on earth, be the simplest explanation for any given human's life story.
Numerology: How could the letters of ones name, which are arbitrary artifacts of the evolution of language, have any bearing on a persons fate? Isn't it simpler to imagine ones fate is tied to a combination of heredity, environment and chance?
Of course, a believer in god would counter that his system is the simplest. You presume god and everything else follows. How can you get any simpler!?! It is of course at this point where any hope for intelligent discourse ends and the scientist and the faithful must part ways.