Galileo was once thought to have discovered kinetic laws important for classical mechanics by himself by means of observations and experiments in contrast to the Scholastics who confined themselves to the interpretation of Aristotle. To be sure he gave such an impression to readers, but the fact is that the Scholastics in 14th century such as Oxford Calculators and Oresme who discovered and developed the Mean Speed Theorem prepared for Galileo’s discovery of kinetic laws. They did not perform experiments except thought experiments, but since the 17th century scientific revolution is the shift from Aristotle-Thomas paradigm to Plato-Archimedes paradigm, we can consider the Oxford Calculators and Oresme to be the pioneer of the paradigm shift, because this paradigm insisted on mathematical models preceding experience.

Magnetism and electrostatic forces were regarded as occult action at a distance from ancient times and the inquiry into it waned when Christianity that banned magic had strong power. Since the Renaissance, however, researchers dared to study the occult magic and thus they pioneered modern electromagnetism and mechanics. Newton and Coulomb recognized gravitation and electromagnetism as action at a distance but today they are explained as action through medium. The lesson we must learn from history of electromagnetic theory is that we should not refuse study in occult phenomena because of its occult appearances but, as accepting action at a distance is not science but occultism, it should be explained as action through medium.

Milindapañha tells that King Milinda, an Indo-Greek king, talked with Nāgasena, a Buddhist sage, embraced the Buddhist faith and abandoned the household life to attain to Arahatship. The book is known to insist that the Buddhist philosophy of nothingness should be superior to the Western philosophy of substances, but actually Nāgasena’s theory was not so sophisticated as the Greek philosophy at that time. King Milinda did not abandon the household life and it is not certain whether he really understood Buddhism. Still he and his successors protected Buddhism, possibly because propagation of Buddhism could contribute to the stable reign.

The original sense of “paradigm” is “exemplar” and Kuhn’s “paradigm” signifies such a textbook theory or an experiment method as students imitate as an exemplar in their scientific education. Normal science engages scientists in puzzle-solving based on a paradigm, which is more economically rational than the frequent revolutions. Even in scientific revolutions new paradigms succeed to the old ones continuously. What changes drastically in a revolution is not the paradigm itself but the balance of power between paradigms. Like political revolutions, scientific revolutions are the struggle for existence and paradigms do not shift to copy the reality better.

The Copernican heliocentric model was not the victory of science over the religious superstition prevailing in the Middle Age. In fact his system was neither simpler nor more accurate than Ptolemy's geocentric model. Copernicus nonetheless proposed the heliocentric model and it was accepted by not a few astronomers, because Neoplatonism that worshipped the Sun was in fashion in those days. The climate background of the sun worship is the modern Little Ice Age, since people tend to accept the common sense of geocentric cosmology in warm periods, while it is doubted in cool periods.

When infinitesimal calculus was first established, the limit of a function was defined in terms of infinitesimal or infinity. As the naïve way at that time contradicted itself, new methods such as the epsilon-delta definition and non-standard analysis were devised to avoid the contradiction. Although mathematicians are not aware of it, it is Kant’s transcendental idealism that lays the foundation for these methods. That is to say, these methods succeed in solving the paradox of infiniteness because they abandon the cognition of “infiniteness in itself” and accomplish the Copernican Revolution that converts the cognition of infiniteness into the infiniteness of cognition.