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Instrumentalism became popular among physicists around the turn of the 20th century, after which logical positivism defined the field for several decades. Logical positivism accepts only testable statements as meaningful, rejects metaphysical interpretations, and embraces verificationism (a set of theories of knowledge that combines logicism, empiricism, and linguistics to ground philosophy on a basis consistent with examples from the empirical sciences). Seeking to overhaul all of philosophy and convert it to a new scientific philosophy, the Berlin Circle and the Vienna Circle propounded logical positivism in the late 1920s. Interpreting Ludwig Wittgenstein's early philosophy of language, logical positivists identified a verifiability principle or criterion of cognitive meaningfulness. From Bertrand Russell's logicism they sought reduction of mathematics to logic. They also embraced Russell's logical atomism, Ernst Mach's phenomenalism—whereby the mind knows only actual or potential sensory experience, which is the content of all sciences, whether physics or psychology—and Percy Bridgman's operationalism. Thereby, only the verifiable was scientific and cognitively meaningful, whereas the unverifiable was unscientific, cognitively meaningless "pseudostatements"—metaphysical, emotive, or such—not worthy of further review by philosophers, who were newly tasked to organize knowledge rather than develop new knowledge. Logical positivism is commonly portrayed as taking the extreme position that scientific language should never refer to anything unobservable—even the seemingly core notions of causality, mechanism, and principles—but that is an exaggeration. Talk of such unobservables could be allowed as metaphorical—direct observations viewed in the abstract—or at worst metaphysical or emotional. Theoretical laws would be reduced to empirical laws, while theoretical terms would garner meaning from observational terms via correspondence rules. Mathematics in physics would reduce to symbolic logic via logicism, while rational reconstruction would convert ordinary language into standardized equivalents, all networked and united by a logical syntax. A scientific theory would be stated with its method of verification, whereby a logical calculus or empirical operation could verify its falsity or truth. In the late 1930s, logical positivists fled Germany and Austria for Britain and America. By then, many had replaced Mach's phenomenalism with Otto Neurath's physicalism, and Rudolf Carnap had sought to replace verification with simply confirmation. With World War II's close in 1945, logical positivism became milder, logical empiricism, led largely by Carl Hempel, in America, who expounded the covering law model of scientific explanation as a way of identifying the logical form of explanations without any reference to the suspect notion of "causation". The logical positivist movement became a major underpinning of analytic philosophy, and dominated Anglosphere philosophy, including philosophy of science, while influencing sciences, into the 1960s. Yet the movement failed to resolve its central problems, and its doctrines were increasingly assaulted. Nevertheless, it brought about the establishment of philosophy of science as a distinct subdiscipline of philosophy, with Carl Hempel playing a key role.

=== Thomas Kuhn ===

In the 1962 book The Structure of Scientific Revolutions, Thomas Kuhn argued that the process of observation and evaluation takes place within a "paradigm", which he describes as "universally recognized achievements that for a time provide model problems and solutions to community of practitioners." A paradigm implicitly identifies the objects and relations under study and suggests what experiments, observations or theoretical improvements need to be carried out to produce a useful result. He characterized normal science as the process of observation and "puzzle solving" which takes place within a paradigm, whereas revolutionary science occurs when one paradigm overtakes another in a paradigm shift. Kuhn was a historian of science and his ideas were inspired by the study of older paradigms that have been discarded, such as Aristotelian mechanics or aether theory. These had often been portrayed by historians as using "unscientific" methods or beliefs. But Kuhn's examination showed that they were no less "scientific" than modern paradigms. A paradigm shift occurred when a significant number of observational anomalies arose in the old paradigm and efforts to resolve them within the paradigm were unsuccessful. A new paradigm was available that handled the anomalies with less difficulty and yet still covered (most of) the previous results. Over a period of time, often as long as a generation, more practitioners began working within the new paradigm and eventually the old paradigm was abandoned. For Kuhn, acceptance or rejection of a paradigm is a social process as much as a logical process. Kuhn explicitly rejected a relativist interpretation of his ideas. He wrote "terms like 'subjective' and 'intuitive' cannot be applied to [paradigms]." Paradigms, as he understood them, are grounded in objective, observable evidence, but our use of them is psychological and our acceptance of them is social.

== Current approaches ==

=== Naturalism's axiomatic assumptions ===

According to Robert Priddy, all scientific study inescapably builds on at least some essential assumptions that cannot be tested by scientific processes; that is, that scientists must start with some assumptions as to the ultimate analysis of the facts with which it deals. These assumptions would then be justified partly by their adherence to the types of occurrence of which we are directly conscious, and partly by their success in representing the observed facts with a certain generality, devoid of ad hoc suppositions." Kuhn also claims that all science is based on assumptions about the character of the universe, rather than merely on empirical facts. These assumptions a paradigm comprise a collection of beliefs, values and techniques that are held by a given scientific community, which legitimize their systems and set the limitations to their investigation. For naturalists, nature is the only reality, the "correct" paradigm, and there is no such thing as supernatural, i.e. anything above, beyond, or outside of nature. The scientific method is to be used to investigate all reality, including the human spirit. Some claim that naturalism is the implicit philosophy of working scientists, and that the following basic assumptions are needed to justify the scientific method: