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Falsifiability (also referred to as the use of refutability) was introduced by Karl Popper and is considered an important concept in epistemology, allowing to draw a line between scientific theories and those that are not. An assertion, a hypothesis, is said to be refutable (falsifiable) if and only if it can be logically contradicted by an empirical test. More precisely, if and only if there are possible observations that can be translated into statements (true / false) logically contradicting the theory.

From a general point of view, to refute (contradict, or deny) a thesis, an opinion, a prejudice, a theory, etc., consists in showing that it is false, because it contains errors (for example, some of its statements do not correspond to the facts), or because it is less apt than another competing theory to describe certain facts (incompleteness): a theory can say more things about the facts than a competing theory about a object of common research through more severe tests that it will have undergone successfully.

Refuting a theory therefore also aims to highlight its limits in relation to another on its capacity to correspond to the facts: it is not possible to identify the limits of the empirical content of a theory, that is to say -to say, all its descriptive content on facts, only on its possibility of being refuted by tests.

According to Popper, falsifiability only makes sense in relation to the search for truth, understood as absolute, which can only be approached through a relative level of truth: corroboration or refutation. Indeed, if it is “true” that a theory is false at the end of tests, this “truth” cannot be taken for certain; and if it is “true” that a theory corresponds to certain facts, it can only be a more or less precise approximation of the truth (precision always relating to tests), certainty always remaining logically out of reach in natural sciences.


The falsifiability

Long before Popper gave it its meaning as a demarcation criterion, refutability taken in the usual sense of “being able to be refuted” was part of the history of Indian logic and Greek refutation techniques. For example, the modus tollens principle was already known in Greece and India at a very early date. The logical refutation, in particular the modus tollens, will play a fundamental role in the technical concept of falsifiability which will be introduced by Popper much later.

The problem of induction

Karl Popper’s falsifiability would hardly be possible without the historical context of the “problem of induction” raised by Hume in 1739. In essence, the problem is that no scientific theory of a universal nature with a predictive content can be verified by the observation: by virtue of its universal character, that is to say, not limited to a specific object in space-time, it predicts much more than what we will ever be able to observe.

It has been known since at least Plato that the validation of knowledge suffers from a problem of infinite regression, insofar as the argument itself must be based on other knowledge which must also be validated. Hume also presented the problem of induction from the angle of infinite regression:

”Should it be said, that we have experience, that the same power continues united with the same object, and that like objects are endowed with like powers, I would renew my question, why from this experience we form any conclusion beyond those past instances, of which we have had experience. If you answer this question in the same manner as the preceding, your answer gives still occasion to a new question of the same kind, even in infinitum; which clearly proves, that the foregoing reasoning had no just foundation.”
– David Hume, Treatise on Human Nature, Book I, Part III, Section VI

The problem of induction is also commonly referred to as the “Hume problem”, although Hume himself does not use the term “induction” to describe his subject. Regarding the conclusion of Hume’s argument, philosopher Marc Lange writes: “We are not entitled to any degree of confidence whatever, no matter how slight, in any predictions regarding what we have not observed.” This argument is echoed by Popper and others. The principle of induction has been essentially eliminated by Hume’s argument. Several ways of attempting to solve the problem of induction have been considered, and some philosophers have come to regard this problem as insurmountable. Popper’s radical solution is that science does not work by induction, but by refutation.

The problem of demarcation

While maintaining this critical approach, Hume defines himself as an empiricist. This duality is considered the paradox of empiricism. This “quartered” empiricism was the way of the time to raise a barrier against the pretensions of metaphysical speculation. This desire to clearly distinguish the scientific or empirical approach from the unscientific approach was found in a marked manner in the 1920s among the neopositivists of the Vienna Circle for whom only analytical statements and empirical statements made sense, that is to say verifiable by observation (in a finite number of steps). In 1936, to respond to the criticism already presented by Hume and taken up by Popper, Rudolf Carnap, then illustrious member of the Circle, considered a weakened version of the principle of induction which he called confirmation. Confirmation does not seek to establish the truth of scientific laws, but only to order the laws by observation, some being more confirmed than others. In this, Carnap came very close to Popper, but without distancing himself too much from the Circle.

Unlike Carnap, Popper has distanced himself entirely from the Vienna Circle. The basic idea of ​​Popper’s solution to the demarcation problem is that instead of asking that the theory be able to be verified or confirmed, one requires that the theory be refutable by observation, but refutable in a precise technical sense.

The crucial experience

Before Popper formulated his criterion, already in 1910, Pierre Duhem had envisaged the role of the refutation and had raised a difficulty, the problem known as of the crucial experience: the refutation cannot be used to prove a theory because the scientific theories or hypotheses do not come in finite numbers. We would have to refute all the other theories, which is impossible. He even considered the fact that a theory (T) does not come in isolation, but with background knowledge (BK). Popper will explain that if the background knowledge BK is well corroborated and if this and the theory T together are refuted, then one can adopt the rule that it is the new theory which must be rejected and not the background knowledge, which is considered well established. It is a convention, a rule of the logic of scientific discovery, as opposed to a rule of traditional logic. Duhem’s thesis (which predated Popper’s logic of scientific discovery) says that even if the background knowledge is not refuted, it cannot be concluded that the new theory must be refuted. We can only conclude that there is a contradiction in the first system and not in the other: “BK Λ T => false” does not mean that T is false, because we do not know if BK is true. The logic of Popper’s scientific discovery does not contradict Duhem’s thesis because it is a methodological logic.

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