Critical Rationalism is Karl Popper's answer to what he considered the most important problems of epistemology and philosophy of science: the problems of the growth of knowledge, notably by induction, and the demarcation of science. He adopted a fallibilist approach to these problems, especially that of induction, without falling into skepticism. His approach was to put in perspective the distinctive role of deductive logic in the development of knowledge, especially in science, in the context of a less rigorous methodology based on critical thinking. The central technical concept in the application of critical rationalism to science is falsifiabiity. Popper first mentioned the term "critical rationalism" in The Open Society and Its Enemies (1945), and also later in Conjectures and Refutations (1963), Unended Quest (1976), and The Myth of the Framework (1994).

Popper admitted that the truth of statements cannot be obtained using only logical definitions and deductions, as this leads to an infinite regress. For Popper, this does not prevent statements from being useful for solving problems, because they can be logically analyzed to draw logical consequences, possibly contradictions with observation statements linked to real tests. Popper wrote that the bulk of scientific activities use deductive logic to evaluate theories.

Popper accepted Hume's argument and the consequences of Duhem's thesis and insisted that there is no logical method for accessing empirical truth, no inductive rule, not even to a small extent. However, he rejected skepticism, the idea that the search for truth is futile. He admitted that, although logic alone says nothing about empirical truth, statements can be related to reality through problem solving, scientific observations and experiments. Popper always insisted on this distinction between the logical aspect and methodological aspect of science. In Realism and the Aim of Science, Popper speaks of a "preferred" theory, not of a "true" or a "false" theory, when one theory is chosen over another given experimental results.

Popper was always aware that empirical truth eludes logic alone, and he was therefore reluctant to refer to the truth of scientific theories. This, he wrote, changed after reading Tarski's semantic theory of truth. He saw this theory as a way of talking about truth as a correspondence with facts. A key aspect of Tarski's theory, which Popper considered important, is the separation between the logical (formal) aspect of language as an object and its semantic interpretation. He saw this as a way of explaining the distinction between the logic of science and its methodology, or rather between logic and the metaphysical component to which methodology refers when it aims, for example, to test theories. The difference is that in Tarski's theory, "facts" are mathematical structures, not an external reality beyond the reach of logic and its language, and which we can only describe artificially in a meta-language as in the argument "Snow is white" (in the object language) is true because snow is white (in the meta-language). This use of Tarski's theory is accepted by some and sharply criticized by others. Popper used it, for example, in Realism and the Aim of Science, to explain the difference between the metaphysical versions of the problem of induction and its logical versions. He wrote that the metaphysical versions of the problem refer to the "meta-theory of physics" and compared this to what Tarski calls the "semantics" in its theory of truth.

For Popper, the bulk of activities in science use deductive logic on statements, but this logical part of science must be integrated within an adequate methodology. The logical part is considered incapable of justifying empirical knowledge on its own. For example, Popper and the members of the Vienna Circle agreed that only statements can be used to justify statements, that is, the use of logic alone in science will not be linked to (empirical, not propositional) evidence. Logic uses accepted or provisionally accepted observation statements to determine whether a theory is logically refuted or not, but the "accepted" observation statement could be empirically false and that will not concern the logical part.

Popper wrote that the bulk of scientific activity takes place in the logical part, using deductive logic to check the consistency of a theory, compare theories, check their empirical nature (i.e., falsifiability) and, most importantly, test a theory, which is possible only when it is falsifiable. He emphasized that, even when theories are tested against observations, deductive logic is largely used. Despite this intensive use of logic, Popper accepted, as do most philosophers and scientists, that logic alone does not connect by itself with evidence. Popper explained this dilemma by stating the existence of a natural separation (not a disconnection) between the logical and the methodological parts of science.

Popper wrote that any criterion, including his famous falsifiability criterion, that applies solely on the logical structure could not alone define science. In The Logic of Scientific Discovery, he wrote "it is impossible to decide, by analysing its logical form [as do the falsifiability criterion], whether a system of statements is a conventional system of irrefutable implicit definitions, or whether it is a system which is empirical in my sense; that is, a refutable system." Popper insisted that falsifiability is a logical criterion, which must be understood in the context of a proper methodology. The methodology can hardly be made precise. It is a set of informal implicit conventions that guide all the decisions that surround the logical work, which experiments to conduct, which apparatus to build, which domain will be financially supported, etc., aspects that were raised by Lakatos in The Methodology of Scientific Research Programmes.

Popper's philosophy was criticized as if the logical part existed alone. For example, Putnam attributed to Popper "the fantasy of doing science using only deductive logic". Putnam further criticized Popper's description of the logical part of science by referring to methodological problems. For example, he wrote "I claim: in a great many important cases, scientific theories do not imply predictions at all." Because Popper does not believe in inductive logic, Wesley Salmon wrote that, for Popper, "there is no ampliative form of scientific argument, and consequently, science provides no information whatever about the future". Regarding the methodological part, Feyerabend wrote that there is no method in science. He considered and rejected methodological rules, but they were those of a naive falsificationist.