[Inquiry] Re: Verities Of Likely Stories

Jon Awbrey jawbrey at att.net
Mon Aug 11 21:40:03 CDT 2003


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VOLS.  Note 5

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| We have Reduction [abduction, Greek 'apagoge'] (1) 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 nevertheless is more probable or
| not less probable than the conclusion;  or (2) if there are not many
| intermediate terms between the last and the middle;  for in all such
| cases the effect is to bring us nearer to knowledge.
|
| (1) E.g., 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.
|
| (2) 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.
|     E.g., 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 lunules -- we should
|     approximate to knowledge.  When, however, BC is not more probable than AC, or
|     there are several intermediate terms, I do not use the expression "reduction";
|     nor when the proposition BC is immediate;  for such a statement implies knowledge.
|
| Aristotle, "Prior Analytics", 2.25.
|
| Aristotle, "Prior Analytics",
| Hugh Tredennick (trans.), in:
|'Aristotle, Volume 1', G.P. Goold (ed.),
| William Heinemann, London, UK, 1938, 1983.

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