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Discontinuous model of scientific progress
Several philosophers of science have supported arguments that the progress of science is discontinuous. In that case, progress isn't a continuous accumulation, but rather a revolutionary process where brand new ideas are adopted and old ideas become abandoned. Thomas Kuhn was a major proponent of this model of scientific progress, as explained in his book The Structure of Scientific Revolutions.
This is especially supported by studying the incommensurability of theories. For example, consider Newtonian mechanics and relativistic mechanics. From a strict vantage point, in newtonian mechanics mass and energy are always conserved, where in relativistc mechanics energy and mass are always interchangeable. (Note the difference between the strict vantage point, and the layperson's vantage point that Newton's theory is applicable at low energies and low velocities relative to the velocity of light.) Because the theories are completely incompatible, scientists using one paradigm will not be able to discuss meaningfully with scientists from the other paradigm.
A discontinuous model of scientific progress may disagree with a realist's construction in the philosophy of science. This is because the intrinsic nature of the objects referred to may change wildly.
History of science as a model of scientific progress
Another model of scientific progress, as put forward by Richard Boyd, and others, is history of science as a model of scientific progress. In short, methods in science are produced which are used to produce scientific theories, which then are used to produce more methods, which are then used to produce more theories and so on.
Note that this does not conflict with a continuous or discontinuous model of scientific progress. This model supports realism in that scientists are always working within the same universe; their theories must be referring to real objects, because they create theories that refer to actual objects that are used later in methods to produce new theories.
An example supporting realism is the case of the electron. It is hard to prove the existence of an electron because it is so small. However, any microscopist will tell you that he knows an electron exists, because he uses it in his electron microscope.
Origins of the concept
Early technological and religious traditions did not concern themselves with gaining knowledge in any systematic way, and thus the concept of scientific progress would have been largely alien to them. Societies deeply invested in tradition were primarily occupied with the verbatim passing of thoughts and practices to the next generation, and did not engage in the scientific method.
Even if some esoteric traditions may have involved themselves with a rudimentary experimental method as the nucleus of their initiation, they did not overtly separate exploration from instruction.
Some classical Greeks like Hippocrates did systematically gather evidence, but as a concept incremental increase of knowledge is first formulated in connection with the art of warfare.
Quotes on scientific progress
Terry Halwes wrote:
What is required for scientific progress is mainly ordinary curiosity, ordinary awareness, ordinary learning, ordinary reasoning, and fairly ordinary communication. Of course scientists work hard to develop and use precise technical terms for many of the things they talk about, but so do lawyers and golfers and cooks. 
The wrong view of science betrays itself in the craving to be right; for it is not his possession of knowledge, of irrefutable truth, that makes the man of science, but his persistent and recklessly critical quest for truth. 
Science progresses in a much more muddled fashion than is often pictured in history books. This is especially true of theoretical physics, partly because history is written by the victorious. Consequently, historians of science often ignore the many alternate paths that people wandered down, the many false clues they followed, the many misconceptions they had. These alternate points of view are less clearly developed than the final theories, harder to understand and easier to forget, especially as these are viewed years later, when it all really does make sense. Thus reading history one rarely gets the feeling of the true nature of scientific development, in which the element of farce is as great as the element of triumph.
Notes and references
- (in French) Marc Audétat (direction), Gaïa Barazzetti, Gabriel Dorthe, Claude Joseph, Alain Kaufmann and Dominique Vinck, Sciences et technologies émergentes : pourquoi tant de promesses ? [Emerging science and technologies: why so many promises?], Éditions Hermann, 2015.
- Nicholas Maxwell, Understanding Scientific Progress, Paragon House, 2017. This book solves fundamental problems associated with scientific progress, including the problem of induction.