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Conjectures and Refutations:
The way in which knowledge progresses, and especially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism: that is, by attempted refutations, which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor even as 'probable' (in the sense of the probability calculus). Criticism of our conjectures is of decisive importance: by bringing out our mistakes it makes us understand the difficulties of the problems which we try to solve. This is how we become better acquainted with our problem, and able to propose more mature solutions: the very refutation of a theory - that is, of a tentative solution to our problem - is always a step forward that takes us nearer the truth. And this is how we can learn from our mistakes. As we learn from our mistakes our knowledge grows, even though we may never know - that is, know for certain. Since our knowledge can grow, there can be no reason here for despair of reason. And since we can never know for certain, the can be no authority here for any claim to authority, for conceit over our knowledge, or for smugness.
The essays and lectures of which this book is composed apply this thesis to many topics, ranging from problems of the philosophy and history of the physical and social sciences to historical and political problems. [via]