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===Abduction===

The ''locus classicus'' for the study of abductive reasoning is found in [[Aristotle]]'s ''Prior Analytics'', Book 2, Chapt. 25.  It begins this way:

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<p>We have Reduction (&#945;&#960;&#945;&#947;&#969;&#947;&#951;, abduction):</p>

<ol>

<li><p>When it is obvious that the first term applies to the middle, but that the middle applies to the last term is not obvious, yet is nevertheless more probable or not less probable than the conclusion;</p></li>

<li><p>Or if there are not many intermediate terms between the last and the middle;</p></li>

</ol>

<p>For in all such cases the effect is to bring us nearer to knowledge.</p>
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By way of explanation, Aristotle supplies two very instructive examples, one for each of the two varieties of abductive inference steps that he has just described in the abstract:

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<ol>

<li><p>For example, let ''A'' stand for "that which can be taught", ''B'' for "knowledge", and ''C'' for "morality".  Then that knowledge can be taught is evident;  but whether virtue is knowledge is not clear.  Then if ''BC'' is not less probable or is more probable than ''AC'', we have reduction;  for we are nearer to knowledge for having introduced an additional term, whereas before we had no knowledge that ''AC'' is true.</p></li>

<li><p>Or again we have reduction if there are not many intermediate terms between ''B'' and ''C'';  for in this case too we are brought nearer to knowledge.  For example, suppose that ''D'' is "to square", ''E'' "rectilinear figure", and ''F'' "circle".  Assuming that between ''E'' and ''F'' there is only one intermediate term &mdash; that the  circle becomes equal to a rectilinear figure by means of [[lunule]]s &mdash; we should approximate to knowledge.</p></li>

</ol>

<p>(Aristotle, ''Prior Analytics'' 2.25, with minor alterations)</p>
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Aristotle's latter variety of abductive reasoning, though it will take some explaining in the sequel, is well worth our contemplation, since it hints already at streams of inquiry that course well beyond the syllogistic source from which they spring, and into regions that Peirce will explore more broadly and deeply.