Science is a craft that depends on the skill of its practitioners
The scientific process is not a set of math theorems that can be proven, but rather, it is a social process, and it is a craft, and it depends upon the skill of its practitioners:
It is unremarkable to observe that many aspects of skilled performance depend on “knowledge” that cannot be articulated as a set of statements or rules (link). The basketball guard’s ability to weave through defenders and find his way to the basket reflects a complex set of representations of the court, the defenders, and probable behaviors of others that can’t be codified. So it seems fairly straightforward to conclude that human cognition incorporates representations and knowledge that do not take the form of explicit systems of statements. Rather, these areas of knowledge are more “intuitive”; they are more akin to “body knowledge.” But they are nonetheless cognitive; they depend on experience, they can be criticized and corrected, and they are representational of the world. (Talk to a skilled athlete about a complex task like finding a shot on goal in hockey or beating the defender to the basket, and you will be struck by the degree of intuition, gestalt, and realism that is invoked. And the same is true if you talk to an experienced labor organizer or a police detective.)
What is striking about Polanyi’s position in Personal Knowledge is that he shows that these forms of practical knowledge do not pertain solely to physical skills like wine-making, playing basketball, or piloting a tug boat. Instead, they extend deeply into the enterprise of scientific knowledge itself. An experimental chemist or physicist has an uncodified ability to interpret instruments, evaluate complex devices, or recognize unexpected results that is the result of experience and training and cannot be reduced to a recipe or algorithm. And the difference between a gifted sociologist and a pedestrian one is his/her ability to probe a set of social facts for the underlying patterns, mechanisms, or questions that they suggest. These are ideas that return again in post-positivist philosophers and historians of science like Thomas Kuhn, Norwood Hanson, and Peter Galison; each of these scholars emphasizes the tight relationship that exists in scientific education and imagination between scientific practices, scientific instruments, and scientific knowledge.