One of the aims of science is to find models that will account for as many observations as possible within a coherent framework. Together, Galileo’s rethinking of the nature of motion and Keplerian cosmology represented a coherent framework that was capable of rivaling the Aristotelian/Ptolemaic framework.

Once a paradigm shift has taken place, the textbooks are rewritten. Often the history of science too is rewritten, being presented as an inevitable process leading up to the current, established framework of thought. There is a prevalent belief that all hitherto-unexplained phenomena will in due course be accounted for in terms of this established framework. Kuhn states that scientists spend most (if not all) of their careers in a process of puzzle-solving. Their puzzle-solving is pursued with great tenacity, because the previous successes of the established paradigm tend to generate great confidence that the approach being taken guarantees that a solution to the puzzle exists, even though it may be very hard to find. Kuhn calls this process normal science.

As a paradigm is stretched to its limits, anomalies — failures of the current paradigm to take into account observed phenomena — accumulate. Their significance is judged by the practitioners of the discipline. Some anomalies may be dismissed as errors in observation, others as merely requiring small adjustments to the current paradigm that will be clarified in due course. Some anomalies resolve themselves spontaneously, having increased the available depth of insight along the way. But no matter how great or numerous the anomalies that persist, Kuhn observes, the practicing scientists will not lose faith in the established paradigm for as long as no credible alternative is available; to lose faith in the solubility of the problems would in effect mean ceasing to be a scientist.

In any community of scientists, Kuhn states, there are some individuals who are bolder than most. These scientists, judging that a crisis exists, embark on what Thomas Kuhn calls revolutionary science, exploring alternatives to long-held, obvious-seeming assumptions. Occasionally this generates a rival to the established framework of thought. The new candidate paradigm will appear to be accompanied by numerous anomalies, partly because it is still so new and incomplete. The majority of the scientific community will oppose any conceptual change, and, Kuhn emphasizes, so they should. In order to fulfill its potential, a scientific community needs to contain both individuals who are bold and individuals who are conservative. There are many examples in the history of science in which confidence in the established frame of thought was eventually vindicated. Whether the anomalies of a candidate for a new paradigm will be resolvable is almost impossible to predict. Those scientists who possess an exceptional ability to recognize a theory’s potential will be the first whose preference is likely to shift in favour of the challenging paradigm. There typically follows a period in which there are adherents of both paradigms. In time, if the challenging paradigm is solidified and unified, it will replace the old paradigm, and a paradigm shift will have occurred.