- A toolbox of methods for generating objective knowledge (i.e. justified true beliefs) about the universe around us.
- The community of professionals using this toolbox of methods, and their workplaces, journals, organizations and institutions.
- The ever increasing edifice of documented facts, observations, hypotheses that have survived testing, models that outperformed all other models, theories that haven't yet been superseded, and probably more besides, commonly called the body of current scientific knowledge.
But not everybody sees it like this. The most controversial issues where this comes up are whether science can address supernatural claims, whether science and religion are incompatible, and whether a scientist has committed the sin of "scientism", i.e. they have overreached and used their authority as a scientist to make claims that go beyond what science can actually support. Often enough when discussing whether science can do this or should not claim that one reads or hears categorical statements from would-be philosophers of science that science is only a method - nothing else. This stance then allows them to claim that science cannot say anything about the existence of gods, for example, because the supernatural (whatever that is) cannot be observed in a biological laboratory while wearing white coats or something like that.
(Note that not even that makes sense to me. Even if reduced to nothing but a method science necessarily has a position towards gods. Because the principle of parsimony is an utterly indispensable part of the scientific method, the position is that things for which there is no empirical evidence should be assumed to not exist. Or to cite the author of the Wonderella webcomic: “When it comes to God, the scientific community has a rigorously enforced 'Pics or it didn't happen' policy”. But for the moment, let us pretend that certain strange claims make at least slightly more sense when pretending that the definition of science does not include a body of knowledge.)
However, discuss the topic of the compatibility or incompatibility of science and religion, and you will curiously see yourself confronted with the second of the three aspects, also to the exclusion of the two others: A tediously familiar counter to the position that science and religion are incompatible is that there are religious scientists. So in this case, the definition of science is, for the purposes of scoring a point, focused not on the method or the worldview but instead on the community of scientists; an overlap between the scientific community and the community of believers is observed, and the case is considered closed.
Finally, you may even encounter those who focus only the worldview aspect of science. They are generally either religious apologists or people of a somewhat postmodernist persuasion, and their aim is to pretend that all worldviews are equally valid, e.g. the belief that the universe was created 6,000 years ago and the belief that it is more than 13 billion years old, or the picturesque belief that somebody's disease was caused by a witch and should be treated by burning her, and the oppressive Western imperialist colonialist belief that it is caused by germs and should be treated with a box of pills that actually work. Throwing out the methodological aspect allows them to distract from the question whether the competing beliefs are true and justified in any way whatsoever.
One could say that this is, in all cases, a divide and conquer strategy. We get much clearer answers to certain questions if we consider science as the whole package, all three aspects included. I have already written about my puzzlement why anybody would think that science cannot address the supernatural, and in particular about the lack of a clear idea what supernatural is even supposed to be; there just does not seem to be a definition that is either useful or coherent, much less both. In the same context, I have also admitted that I have run into people who represent the boogeyman of scientism only all too well, although I think that they are much rarer than some philosophers believe.
As for the last, very controversial, question of the compatibility or incompatibility of science and religion, we can first observe that religion does, of course, also contain all three aspects: it is a set of methods of forming beliefs, a community of believers and their institutions, and finally a worldview or set of beliefs. No matter how convenient that pretense would be for some people, e.g. those who stress the community aspect to distract from concrete, harmful beliefs, it is not merely one of the three. So let's look at the three aspects of science and religion one after the other.
Science (method) is clearly incompatible with religion (method) when applied to the same questions. The former employs empirical evidence, hypothesis testing, model selection, inference to the best explanation, parsimony, critical review, etc., the latter employs faith, tradition, subjective personal experiences and feelings, revelation, holy books, etc. To belabor the obvious, "I know it in my heart" is not methodologically compatible with peer review, revealed dogma written down in scripture considered holy a priori is not methodologically compatible with thorough hypothesis testing, and faith in entities whose existence can be neither demonstrated nor refuted is methodologically incompatible with the principle of parsimony. The only possible solution would be to apply the two methods to different questions, the popular idea of science and religion constituting "non-overlapping magisteria" (NOMA). However, even a cursory glance at historical and contemporary religious beliefs shows that religion constantly makes claims about material reality, the area that clearly falls into the magisterium of science. After all, the only religion that would not make any such claims would be one whose supernatural entities have never done and never do anything whatsoever, which would be quite pointless.
It is of course correct that science (community) is compatible with religion (community). Clearly a scientist can be religious, and clearly all scientists could theoretically be religious. But that merely demonstrates that humans are possible of intellectual inconsistency, of holding two contradictory beliefs at the same time. In this case, for example, the belief "one should not accept the existence of things for whose existence one doesn't have any evidence" and the belief "but that arbitrarily does not apply to this case which is relevant for my personal religious beliefs and/or peace of mind". Shocker, I know. A popular reductio ad absurdum to the argument from religious scientists is the observation that, by the same logic, traditional marriage and adultery are compatible because there are married people who cheat on their spouses.
Finally, science (worldview) and religion (worldview). This is the trickiest of the three. In my opinion, there is no incompatibility in principle because three thousand years ago it would have been theoretically possible that at least one religion is very much correct about the world, and that subsequently science (community) would have gone on to produce a science (worldview) using science (method) that is completely identical to religion (worldview), either by lucky happenstance or because a god actually revealed correct information to the religion (community). Sorry about that sentence.
It could have been the case, for example, when the scientific exploration of the world started, that the researchers had found the sky to be a firmament and the earth to be flat, that they had discovered an angel with a flaming sword standing in front of a gate to an otherworldly realm somewhere, that they had found no fossils from before 6,000 years ago and indeed no indication of common descent and phylogenetic structure in life, that they had found no physical or chemical trauma short of death to be able to erase memories or change the character of a person because all that information is carried by an immaterial souls, that they had found diseases best cured by casting out demons, that they had managed to summon the spirits of the dead into a pentagram and extract reliable, testable information about the previously unknown location of historical artifacts and sites from them, and so on.
However, we are not in that situation any more. In the last couple of hundred years, science (worldview) has become quite a large edifice of mutually supporting observations, theories, models and explanations. There are a lot of things about the universe we now know as well as anything empirical can ever be known, i.e. always tentatively but so well supported that it would be perverse to still assign any significant probability to the opposite being true, and many of these parts of the body of scientific knowledge directly contradict core religious beliefs of basically every religion that makes claims going beyond agnosticism.
In other words, basically any actual religion (worldview) that deserves to be called a belief system is incompatible with contemporary science (worldview). Souls of any practical utility value appear incompatible with what we know about the effects of brain damage; resurrection and virgin birth appear incompatible with human physiology and reproductive biology; special creation is plainly incompatible with geology, biology and astrophysics. If you want to object that this incompatibility does not matter because miracles or because science cannot prove a negative, please refer back to the paragraph about the incompatibility of science (method) with religion (method).
So the major point I want to make here is that when discussing the demarcation problem or the incompatibility question, one first has to make sure what everybody means by science. The minor point, as mentioned above, is that I personally do not think that one of the three aspects can define science in isolation. Seeing science only as a method is pointless because the method is there to achieve something, which is to generate a body of scientific knowledge. Arguing from the existence of the religious scientist is pointless because it sidesteps the question about the compatibility of methodologies. Seeing science only as one worldview among many is to avoid the question of epistemology. Et cetera.