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Critical rationalism is an epistemological philosophy advanced by Karl Popper on the basis that, if a statement cannot be logically deduced (from what is known), it might nevertheless be possible to logically falsify it. Following Hume, Popper rejected any inductive logic that is ampliative, i.e., any logic that can provide more knowledge than deductive logic. In other words if we cannot assert it logically, we should at the least try to logically falsify it, which led Popper to his falsifiability criterion.
Popper wrote about critical rationalism in many works, including: The Logic of Scientific Discovery (1934/1959), The Open Society and its Enemies (1945), Conjectures and Refutations (1963), Unended Quest (1976), and The Myth of the Framework (1994).