The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge understood in the classic philosophical sense,Vickers, John, "Can induction be justified?", The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed...
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In my book Understanding Scientific Progress (Maxwell 2017), I argue that fundamental philosophical problems about scientific progress, above all the problem of induction, cannot be solved granted standard empiricism (SE), a doctrine which most scientists and philosophers of science take for granted. A key tenet of SE is that no permanent thesis about the world can be accepted as a part of scientific knowledge independent of evidence. For a number of reasons, we need to adopt a rather different conception of science which I call aim-oriented empiricism (AOE). This holds that we need to construe physics as accepting, as a part of theoretical scientific knowledge, a hierarchy of metaphysical theses about the comprehensibility and knowability of the universe, these theses becoming increasingly insubstantial as we go up the hierarchy. Fundamental philosophical problems about scientific progress, including the problems of induction, theory unity, verisimilitude and scientific discovery, which cannot be solved granted SE, can be solved granted AOE. In his review of Understanding Scientific Progress, Moti Mizrahi makes a number of criticisms, all of which are invalid in quite elementary ways