One of the discussions that regularly fires up again in one part of the blogosphere that I am reading is about the demarcation problem. There are several angles to the issue. One is simply how to differentiate science from non-science, which may be legitimate rational inquiry that simply is not science at one end and pseudo-science at the other. Another angle is concerned with the concept of "scientism", the charge that there are many scientists who think that science is the only way that knowledge can be generated and that all the humanities are basically worthless. Thus defined and directed at the majority of scientists, scientism is probably a strawman, but not entirely; I have surely come across people who think that way. The final angle worth mentioning here is that of whether science can address supernatural claims, in particular whether science can take a stance on topics such as the existence of gods or souls.
It should be obvious that one's stance on the whole complex of issues depends at least in part on one's definition of the term "science", and consequently I want to develop my thoughts on that matter, always aware that I am certainly not a philosopher of science. (I am, however, a professional scientist and thus perhaps not completely unqualified to write about science.) Note that defining the term science is not entirely the same question as the demarcation problem as such: first you need a useful definition of the concept, then you can apply it to various things to see whether they do, under that definition, fall under the concept or not.
One person who appears to want to fence science into the smallest space possible is the biologist-philosopher Massimo Pigliucci. After lengthy discussions over at his blog, the impression I have gained is that he basically only considers science to be double-blind hypothesis testing experiments conducted while wearing lab coats inside a research institute. That may be a slight exaggeration, but not by much; he does not, for example, count naturalists collecting samples and describing nature as scientists. On the other hand, he appears to have no problem with calling nearly every public policy discussion "philosophy", expanding the definition of that term to the same degree that he narrows that of "science". Anyway, I consider his definition of the latter to be much too narrow. The naturalist deals with empirical data just as much as a physicist or medical researcher, and there are implicit models, hypotheses and inferences to the best explanation involved.
I also find the demarcation between the sciences and the humanities utterly artificial*. Basically it is about whether somebody works on "nature" (another word that has to be defined first) or on human culture and ideas. But are we humans not a part of nature? And surely a historian testing hypotheses against ancient texts and archeological artifacts is much closer in their modus operandi to an evolutionary biologist testing hypotheses against fossils than either is to a literature critic. Surely a sociologist developing a model of communication in a village is comparable to an ecologist developing a model of trophic interactions in a forest, at least if the former is also testing the model against empirical data.
At the opposite end of the spectrum, there are those who want to expand the concept of science to cover, by definition, all that can legitimately be called knowledge. A few of them are making their case in this recent comment thread on Jerry Coyne's website. I think that that is a bridge too far. Surely mathematicians and philosophers generate genuine knowledge, but the way they distinguish between true and false is fundamentally different from the way a scientist does it. Mathematicians use completely different kinds of "proof" than scientists. Most importantly from my perspective, the former do not use empirical data, the latter do.
And this is then how I personally define science: If you use empirical data from the observable universe around you to test your ideas, then you are a scientist. In other words, the scientist differs from other types of scholars in the use of empirical data and from pseudo-scientists in asking the question "what should I be able to observe if my idea were false?" The ways that latter test can be made are, however, simply too diverse to limit science to double blind experiments in a laboratory. You can formulate a hypothesis and then see if you can disprove it, accepting it tentatively if it survives the test intact. You can compare different models and see how well each fits the data, tentatively accepting the best of them until somebody comes up with an even better one. You can take several options, assign them prior probabilities of being true, add more data and apply Bayes' theorem. All of those (and more) are science because in all cases you use empirical data and change your mind if it turns out that said data contradicts what you previously thought.
My definition has several consequences. One that I already indicated is that I see large parts of the humanities as science or, perhaps more correctly, potentially science. Economics and history can be science to the degree that the scholars in that area are willing to test their ideas against empirical evidence; that not all of them are willing to do so does not change that. As a less contentious example, medicine as a whole is certainly a science even if some of the people claiming to practice it shut their eyes to all evidence for the ineffectiveness of homeopathy. Another argument that one often hears is that economics is too messy to be a science and does not allow for simple experiments, but that argument can only make sense to those who have never tried to study ecology.
The second consequence is that by my definition mathematics and philosophy are not science because they do not deal with empirical evidence. In fact the knowledge that they generate is completely independent of the actual nature of the universe. For example, in Euclidean geometry there is a certain relationship between the circumference and the radius of a circle even if there is not a single perfect circle in existence in the entire universe, yes even if the entire universe is distinctly non-Euclidean. Similarly, 1+1=2 even if the universe does not contain two particles to add up. The same goes for many of the topics of philosophy. It can, for example, examine the logical consistency of an idea (e.g. omnipotent and omniscient god, married bachelor) regardless of whether somebody ever goes out to look for empirical support for the idea (i.e. makes the futile attempt to find a god or bachelor with those attributes).
Third, because of these considerations, I would conclude that there are ways of generating knowledge (distinguishing objectively between what is true and what is false) that are not scientific: at a minimum, aforementioned math and philosophy. The only alternative appears to be a tautological definition of science as every activity that generates knowledge, without regard for the methodology used or what the knowledge is about. Thus I would not consider myself to be guilty of scientism: I accept "other ways of knowing". But I only accept a proposed way of knowing as a way of knowing if it actually has an objective methodology for distinguishing true from false. "I feel it in my heart" or "look, it's written in the bible" does not cut it. Whatever the beliefs supported by those arguments are, they are not knowledge.
The final question, whether I think that science as I define it can address the supernatural, is a topic for another time.
*) My native language, interestingly, calls the natural sciences Naturwissenschaften and the humanities Geisteswissenschaften (mind-sciences).