Infinite recourse

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The expression infinite regress (also infinite regress or infinite recursion ; regressus in / ad infinitum) describes an "endless [n] decline in an infinite series". It is used generally in philosophy, especially in logic and argumentation theory as well as in mathematics and computer science .

Infinite regress in the sense of logic (argumentation theory)

The infinite regress is a special case of the regress in the logical sense . As a rule, a linear and not a circular series (see circular proof ) is thought of. The series can in particular be a series of causes and effects, conditional and conditional, concepts and sentences.

An infinite regress is actually not possible.

If an argument leads to an infinite regress, it is considered refuted according to the scheme of reductio ad absurdum .

Aristotle used the argument of the infinite regress to demonstrate that "when restricting to exclusively deductive justification procedures, unprovable propositions must be assumed."

In philosophy , the infinite regress is the second of the Five Tropics of Agrippa and thus one of the three undesirable alternatives in the Munchausen Trilemma (every justification must be justified again, without this sequence ever coming to an end). Partial acceptance of an impossible infinite regress plays a role in the discussion of the concept of an infinite pro gresses .

According to Karl Popper , Fris pointed out that sentences can only be traced back to sentences if one always asks for a logical justification and does not want to introduce the sentences dogmatically. If one wants to avoid both dogmatism and infinite regress, the only remaining assumption is that sentences can also be traced back to perceptual experiences ( psychologism ). The perceptual experiences are recorded in an observation sentence.

Infinite Regress in Mathematics and Computer Science

In mathematics and computer science , “infinite regress” describes an endless self-appeal. An infinite regress, for example, arises from a function that refers to itself ( recursion ) without a valid termination condition ever ending the process.

For example, the Fibonacci sequence is recursive , but there is no infinite regress. This is defined as:

d. That is, the first two sequence members are defined as one, and the nth as the sum of the two previous sequence members. An example of an infinitely regressive sequence would be

.

If you want to calculate the nth term in the sequence, this process enters an endless loop according to the functional rule . The function constantly calls itself without - as with the Fibonacci sequence - tracing the result back to one of the initial conditions.

To detect and avoid infinitem recourse, particularly computer programs , one uses the semantic verification of recursive functions. The proof that there is no infinite regress is then mostly provided by means of a loop invariant (see also invariant ). However, this proof is not always possible after a certain procedure (see holding problem ).

Individual evidence

  1. Christian Thiel : regressus ad infinitum , in: Jürgen Mittelstraß (Ed.): Encyclopedia Philosophy and Philosophy of Science. 2nd Edition. Volume 7: Re - Te. Stuttgart, Metzler 2018, ISBN 978-3-476-02106-9 , p. 46
  2. Christian Thiel : regressus ad infinitum , in: Jürgen Mittelstraß (Ed.): Encyclopedia Philosophy and Philosophy of Science. 2nd Edition. Volume 7: Re - Te. Stuttgart, Metzler 2018, ISBN 978-3-476-02106-9 , p. 46
  3. Karl Popper: Basisprobleme , in: Logic of research , z. B. ISBN 978-3-05-005708-8