====== Circular reasoning ======

A form of logical fallacy in which the position that still has to be proven is already presupposed in a premise.

Take for example the following statement:

> <u questionable "Circular reasoning">The Bible is God’s Word, for it is written [in the Bible] that "all Scripture is inspired by God".</u>

===== Other names =====

  * Circular argument
  * <i :de>[[de>logik/fehlannahmen/praemissenfehler/zirkelschluss|Zirkelschluss]]</i>
  * <i :la "Lat.: circle in proving">Circulus/-um in probando</i> (Lat.: "circle in proving")
  * <i :la "Lat.: circle in the proof">Circulus/-um in demonstrando</i> (Lat.: "circle in the proof")
  * <i :la "Lat.: the same by the same">Idem per idem</i> (Lat.: "the same by the same")
  * <i :grc-Latn>hýsteron próteron</i> [<span :grc "hýsteron próteron">Ὕστερον πρότερον</span>] (grc.: "the later [is the] earlier")

Occasionally, the term "<i :la>[[relevancy:petitio_principii|petitio principii]]</i> " ("postulation of the beginning") is used as a synonym for //circular reasoning//. However, the specific meaning of this expression is inconsistent and has changed over time. It is used here as a [[rhetoric:index|rhetoric]] figure that is analogous to //circular reasoning//. 

<aside info filled rounded>
**Note:** also the terms <i :la "Lat.: vicious circle">circulus vitiosus</i> and its translation "vicious circle" are sometimes understood as synonyms for //circular reasoning//. However, as these terms mainly refer to //negative feedback systems//, they are not recommended for use in this context.
</aside>

===== Description =====

The //circular argument// is closely related to the concept of a logical [[glossary:tautology|tautology]], as for both can be said that when the premises are //true// it also holds //true//:

> <u questionable "Tautology">The sky is blue, because it is blue.</u>

This also includes circular forms of [[logic:inferences:sorites|Sorites]] arguments, in which the last step leads back to the starting point:

> <u questionable "Circular argument"><var>A₁</var> → <var>A₂</var> → <var>A₃</var> → … → <var>Aₙ</var> → <var>A₁</var></u>

However, //circular reasoning// covers also situation in which further assumptions may be made, which are not //necessarily true//. For an argument to be considered //circular//, it is enough if //one of the premises// already implies what is yet to be proven:

> <u questionable "From A and B follows A (circular argument)"><var>A</var> ∧ <var>B</var> -> <var>A</var></u> (from <var>A</var> and <var>B</var> follows <var>A</var>)

===== See also =====

  * <i :la>[[relevancy:petitio_principii|Petitio principii]]</i>
  * [[logic:inferences:sorites|Sorites]]
  * [[glossary:tautology|Tautology]]

===== More Information =====

  * [[wp>Circular reasoning]] on //Wikipedia//