Two conflicting systems of thought are separated by a logical gap. "Formal operations relying on one framework of interpretation cannot demonstrate a proposition to persons who rely on another framework. Its advocates may not succeed in getting a hearing from them, since they must first teach them a new language, and no one can learn a new language unless he first trusts that it means something. A hostile audience in fact may in fact deliberately refuse to entertain novel conceptions ... because its members fear that once they have accepted this new framework they will be lead to conclusions which they -- rightly or wrongly -- abhor. Proponents of a new system can convince their audience only by first winning their intellectual sympathy for a doctrine they have not yet grasped. Those who listen sympathetically will discover for themselves what they would otherwise have never understood. Such an acceptance is a heuristic process, a self-modifying act, and to this extent a conversion. It produces disciples forming a school, the members of which are separated for the time being a logical gap from those outside it. They think differently, speak a different language, live in a different world, and at least one of the two schools is excluded to this extent for the time being (whether rightly or wrongly) from the community of science" (Personal Knowledge 151).
The above has some resemblance to the idea of different paradigms posited by Thomas Kuhn in his book The Structure of Scientific Revolutions (link). Polanyi's book was published three years before Kuhn's. Kuhn's book refers to Polanyi or Personal Knowledge only about tacit knowledge, which is acquired through practice but not explicitly articulated. However, it seems Kuhn made the gap between the adherents of different schools of thought wider.
Polanyi titled his book Personal Knowledge in contrast to the widely held idea that true knowledge is deemed impersonal and objective. Polanyi holds that tacit knowledge is a significant part of personal knowledge, yet not subjective.
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