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Problem of induction

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The problem of induction (also: Humean problem or Hume problem) is a basic problem of epistemology. It relates to the question of whether and when a conclusion by inducing individual cases to a generally applicable law is permissible. It was first mentioned by David Hume around 1740 .

Although the problem of induction was formulated in empiricism, it is a problem of all philosophies or sciences that admit induction inferences as a method of proof. It is a modern variant of nominalism that denies the reasonable orders of rationalism, but also the measurement- based generalizations of the natural sciences, an observer-independent reality.

David Hume

Hume developed the problem of induction in his debut work A Treatise of Human Nature and in its revision An Inquiry Concerning Human Understanding .

Hume first encountered this problem in his treatment of causality: if, based on observed cause-consequence relationships, constant cause-effect relationships are assumed and these assumptions are called knowledge, then in his view this is based on ‘principles’ of human nature, which our thinking follows, and not on a state of affairs in the world. Our judgment follows the association of impressions as our minds perceive and process them, not the facts in the world. We consider events to be causes and effects when we see them repeatedly following one another, since we then automatically believe that this consequence can also be expected in the future.

“It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future, since all these arguments are founded on the supposition of that resemblance.”

One process follows the other; however, they are only conjoined but not connected. The naturally necessary assumption that a certain event brings about a certain subsequent event is, according to Hume, a statement about relationships that merely correspond to the ‘principles’ of human nature.

Human knowledge is gained either intuitively (that a bachelor is unmarried, follows from the usage), or deductive (through inferences such as ‘All men are mortal.’ Socrates is a human. So Socrates is mortal) or empirical (through the perception of repetitions , e.g. that the sun rises every morning).

Buck Creek Crossing
Sursa https://en.wikipedia.org/wiki/File:Buck_Creek_IN_-_sunrise.jpg 

(Usually inferred from repeated observations: “The sun always rises in the east.” )

Induction is understood as a principle method of justification which claims general validity in its justification. A necessary prerequisite for this method is the assumption that something will behave in the future as it did in the past. In order for the induction principle to rightly claim general validity, it must be impossible that this requirement does not apply ( theorem of excluded contradiction). However, the opposite assumption of this premise that the future is not the same as the past does not contain any contradiction. So it also applies and is quite conceivable. But if both assumptions are equally possible, the premise that events are foreseeable may be impossible to be necessary or general. Therefore the claim of the induction method to a generally valid justification is necessarily wrong.

The type of knowledge of “moral reasoning” relates to facts and experience. Any such knowledge is based on the principle of cause and effect. But the connection between cause and effect assumes that this will also apply in the future. What is to be proven is presupposed, whereby this kind of knowledge is ruled out.

Thus, Hume has shown that there is no inference rule in his model of human knowledge that justifies induction. Humans do not come from logical operations of thought, but from habit of inferring the future from previous experiences.

Immanuel Kant

Immanuel Kant attributed the credit to Hume for having awakened him from dogmatic slumber with his skeptical arguments. The main epistemological work of Kant, the Critique of Pure Reason , deals with the question of how one can arrive at reliable knowledge despite the problems raised by Hume. That such knowledge is possible and actually present in some sciences – such as physics or mathematics – was beyond question for Kant. Kant’s approach tries to explain this through a theory that unites elements of the conflicting epistemological directions of his time – namely, rationalism in the tradition of Leibnizand Christian Wolff and empiricism in that of John Locke and Isaac Newton.

Kant distinguishes on the one hand between analytical and synthetic judgments and on the other hand between judgments a priori and judgments a posteriori. Analytical judgments are so-called “explanatory judgments”. In Kant’s example, “All bodies are expanded”, only something is said about bodies that is already contained in the mathematical term body. For Kant, there is no gain in knowledge associated with analytical judgments. Synthetic judgments, on the other hand, are “expansion judgments”, they link something with the term that was not already contained in it, for example in “All bodies are heavy” – they represent, if true, a gain in knowledge.

