Georg Cantor Quotes
There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.
Cantor, Georg. "Mitteilungen zur Lehre vom Transfiniten." Zeitschrift für Philosophie und philosophische Kritik, vol. 91, 1887. Printed in Georg Cantor Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, edited by Ernst Zermelo, Julius Springer, 1932, p. 404.
At the time, American medicine was not much of a science, but mostly controlled by ideological opinion of prestigious physicians espousing theories in the speculative non-scientific sense. Beaumont, who had made discoveries that contradicted the established ideology of most physicians, laid down a scientific principle. However, it would take American medicine another century to accept scientific method as the driver of medical practice. Even into the 21st century, there were some physicians who did not accept scientific research as determinative. In 2009, it became a major area of political controversy as to whether scientific research should control what the Government would or would not pay for when public funds were involved. There was still a part of the society that saw scientists as elitist and not to be trusted in public policy making.
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician. He created set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact he was well aware of.
