Karl Popper

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Problem of Induction
One of the most influential and controversial views on the problem of induction has been that of Karl Popper, announced and argued in (Popper LSD). Popper held that induction has no place in the logic of science. Science in his view is a deductive process in which scientists formulate hypotheses and theories that they test by deriving particular observable consequences. Theories are not confirmed or verified. They may be falsified and rejected or tentatively accepted if corroborated in the absence of falsification by the proper kinds of tests: A theory of induction is superfluous. It has no function in a logic of science. The best we can say of a hypothesis is that up to now it has been able to show its worth, and that it has been more successful than other hypotheses although, in principle, it can never be justified, verified, or even shown to be probable. This appraisal of the hypothesis relies solely upon deductive consequences (predictions) which may be drawn from the hypothesis: There is no need even to mention “induction” (Popper LSD, 315). Popper gave two formulations of the problem of induction; the first is the establishment of the truth of a theory by empirical evidence; the second, slightly weaker, is the justification of a preference for one theory over another as better supported by empirical evidence. Both of these he declared insoluble, on the grounds, roughly put, that scientific theories have infinite scope and no finite evidence can ever adjudicate among them (Popper LSD, 253–254, Grattan-Guiness 2004). He did however hold that theories could be falsified, and that falsifiability, or the liability of a theory to counterexample, was a virtue. Falsifiability corresponds roughly to to the proportion of models in which a (consistent) theory is false. Highly falsifiable theories thus make stronger assertions and are in general more informative. Though theories cannot in Popper's view be supported, they can be corroborated: a better corroborated theory is one that has been subjected to more and more rigorous tests without having been falsified. Falsifiable and corroborated theories are thus to be preferred, though, as the impossibility of the second problem of induction makes evident, these are not to be confused with support by evidence. Popper's epistemology is almost exclusively the epistemology of scientific knowledge. This is not because he thinks that there is a sharp division between ordinary knowledge and scientific knowledge, but rather because he thinks that to study the growth of knowledge one must study scientific knowledge: Most problems connected with the growth of our knowledge must necessarily transcend any study which is confined to common-sense knowledge as opposed to scientific knowledge. For the most important way in which common-sense knowledge grows is, precisely, by turning into scientific knowledge (Popper LSD, 18).

Concept of Verification and Falsification
Science is guesswork, doxa rather than episteme.  In place of the old ideal (or rather idol) of science as the search for absolutely certain, demonstrable knowledge, Popper argues that the “demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative for ever.”   Verification of scientific knowledge is replaced by falsification.  Accumulation of irrefutable facts is replaced by conjecture and refutation. Strictly speaking, the truth value of any scientific theory must be regarded as false.  If it has been falsified, it is false; if not, then it will at some future point be demonstrated false.  A theory is corroborated if it has withstood genuine attempts at falsification, but it is never anything more than a working hypothesis, never demonstrated true.  This is born out according to the logical asymmetry between verification and falsification.  While it is impossible to verify a universal law by reference to some putative confirming experience, a single...
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