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“It is interesting to transport one's self back to the times when Astronomy began; to observe how discoveries were connected together, how errors have got mixed up with truth, have delayed the knowledge of it, and retarded its progress; and, after having followed the various epochs and traversed every climate, finally to contemplate the edifice founded on the labours of successive centuries and of various nations.”

“If human thought is a growth, like all other growths, its logic is without foundation of its own, and is only the adjusting constructiveness of all other growing things. A tree cannot find out, as it were, how to blossom, until comes blossom-time. A social growth cannot find out the use of steam engines, until comes steam-engine-time.”

“The phrase 'contrary to all expectations' rings through the story of the progress of human knowledge. It was 'contrary to all expectations' that the Earth was found to revolve around the sun, and not the other way round, and that a mould growing in one of Dr. Alexander Fleming's dishes was found to be capable of destroying bacteria. When in 1989 the spacecraft Voyager 2 got close enough to the planet Naptune to take detailed pictures of the surface, they were 'contrary to all expectations'.”

“But weightier still are the contentment which comes from work well done, the sense of the value of science for its own sake, insatiable curiosity, and, above all, the pleasure of masterly performance and of the chase. These are the effective forces which move the scientist. The first condition for the progress of science is to bring them into play.”

“There is not a single rule, however plausible, and however firmly grounded in epistemology, that is not violated at some time or other. It becomes evident that such violations are not accidental events, they are not results of insufficient knowledge or of inattention which might have been avoided. On the contrary, we see that they are necessary for progress.”

“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 rationale for accepting or rejecting any theory is thus fundamentally based on the idea of problem-solving progress. If one research tradition has solved more important problems than its rivals, then accepting that tradition is rational precisely to the degree that we are aiming to "progress," i.e., to maximize the scope f solved problems. In other words, the choice of one tradition over its rivals is a progressive (and thus a rational) choice precisely to the extent that the chosen tradition is a better problem solver than its rivals.”

“The essence of science is that it is always willing to abandon a given idea, however fundamental it may seem to be, for a better one; the essence of theology is that it holds its truths to be eternal and immutable. To be sure, theology is always yielding a little to the progress of knowledge, and only a Holy Roller in the mountains of Tennessee would dare to preach today what the popes preached in the Thirteenth Century, but this yielding is always done grudgingly, and thus lingers a good while behind the event.”

“A mind that is stretched by a new experience can never go back to its old dimensions.”

“It is they [men of science] who hold the secret of the mysterious property of the mind by which error ministers to truth, and truth slowly but irrevocably prevails. Theirs is the logic of discovery, the demonstration of the advance of knowledge and the development of ideas, which as the earthly wants and passions of men remain almost unchanged, are the charter of progress, and the vital spark in history.”