Infinite regress

The expression of infinite regress (even infinite regress or infinite recursion; regress / ad infinitum ) is commonly used in philosophy, especially in logic and argumentation theory, as well as mathematics and computer science.

Infiniter recourse in the sense of logic ( argumentation theory )

The infinite regress is a special case of recourse in the logical sense and refers to the return falls to infinity in an infinite series. An argument that amounts to an infinite regress, is considered not particularly convincing. For example, Aristotle tried opposing positions thereby refute that he proved them an infinite regress.

An infinite regress exists " if the condition (cause) is itself contingent ( effect ), and this continues indefinitely ."

In the philosophy of the infinite regress of the second of the five tropes of Agrippa, and thus one of the three undesirable alternatives in the Münchhausen trilemma is ( any justification must in turn be justified without this episode ever comes to an end ). Partial acceptance of an impossible infinite regress plays a role in the discussion of the concept of an infinite progress.

Infiniter recourse in mathematics and computer science

In mathematics and computer science called " of infinite regress " an endless self- call. One of infinite regress arises, for example, by a function that refers to itself ( recursion) without a valid termination condition the process never ends.

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

That is, it can be defined as the first two terms of the sequence, the One, and as the n-th sum of the two previous terms of the sequence. Would be an example of an infinitely regressive sequence

If you want to calculate the n-th follower here, as occurs after function provision of this process in an infinite loop. The function constantly calls itself, without - return the result to the initial conditions - as in the Fibonacci sequence.

To detect and avoid infinitem recourse, especially of computer programs, one uses the semantic verification of recursive functions. Proving that not of infinite regress exists, is then usually performed by means of a loop invariant (see also invariant ). This evidence is, however, not always possible to find a method (see halting problem ).