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| − | [[Circular reasoning]] is a form of [[Logical fallacy#Proof by assertion|proof by assertion]] in which one assumes the fact that one is trying to prove, and then "proves" the fact by a chain of inferences that lead back to the original assertion. This is also known as ''petitio principii'' or ''begging the question.''
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| − | == An analysis ==
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| − | The simplest argument is a single inference, as per the Law of Detachment:
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| − | *If P, then Q.
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| − | *P.
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| − | *Therefore, Q.
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| − | The Law of the Syllogism uses Detachment to establish an ''intermediate'' conclusion between the original premise and the eventual conclusion. Thus:
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| − | *If P, then Q.
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| − | *If Q, then R.
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| − | *Therefore, if P, then R.
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| − | *P.
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| − | *Therefore, Q and R.
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| − | ''Contraposition'' uses Detachment in reverse to show that a thing is ''not'' true:
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| − | *If P, then Q.
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| − | *Not Q.
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| − | *Therefore, not P.
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| − | All these proofs start with a proposition already verified or denied.
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| − | This is the classic structure of circular reasoning, that is an abuse of the Law of the Syllogism:
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| − | *If P, then Q.
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| − | *If Q, then R.
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| − | *If R, then P.
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| − | *P.
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| − | *Therefore, Q.
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| − | *Therefore, R.
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| − | *Therefore, P.
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| − | Each of these three conditional statements would be valid by itself. Together, they create a flawed argument, because P now depends on itself to be true. The line of reasoning ends where it began, and is thus a circle. The only difference between this and ''proof by assertion'' is that the latter attempts to use a single conditional statement--"if P, then P"--while circular reasoning uses at least two, and typically three or more, syllogisms.
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| − | Circular arguments can be very difficult to detect. Circular arguments found in the professional literature, or in [[propaganda]], typically use five or six (or more) syllogisms.
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| − | Every logical system ''must'' begin with a set of generally accepted assumptions called ''postulates'' or ''axioms'' (from the [[Greek]] '''αξιος''' or ''axios'' worthy or deserving). Similarly, any set of definitions must start with a set of fundamental terms that need no definition. An axiom is usually a fundamental property of nature upon which all agree. Persons attempting to show that something is a fundamental property of nature when it is not, or a value of that property that is contrary to fact, typically use circular reasoning to make such an attempt.
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| − | == Reference ==
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| − | <table style="border:1px solid #AAAAAA; background: #EDF1F1; float:right; width:100px; margin-left:15px;">
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| − | <tr><td>{{fallacy|circular reasoning}}
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| − | <tr><td>Use the <nowiki>{{fallacy|circular reasoning}}</nowiki> template to insert this warning on a page containing an example of ''[[circular reasoning]]''. The warning label will then link back to this page.
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| − | </table>
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| − | * [http://creationwiki.org/Circular_reasoning Circular reasoning] by [[CreationWiki]]
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| − | [[Category:Logical fallacy]]
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