Changes

|}

|}

Here, "''X'' subsumes ''Y''" means that "''X'' applies to all ''Y''", or that "''X'' is predicated of all of ''Y''".  When there is no danger of confusion, we may write this as "''X'' >= ''Y''".

Here, “''X'' subsumes ''Y''” means that “''X'' applies to all ''Y''”, or that “''X'' is predicated of all ''Y''”.  When there is no danger of confusion we may write this as “''X'' ≥ ''Y''”.

{| cellpadding=2 width=90%

{| cellpadding=2 width=90%

| width=36 |  

| width=36 |  

| We have Reduction ['apagoge', or 'abduction']:  (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.

| We have Reduction (απαγωγη) [abduction]:  (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.

| (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.

| (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.

|-

|-

|  

|  

| Aristotle, "Prior Analytics" 2.25, in ''Aristotle, Volume 1'', H.P. Cooke and H. Tredennick (trans.), Loeb Classical Library, William Heinemann, London, UK, 1938.

|

<p>Aristotle, &ldquo;Prior Analytics&rdquo; 2.25, in ''Aristotle, Volume 1'', H.P. Cooke and H. Tredennick (trans.), Loeb Classical Library, William Heinemann, London, UK, 1938.</p>

|}

|}