A priori judgments are valid regardless of all experience; Judgments whose validity comes from experience are a posteriori. You know that the bachelor is unmarried, even if you have never seen one, but knowing what water is safe to drink requires empiricism, since drinkability is a relationship between biological organisms and fluids that can only be determined by looking at both fluid and organism.

Four possible combinations result from the two distinctions:

  1. analytical judgments a priori, e.g. all bodies are extended,
  2. analytic judgments a posteriori, are omitted because analytical judgments apply before experience (although they can be discovered on the basis of experience),
  3. synthetic judgments a posteriori, e.g. water is drinkable,
  4. synthetic a priori judgments, in which Kant asks himself how they are possible.

The question of whether and how valid extension judgments are possible independent of experience is the task of Kant’s work Critique of Pure Reason.

Kant affirms the possibility of synthetic judgments a priori. They are possible because our experience only takes place in certain forms of perception (space and time) and under categories (a total of 12, including causality). These conditions of the possibility of experience are then attached to everything that can be experienced at all: it is not the objects that determine the knowledge, but the knowledge determines the objects. Therefore, experience-independent extension judgments are possible for the area of ​​possible experience, the validity of which is not based on induction but on a priori discursive knowledge. In a natural philosophy as he describes it in his work Metaphysical Foundations of Natural Science.

In empirical physics, however, general laws are also possible as reasonably formed hypotheses that can be tested experimentally. The formation of the general statements is not based on psychological association, but on rational speculation that can be operationalized with the help of the imagination in predictions for the experience. In Kant’s view, this method has been in use in physics since Galileo Galilei, which is how it became a science.

Classical position of critical rationalism

Karl Raimund Popper (1902–1994) agrees with Hume’s result in various writings (including the logic of research, objective knowledge ): there is no valid induction that necessarily requires special observational sentences of the type “This swan is white” to the general statement “ All swans are white “can pass over.

The truth of the sentence “All swans are white” cannot be proven by individual observational sentences of the type “This swan is white”. Because a single observed black swan is enough to refute such a universal proposition. It would have to be ruled out that there could be black swans at all. There is an asymmetry between existential clauses (“There is a white swan”), as used to describe observations, and the universal clauses (“All swans are white”), which Popper believes make up scientific theories – existence clauses, on the other hand, can be considered true be recognized by empirically verifying them. This does not apply to scientific theories that consist of general statements: they can only be falsified (Falsificationism ).

Popper therefore formulates the steps of the scientific method as follows: First, new hypotheses are set up as answers to problems. Then an attempt is made to falsify this through observations. If this does not succeed, there is no guarantee that it will not succeed in the future, but at least this makes the theory superior to already falsified theories.

New version and proposed solutions

Hume’s statement was generalized by Critical Rationalism ( Hans Albert ), according to which ultimate justifications are in principle not possible because of the Munchausen trilemma. Every proof is based on rationally unjustifiable assumptions, which, however, for certain special cases by Apel, Kuhlmann, Hösle et al. is disputed (reflexive final justification).

There are other proposed solutions to the induction problem:

  • Peter Frederick Strawson (1919-2006) says that the standards of inductive reasoning themselves are what is meant by “justification”.
  • Richard Bevan Braithwaite assumed in 1953 that the reliability of certain inductive conclusions could be justified inductively by using a rule of inference, the reliability of which should first be proven by the argument itself , without this being a circular reason.
  • Rafael Ferber sees the extra-logical “legal reason” for the reasonableness of induction inferences in a hypothetical requirement of practical reason: the induction principle is a natural and justified requirement of practical reason. A ban on induction would be tantamount to an invitation to commit suicide.”
  • Hans Reichenbach (1891-1953) argued that Hume was right that one cannot demonstrate the reliability of inductive reasoning in a circular manner, but that inductive reasoning is the best we can do to make predictions about future events and event frequencies. Reichenbach’s approach was expanded by Gerhard Schurz to justify the optimality of meta-induction (inductive reasoning applied to the success records of competing prediction methods) on a strictly mathematical basis.
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