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redo blockquotes
==Classical sources==
==Classical sources==
===Deduction===
===Deduction===
<blockquote>
When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism. By 'middle term' I mean that which both is contained in another and contains another in itself, and which is the middle by its position also; and by 'extremes' (a) that which is contained in another, and (b) that in which another is contained. For if ''A'' is predicated of all ''B'', and ''B'' of all ''C'', ''A'' must necessarily be predicated of all ''C''. … I call this kind of figure the First. (Aristotle, ''Prior Analytics'', 1.4).
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</blockquote>
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<p>When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism. By 'middle term' I mean that which both is contained in another and contains another in itself, and which is the middle by its position also; and by 'extremes' (a) that which is contained in another, and (b) that in which another is contained. For if ''A'' is predicated of all ''B'', and ''B'' of all ''C'', ''A'' must necessarily be predicated of all ''C''. … I call this kind of figure the First. (Aristotle, ''Prior Analytics'', 1.4).</p>
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===Induction===
===Induction===
<blockquote>
Induction, or inductive reasoning, consists in establishing a relation between one extreme term and the middle term by means of the other extreme; for example, if ''B'' is the middle term of ''A'' and ''C'', in proving by means of ''C'' that ''A'' applies to ''B''; for this is how we effect inductions. (Aristotle, ''Prior Analytics'', 2.23).
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</blockquote>
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<p>Induction, or inductive reasoning, consists in establishing a relation between one extreme term and the middle term by means of the other extreme; for example, if ''B'' is the middle term of ''A'' and ''C'', in proving by means of ''C'' that ''A'' applies to ''B''; for this is how we effect inductions. (Aristotle, ''Prior Analytics'', 2.23).</p>
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===Abduction===
===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:
The ''locus classicus'' for the study of [[abductive reasoning]] is found in [[Aristotle]]'s ''[[Prior Analytics]]'', Book 2, Chapt. 25. It begins this way:
<blockquote>
We have Reduction (απαγωγη, [[abductive reasoning|abduction]]):
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<p>We have Reduction (απαγωγη, [[abductive reasoning|abduction]]):</p>
For in all such cases the effect is to bring us nearer to knowledge.
</blockquote>
<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:
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:
<blockquote>
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([[Aristotle]], "[[Prior Analytics]]", 2.25, with minor alterations)
<ol>
</blockquote>
<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 — that the circle becomes equal to a rectilinear figure by means of [[lunule]]s — 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.
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.