What is conjectures and refutations?

Karl Popper, answered from the texts and cited to the page.

Karl Popper answers

Knowledge grows not by accumulation but by the elimination of error. That is the central idea, and it is simpler than its critics suppose. We do not begin with observations and work upward to theories — that is the Baconian myth, and it is a myth.1 We begin with problems, propose bold guesses as tentative solutions, and then subject those guesses to the most severe criticism we can devise.

Observations and experiments enter the process, but their significance depends entirely upon whether they can be used to criticize theories.2 The logic runs in one direction only: a theory can be refuted by an observation that contradicts its predictions, but no accumulation of confirming observations can establish a theory as certainly true or even as probable in the sense of the probability calculus.3

The practical upshot is this. When you ask me how I know something, my honest answer is that I do not know — I only propose a guess, and I invite you to criticize it.4 If your criticism succeeds, we have learned something: we have eliminated an error, and that elimination is itself a step forward. Even the refutation of a serious conjecture takes us nearer to the truth, because it sharpens our understanding of the problem we are trying to solve.5

This method is not the private property of the natural sciences. I believe it can be applied to philosophical problems, and — following Lakatos, who persuaded me on the point — even to arithmetic, which I once thought could rest on secure foundations.6 Nothing in our intellectual life is exempt from the process of criticism and error elimination.7

The tradition behind the method is ancient. Critical discussion of this kind was invented once, in Ionia, lost after two or three centuries (partly through the Aristotelian demand for certain and demonstrable epistēmē), and consciously revived in the Renaissance by Galileo.8 Galileo and Einstein are the two figures who most clearly understood that there is no inductive procedure — that knowledge proceeds, as it always has, by conjectures and refutations.9

Sources

  1. there is no way that starts from observation or experiment. In the development of science observations and experiments play only the role of critical arguments.
    Conjectures and Refutations, pp. 151–152
  2. the significance of observations and experiments depends entirely upon the question whether or not they may be used to criticize theories.
    Conjectures and Refutations, pp. 151–152
  3. 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).
    Conjectures and Refutations, pp. 1–2
  4. If you ask me, 'How do you know?' my reply would be, 'I don't; I only propose a guess. If you are interested in my problem, I shall be most happy if you criticize my guess, and if you offer counter-proposals, I in turn will try to criticize them.'
    The World of Parmenides, p. 26
  5. the very refutation of a theory--that is, of any serious tentative solution to our problem--is always a step forward that takes us nearer to the truth. And this is how we can learn from our mistakes.
    Conjectures and Refutations, pp. 1–2
  6. my former colleague, Imre Lakatos, converted me four or five years before the first version of this essay was written to the opposite belief: I owe to him my present view that it is not only the natural sciences (and, of course, philosophy) but also arithmetic that has no foundations.
    The World of Parmenides, p. 173
  7. Nothing in our intellectual life is exempt from this process of criticism and error elimination.
    The World of Parmenides, p. 173
  8. The rationalist tradition, the tradition of critical discussion, represents the only practicable way of expanding our knowledge... It was lost after two or three centuries, perhaps owing to the rise of the Aristotelian doctrine of epistēmē... It was rediscovered and consciously revived by the Renaissance, especially by Galileo Galilei.
    Conjectures and Refutations, pp. 151–152
  9. Two of the greatest men who clearly saw that there was no such thing as an inductive procedure, and who clearly understood what I regard as the true theory of knowledge, were Galileo and Einstein.
    The World of Parmenides, p. 26