Intellectual honesty consists in stating the precise conditions under which one will give up one's belief.

The proving power of the intellect or the senses was questioned by the skeptics more than two thousand years ago; but they were browbeaten into confusion by the glory of Newtonian physics.

Philosophy of science without history of science is empty; history of science without philosophy of science is blind.

That sometimes clear ... and sometimes vague stuff ... which is ... mathematics.

Man's respect for knowledge is one of his most peculiar characteristics. Knowledge in Latin is scientia, and science came to be the name of the most respectable kind of knowledge.

The great scientific achievements are research programmes which can be evaluated in terms of progressive and degenerative problemshifts; and scientific revolutions consist of one research programme superceding (overtaking in progress) another. This methodology offers a new rational reconstruction of science.

The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.