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.

It is not that we propose a theory and Nature may shout NO; rather, we propose a maze of theories, and Nature may shout INCONSISTENT.

In degenerating programmes, however, theories are fabricated only in order to accommodate known facts

If even in science there is no a way of judging a theory but by assessing the number, faith and vocal energy of its supporters, then this must be even more so in the social sciences: truth lies in power.

Einstein's results again turned the tables and now very few philosophers or scientists still think that scientific knowledge is, or can be, proven knowledge.

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.

One may rationally stick to a degenerating research programme until it is overtaken by a rival and even after. What one must not do is to deny its poor public record... It is perfectly rational to play a risky game: what is irrational is to deceive oneself about the risk.