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The central notion in the philosophy of science of Popper, although foreshadowed by Whewell and Peirce . In his Logik der Forschung (1934), Popper argued that the central virtue of science, as opposed to pseudo-science, is not that it puts forward hypotheses that are confirmed by evidence to some high degree, but that its hypotheses are capable of being refuted by evidence. That is, they genuinely face the possibility of test and rejection through not conforming to experience. The scientific method is not, therefore, the mechanical induction of generalizations from accumulated data, but the formation of bold hypotheses that are then subjected to rigorous test: a method of conjectures and refutations. It is no fault in a scientist to put forward an interesting conjecture that is subsequently refuted, but it would be a fault to put forward one which then permits no refutation, or to hold one in the face of refuting evidence.

Popper's idea found an enthusiastic following amongst working scientists, but philosophers of science have detected gaps and oversimplifications in the story. First, by removing induction and confirmation entirely, Popper seems to give no account of the extent to which it is rational to rely upon scientific theory in practice (for having survived tests so far is no indication of likely truth). Secondly, the actual picture of acceptance and rejection of scientific hypothesis is more complex than Popper suggests: something that one scientist regards as a refutation another might regard as an anomaly, depending on such things as the momentum of the research programme that threw up the hypothesis and the availability of alternative explanations. This blurs the difference between a scientist quite reasonably committed to some general framework of theory, such as Newtonian or relativistic physics, and the Marxists or Freudians whose pseudo-scientific pretensions were one of Popper's targets. See also confirmation theory, demarcation problem, verisimilitude.