Science is an activity of accumulation (Science, 1965). The cumulative theory states that scientific development is due to a gradual growth of knowledge based on a sum of facts accumulated by scholars, institutions and other actors (Haskins, 1965; Godin, 2001). In particular, Seidman (1987, pp. 121-122) argues that: “The cumulative addition of facts and verified propositions, conceptual refinements, or analytical developments dislodge erroneous theories, and propels us toward theories which are closer to the truth about society….   virtually every current social scientific theory strives to achieve legitimacy and dominance by reconstructing the past as a cumulative development crystallizing in its own systematization”. In this context of the accumulation of knowledge, basic and applied sciences evolve and converge creating a deeper unity within the overall structure of science (Coccia and Wang, 2016; Haskins, 1965). Moreover, in this approach the evolution of science is irreversible and can never go back (Science, 1965).

The scientific development is due to accumulation of “normal science”^[1], interrupted by discontinuous transformations generated by new theoretical and empirical approaches that support the transition from an existing scientific paradigm to an emerging one. In fact, paradigm shifts are the major source of scientific change in society (Kuhn, 1962). Moreover, in this theory, scientific paradigm shift can be major in the presence of discontinuity with previous theoretical framework (e.g., target therapy vs. chemotherapy in cancer treatments; cf. Coccia, 2012b, 2012c, 2014a, 2015a, 2016a), and minor whether it generates continuity between successive paradigms (e.g., nanoparticle-delivered chemotherapy in oncology that combines traditional chemotherapy and emerging nanotechnologies; Coccia and Wang, 2015; cf., Clark, 1987). In general, major or minor paradigm shifts support the long-run evolution of science, disciplines and research fields over time. [1] “ ‘normal science’ means research firmly based upon one or more past scientific achievements that some particular scientific community acknowledges for a time as supplying the foundation for its further practice’’ (Kuhn, 1962, p. 10, original emphasis).

Lakatos (1968, p. 168, original Italics and emphasis) argues that:

The programme consists of methodological rules: some tell us what paths of research to avoid (negative heuristic), and others what paths to pursue (positive heuristic)

Lakatos’ theory of research programme is based on a hard core of theoretical assumptions that cannot be abandoned or altered without abandoning the programme altogether. The evolution of science here is due to the creation of a research programme that guides the scientific development of one or more research fields and/or disciplines over time (Lakatos, 1978). Finally, Lakatos’ theory also argues that a research programme, in the presence of troublesome anomalies, remains progressive despite them.

Tiryakian (1979) argues that the scientific school is the unit of analysis for a model of scientific development. Major schools develop scientific disciplines by providing new methodologies or new conceptual schemes of social reality. Tiryakian (1979) rejects both the empiricist approach that discoveries initiate scientific change and the rationalist claim that conceptual refinements of theoretical models stimulate a scientific change. In short, the formation of a school offers new scientific directions to study social reality that initiates significant scientific advances over time (e.g., in economics, the Monetarism is a new school of thought based on control of money to affect price levels and economic growth versus Keynesian economics based on government expenditures with fiscal policy to support economic development).

Seidman (1987) argues that: “the discovery of anomalies or analytical criticisms of one or another dimension of a theory sets in motion a process of theoretical revision”. Unlike Kuhn (1962), Alexander (1979) proposes that scientific theories do not change in a revolutionary manner. Scientific theories are based on different autonomous entities, such as presuppositions, ideologies, models, laws, concepts, propositions, methodologies, etc. that shape science, articulate its problems, and have a distinctive mode of discourse with its own standards of assessment. In short, Tiryakian (1979) analyzes the tensions and dynamics of the social structure of the school and its relation to scientific community. By contrast, Alexander (1983, p. 349) argues that the engine of scientific change is due to new theoretical frameworks of scholars that generate a revision of current conceptual scheme in specific field of research, marking the life-history of a school.