The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's DictumMacmillan, 1869 - 86 pages |
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Page 16
... hand , as in a b c do not enable us to make any inference concerning the relation of a and c ; for if these quantities are equal , they may both differ from b , and 16 THE SUBSTITUTION OF SIMILARS , THE MODIFIED DICTUM II.
... hand , as in a b c do not enable us to make any inference concerning the relation of a and c ; for if these quantities are equal , they may both differ from b , and 16 THE SUBSTITUTION OF SIMILARS , THE MODIFIED DICTUM II.
Page 17
... relations to each other will show , I think , that the deductive power always resides in an equality , and that difference as such is incapable of affording any inference . My meaning will be more plainly exhibited by placing the ...
... relations to each other will show , I think , that the deductive power always resides in an equality , and that difference as such is incapable of affording any inference . My meaning will be more plainly exhibited by placing the ...
Page 19
... relation in which a sub- stitution may be made are by no means restricted to relations of equality or difference . If a = b , then in whatever way a third quantity c is related to one of them , in the same way it must be related to the ...
... relation in which a sub- stitution may be made are by no means restricted to relations of equality or difference . If a = b , then in whatever way a third quantity c is related to one of them , in the same way it must be related to the ...
Page 20
... relation to the other ; or if , lastly , c be greater than b by n or less than c by n , it will also be greater or less than a by n . In this all - powerful form we actually seem to have brought together the whole of the processes by ...
... relation to the other ; or if , lastly , c be greater than b by n or less than c by n , it will also be greater or less than a by n . In this all - powerful form we actually seem to have brought together the whole of the processes by ...
Page 21
... relation between a and c ; and I think the reader will not find it easy to explain why these do not and the former do , without im- plying the use of an equation or identity . The truth is , that the formulæ , a > b > c , a < b < c ...
... relation between a and c ; and I think the reader will not find it easy to explain why these do not and the former do , without im- plying the use of an equation or identity . The truth is , that the formulæ , a > b > c , a < b < c ...
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