The methodological foundation of modern science was laid during the scientific revolution of the sixteenth and seventeenth centuries. Whereas one school of thought, going back to Francis Bacon, emphasized induction from particular observations and experiments, the followers of René Descartes favored a more hypothetical-deductivist approach. In the mid-nineteenth century, the two kinds of methodology were refined and developed by, among others, John Stuart Mill and William Whewell. It is commonly recognized that both methods are employed in real science and that they do not constitute two different ways of doing science. Moreover, the favored methods differ from one science to another. The methods of the astrophysicist are not the same as those of the botanist, yet they are not entirely different either.
Science is organized in a large number of disciplines and subdisciplines, including areas of research of a transdisciplinary nature. Although there have been many attempts to establish hierarchical, more or less natural classifications among the sciences, in the early twenty-first century these have largely been abandoned. All of the particular sciences have a limited area of validity, a domain of nature within which they are relevant and about which they can claim cognitive authority. Nevertheless, there is no one-to-one correspondence between domains and scientific disciplines, and many cases in which science has the "right" to speak about a certain domain is a matter of controversy. According to some positivistically minded thinkers, science as a whole covers all domains of nature, consciousness, and society in the sense that all meaningful questions can be answered scientifically, and they ought to be answered so. This point of view, which expresses a kind of scientific imperialism as it denies the legitimacy of, say, social, metaphysical, and religious explanations, is often referred to as scientism. Although few thinkers have endorsed scientism in a pure form, it is not unusual for scientists to believe that social and ethical questions can in the last resort be reduced to scientific questions. In his book Consilience (1998), the biologist Edward O. Wilson holds that the unification of the natural sciences with the social sciences and humanities can be achieved on terms dictated by science. It is a matter of debate how stringently a scientific theory should be restricted to its original domain. Nature does not tell what is the proper domain of a scientific theory or principle. According to "restrictionists" a theory can be legitimately applied only to its scientific context, whereas "expansionists" are willing to extrapolate it to very different areas, for instance by means of analogies. Scientism is typically more appealing to expansionists than to restrictionists.
It is a major aim of history and philosophy of science to establish how science develops over time. Science has been hugely successful, but how is it that scientists know so much more of nature, and so much more reliably, than their predecessors? How is cognitive progress achieved? The traditional view is that new scientific theories build on earlier theories, which are criticized and improved upon, typically because they fail to account for new phenomena. They are modified or rejected in order to give way to new theories, although most of the old experimental data will still be valid and have to form part of the new theories as well. According to this picture, science essentially evolves cumulatively, by adding knowledge to knowledge or replacing obsolete knowledge with better knowledge. Whereas the picture stresses the evolutionary and conservative aspects of science development, it pays little attention to major conceptual restructurings of knowledge.
In his The Structure of Scientific Revolutions (1962), Thomas S. Kuhn argued that cumulative progress occurs only in periods of "normal science" when the community of scientists within a given field agree upon the standards of science, its paradigm. During revolutionary changes a new paradigm replaces the older one, and the two kinds of science are so different that they cannot be compared rationally. They are incommensurable in the sense that there is no neutral, transparadigmatic way to define progress across a revolution. According to the strong version of Kuhnian revolutionary changes, paradigms constitute separate worlds between which no communication is possible. Consequently Kuhn's theory opens up for relativism, with all its problems (as discussed further below). The strong Kuhnian picture, however, does not agree very well with the history of science, which includes many examples of scientists who have had no problems in maneuvering between competing paradigms. Although revolutions in the strong sense rarely or never occur, science often experiences major transformations that may involve drastic reinterpretations of past knowledge. Yet even in such cases—quantum mechanics may be an example—new theories are usually designed to account also for the successes of past science.