The philosophy of science devotes a large fraction of its wattage to this question: what is the logic of empirical confirmation for scientific beliefs? (A good short introduction is Samir Okasha, Philosophy of Science: A Very Short Introduction.) In the natural sciences this question became entangled with the parochial fact about the natural sciences, that scientific theories postulated unobservable entities and processes and that the individual statements or axioms of a theory could not be separately confirmed or tested. So a logic of confirmation was developed according to which theories are empirically evaluated as wholes; we need to draw out a set of deductive or probabilistic consequences of the theory; observe the truth or falsity of these consequences based on experiment or observation; and then assign a degree of empirical credibility to the theory based on the success of the observational consequences. This could be put as a slogan: “No piecemeal confirmation of scientific beliefs!”
This is the familiar hypothetico-deductive model of confirmation (H-D), articulated most rigorously by Carl Hempel and criticized and amended by philosophers such as Karl Popper, Nelson Goodman, Norwood Hanson, and Imre Lakatos. These debates constituted most of the content of the evolution of positivist philosophy of science into post-positivist philosophy of science throughout the 1960s and 1970s.
I don’t want to dive into this set of debates, because I am interested in knowledge in the social sciences; and I don’t think that the theory-holism that this train of thought depends upon actually has much relevance for the social sciences. The H-D model of confirmation is approximately well suited — but only to a certain range of scientific areas of knowledge (mathematical physics, mostly). But the social sciences are not theoretical in the relevant sense. Social science “theories” are mid-level formulations about social mechanisms and structures; they are “theories of the middle range” (Robert Merton, On Theoretical Sociology). They often depend on formulations of ideal types of social entities or organizations of interest — and then concrete empirical investigation of specific organizations to determine the degree to which they conform or diverge from the ideal-typical features specified by the theory. And these mid-level theories and hypotheses can usually be empirically investigated fairly directly through chains of observations and inferences.
This is not a trivial task, of course, and there are all sorts of challenging methodological and conceptual issues that must be addressed as the researcher undertakes to consider whether the world actually conforms to the statements he/she makes about it. But it is logically very different from the holistic empirical evaluation that is required of the special theory of relativity or the string theory of fundamental physics. The language of hypothesis-testing is not quite right for most of the social sciences. Instead, the slogan for social science epistemology ought to be, “Hurrah, piecemeal empirical evaluation!”
I want to argue, further, that this epistemological feature of social knowledge is a derivative of some basic facts about social ontology: social processes, entities, and structures lack the rigidity and law-governedness that is characteristic of natural processes, entities, and structures. So general, universal theories of social entities that cover all instances are unlikely. But second, it is a feature of the accessibility of social things: we interact with social entities in a fairly direct manner, and these interactions permit us to engage in scientific observation of these entities in a way that permits the piecemeal empirical investigation that is highlighted here. And we can construct chains of observations and inferences from primary observations (entries in an archival source) to empirical estimates of a more abstract fact (the level of crop productivity in the Lower Yangzi in 1800).
Let’s say that we were considering a theory that social unrest was gradually rising in a region of China in the nineteenth century because of a gradual shift in the sex ratios found in rural society. The connection between sex ratios and social unrest isn’t directly visible; but we can observe features of both ends of the equation. So we can gather population and family data from registries and family histories; we can gather information about social unrest from gazettes and other local sources; and we can formulate subsidiary theories about the social mechanisms that might connect a rising male-female ratio to the incidence of social unrest. In other words — we can directly investigate each aspect of the hypothesis (cause, effect, mechanism), and we can put forward an empirical argument in favor of the hypothesis (or critical of the hypothesis).
This is an example of what I mean by “piecemeal empirical investigation”. And the specific methodologies of the various social and historical sciences are largely devoted to the concrete tasks of formulating and gathering empirical data in the particular domain. Every discipline is concerned to develop methods of empirical inquiry and evaluation; but, I hold, the basic logic of inquiry and evaluation is similar across all disciplines. The common logic is piecemeal inquiry and evaluation.
(I find Tom Kelly’s article on “Evidence” in the Stanford Encyclopedia of Philosophy to be a better approach to justification in the social sciences than does the hypothetico-deductive model of confirmation, and one that is consistent with this piecemeal approach to justification. Kelly also reviews the essentials of H-D confirmation theory.)