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: ''Adapted from an article in [[CreationWiki]], which is under GNU Free Documentation License''--[[User:TerryH|TerryH]] 23:51, 5 March 2007 (EST)
[[Circular reasoning]] is a form of [[logical fallacy]] in which one assumes the fact that one is trying to prove.
== An analysis ==
Usually, if one is trying to prove something, one must start with something else already accepted as valid. Thus the simplest argument would use the Law of Detachment and run this way:
*If P, then Q.
*P.
*Therefore, Q.
For a slightly more complex example, one uses the Law of the Syllogism to establish an ''intermediate'' fact between the already-accepted fact and the fact one wishes to prove. Thus:
*If P, then Q.
*If Q, then R.
*Therefore, if P, then R.
*P.
*Therefore, Q and R.
Finally, one can use ''contraposition'' to prove that a thing is ''not'' true:
*If P, then Q.
*Not Q.
*Therefore, not P.
Notice that all these proofs ''must'' start with a proposition already verified or denied.
Now examine this line of reasoning:
*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 might be part of a valid argument if one uses it alone. But when one uses them all together, and then tries to assert P, one finds that ''the assertion is a necessary step in the proof.'' The line of reasoning is thus not a line at all, but a ''circle.'' One might as well assert "P; therefore P" and expect that to stand--and thus commit the related fallacy of ''proof by assertion.''
For this reason, 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.) But an axiom, by definition, must be a fundamental property of nature ''upon which all reasonable people can agree.'' To attempt to ''prove'' an axiom by asserting a condition that depends upon it, is unavailing and unacceptable.
== An example ==
<table style="border:1px solid #AAAAAA; background: #EDF1F1; float:right; width:100px; margin-left:15px;">
<tr><td>{{fallacy|circular reasoning}}
<tr><td>Use the <nowiki>{{fallacy|circular reasoning}}</nowiki> template to insert the above warning on a page containing an example of ''[[circular reasoning]]''. The warning label will then link back to this page.
</table>
Circular reasoning would include using any [[science|scientific]] model that assumed a particular fact of nature in order to infer that fact later on. The classic example of this is the use of [[carbon-14 dating]] to infer a great age for the earth. According to this model, cosmic rays strike atoms of nitrogen (specifically, <sup>14</sup>N) and convert them to <sup>14</sup>C. This <sup>14</sup>C then combines with oxygen in the air to form radioactive carbon dioxide. Plants take this up and form radioactive [[glucose]], and animals that consume these plants consume the sugars and thus take in <sup>14</sup>C into their bodily systems. As long as the animals are alive, the <sup>14</sup>C in their systems is in dynamic equilibrium with the level of <sup>14</sup>C in the atmosphere. When they die, the <sup>14</sup>C begins to decay and is no longer subject to replacement. Thus, by knowing the level of <sup>14</sup>C in the atmosphere and comparing it to the level of <sup>14</sup>C in the animal's remains, one can determine how long ago the animal died.
The problem is that ''the model assumes that the level of <sup>14</sup>C in the atmosphere is itself in dynamic equilibrium.'' That in turn requires the earth to be very old. If the earth is ''young,'' then the level of <sup>14</sup>C would ''not'' have been at equilibrium in the earliest years of the earth (and still might not be), and thus all computed "ages" for organic fossils would be exaggerated, some greatly.
== See Also ==
* [[Logical fallacy]]
[[Category:Philosophy]]
[[Category:Logical fallacy]]
: ''Adapted from an article in [[CreationWiki]], which is under GNU Free Documentation License''--[[User:TerryH|TerryH]] 23:51, 5 March 2007 (EST)
[[Circular reasoning]] is a form of [[logical fallacy]] in which one assumes the fact that one is trying to prove.
== An analysis ==
Usually, if one is trying to prove something, one must start with something else already accepted as valid. Thus the simplest argument would use the Law of Detachment and run this way:
*If P, then Q.
*P.
*Therefore, Q.
For a slightly more complex example, one uses the Law of the Syllogism to establish an ''intermediate'' fact between the already-accepted fact and the fact one wishes to prove. Thus:
*If P, then Q.
*If Q, then R.
*Therefore, if P, then R.
*P.
*Therefore, Q and R.
Finally, one can use ''contraposition'' to prove that a thing is ''not'' true:
*If P, then Q.
*Not Q.
*Therefore, not P.
Notice that all these proofs ''must'' start with a proposition already verified or denied.
Now examine this line of reasoning:
*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 might be part of a valid argument if one uses it alone. But when one uses them all together, and then tries to assert P, one finds that ''the assertion is a necessary step in the proof.'' The line of reasoning is thus not a line at all, but a ''circle.'' One might as well assert "P; therefore P" and expect that to stand--and thus commit the related fallacy of ''proof by assertion.''
For this reason, 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.) But an axiom, by definition, must be a fundamental property of nature ''upon which all reasonable people can agree.'' To attempt to ''prove'' an axiom by asserting a condition that depends upon it, is unavailing and unacceptable.
== An example ==
<table style="border:1px solid #AAAAAA; background: #EDF1F1; float:right; width:100px; margin-left:15px;">
<tr><td>{{fallacy|circular reasoning}}
<tr><td>Use the <nowiki>{{fallacy|circular reasoning}}</nowiki> template to insert the above warning on a page containing an example of ''[[circular reasoning]]''. The warning label will then link back to this page.
</table>
Circular reasoning would include using any [[science|scientific]] model that assumed a particular fact of nature in order to infer that fact later on. The classic example of this is the use of [[carbon-14 dating]] to infer a great age for the earth. According to this model, cosmic rays strike atoms of nitrogen (specifically, <sup>14</sup>N) and convert them to <sup>14</sup>C. This <sup>14</sup>C then combines with oxygen in the air to form radioactive carbon dioxide. Plants take this up and form radioactive [[glucose]], and animals that consume these plants consume the sugars and thus take in <sup>14</sup>C into their bodily systems. As long as the animals are alive, the <sup>14</sup>C in their systems is in dynamic equilibrium with the level of <sup>14</sup>C in the atmosphere. When they die, the <sup>14</sup>C begins to decay and is no longer subject to replacement. Thus, by knowing the level of <sup>14</sup>C in the atmosphere and comparing it to the level of <sup>14</sup>C in the animal's remains, one can determine how long ago the animal died.
The problem is that ''the model assumes that the level of <sup>14</sup>C in the atmosphere is itself in dynamic equilibrium.'' That in turn requires the earth to be very old. If the earth is ''young,'' then the level of <sup>14</sup>C would ''not'' have been at equilibrium in the earliest years of the earth (and still might not be), and thus all computed "ages" for organic fossils would be exaggerated, some greatly.
== See Also ==
* [[Logical fallacy]]
[[Category:Philosophy]]
[[Category:Logical fallacy]]