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'''Circular reasoning''' is a form of [[Logical fallacy#Proof by assertion|proof by assertion]] in which one uses a conclusion of an argument as the [[premise]] to that same argument. This is also known as ''petitio principii'' or ''begging the question.''
It is considered invalid and therefore is not permitted by the rules of [[formal logic]].
== An analysis ==
The simplest argument is a single inference, as per the Law of Detachment:
*If P, then Q.
*P.
*Therefore, Q.
The Law of the Syllogism uses Detachment to establish an ''intermediate'' conclusion between the original premise and the eventual conclusion. Thus:
*If P, then Q.
*If Q, then R.
*Therefore, if P, then R.
*P.
*Therefore, Q and R.
''Contraposition'' uses Detachment in reverse to show that a thing is ''not'' true:
*If P, then Q.
*Not Q.
*Therefore, not P.
All these proofs start with a proposition already verified or denied.
This is the classic structure of circular reasoning, that is an abuse of the Law of the Syllogism:
*If P, then Q.
*If Q, then R.
*If R, then P.
*P.
*Therefore, Q.
*Therefore, R.
*Therefore, P.
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.
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.
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.
== Reference ==
* [http://creationwiki.org/Circular_reasoning Circular reasoning] by [[CreationWiki]]
[[Category:Logical Fallacies]]