Positivism is the belief that human knowledge is produced by the scientific interpretation of observational data.

The approach has been an ongoing "theme in the history of western thought from the Ancient Greeks to the present day". The term was used in the early 19th century by the philosopher and founding sociologist, Auguste Comte.

Comte, a sociologist, believed in a three part model of human knowledge. He claimed that it had gone through phases. There was a religious worldview, and a metaphysical worldview before the scientific interpretation was considered. The positivistic method should, said Comte, no longer aim at a revealing ultimate causes. It should rather focus on how data are linked together. Scientists would simply interpret these correlations. All human knowledge could only be relatively true, so Comte with a look at these interpretations. Late 19th-century philosophers of the sciences from Heinrich Hertz to Ernst Mach eventually discussed specific requirements of operable scientific theories and physical laws such as the predictability of results in experiments and the functionality of laws in computations.

Principles
In its strongest original formulation, positivism could be thought of as a set of five principles:
 The unity of the scientific method – i.e., the logic of inquiry is the same across all sciences (social and natural).
 The aim of science is to explain and predict.
 Scientific knowledge is testable. Research can be proved only by empirical means, not arguments alone. Research should be mostly deductive, i.e. deductive logic is used to develop statements that can be tested (theory leads to hypothesis which in turn leads to discovery and/or study of evidence). Research should be observable with the human senses. Arguments are not enough, sheer belief is out of the question.
 Science does not equal common sense. Researchers must be careful not to let common sense bias their research.
 Science should be as value-neutral as possible. The ultimate goal of science is to produce knowledge, regardless of any politics, morals, or values held by those involved in the research. Science should be judged by logic, and ideally produce universal conditionals.
 Experiments must be able to verify a statement anytime and anywhere.

Unlike materialists positivists do not make any claims about a primary substance such as matter. They assume that we have data and that we interpret the data. The idea of a material world with three dimensions is, for positivists, just a good model to handle the experiences of everyday life. If astronomy has to deal with more complex data that cannot be handled consistently in such a model, they will have to think of a different model. Early 20th-century positivists like Ernst Mach said that the best model is the most "economical" model, that is the model we can use best in calculations and predictions.

The idea that all physical laws could be useful dates back to Auguste Comte. Comte said that all theories were merely "relatively" true, and that even Isaac Newton's law of universal gravitation was strictly speaking nothing but a social convention  true until new data force us to find a better theory.

Logical positivism 

This was an important development in early 20th century Vienna, led by Moritz Schlick and widened by Ludwig Wittgenstein. The logical positivists held that statements that cannot be proven true or false have no meaning.

It held not only that propositions were true or false, but that statements which could not be shown to be either true or false were meaningless. Thus statements like "There is a God" or "There is no God" are not true or false, but meaningless because they cannot be proven or disproven.

Operationalism 
This was the idea of P.W. Bridgman, Nobel Prize in Physics for 1946. It was that a concept in science was defined by the way one measured it. If one thinks of electron spin, or the curvature of space, these are not everyday ideas. In everyday life, electrons are not seen, and neither is space seen to be curved. They rest on the results of experiments which measured fundamental properties like time, light, mass, electrical charge, and so on. What Bridgman meant is that their meaning is in the way the measurements were done.

Examples 
The special theory of relativity depended on operational definitions for simultaneous events and distance, that is, providing the operations needed to define these terms.
In quantum mechanics the notion of operational definitions is closely related to the idea of "observables", that is, definitions based upon what can be measured.
Operationalism is found in other sciences. In psychology, intelligence has often been defined as the result of measurement by a standard IQ test. Obviously that is controversial, because our everyday understanding of the word "intelligence" is much more complex and varied.

Comtean positivism 
19th-century positivism – or "Comtean positivism" – included the outline of a proposed development. This would lead from primitive explanations, through religious thought and monotheism, to positivism as the universal theory and scientific practice. The theory was very influential among cultural historians. It led Comte to the creation a "religion of humanity" as a secular substitute for all religions. This caused an outcry among scientists, who were ready to adopt the scientific premises but not interested in creating a substitute religion.

One can today still visit temples in Rio de Janeiro, Porto Alegre, and  Curitiba in Brazil, and Paris built by 19th-century Comtean positivists. London had a society of positivists. The Turkish leader Mustafa Kemal Atatürk was strongly interested in positivism as the basis of a secularisation of the nation, he was trying to build.

The term positivism is today no longer connected to the construct of a secular religion, but more to describe a scientific method.

References

Further reading on positivism 
 Giddens, Anthony. Positivism and sociology. Heinemann. London. 1974.
 Mill, John Stuart. August Comte and positivism.  
 Mises, Richard von. 1951. Positivism: a study in human understanding. Harvard University Press. Cambridge, Mass.
 Pickering, Mary. 1993. Auguste Comte: an intellectual biography. Cambridge University Press, Cambridge.
 Richard Rorty 1982. Consequences of pragmatism

Other websites 
 Positivists Worldwide

Philosophical movements and positions
Ethics