The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 16
... inequalities , on the other hand , as in a s b s 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 ,
... inequalities , on the other hand , as in a s b s 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 ,
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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A B C D abacus ABCDE affirmative proposition Algebra analogy applied Aristotle ARISTOTLE'S DICTUM ARITHMETIC assert axiom BEGINNERS Bentham Boole Boole's BROOKE FOSS WESTCOTT CALCULUS Cambridge canon Christ's College Church Clifton College cloth combinations conclusion CONIC SECTIONS consists copula Crown 8vo denote EDUCATIONAL BOOKS Edward Thring ELEMENTARY TREATISE English equal Euclid Examination Papers Examples expression Extra fcap fallacy Fellow of St follows forms of reasoning formula GEOMETRY George Bentham Grammar Head Master hence HISTORY identity illustrated indirect inequalities inference Iron J. S. Mill John's College late Fellow Latin law of duality Laws of Thought ledge logicians ment metals are elements method MIXED MATHEMATICS ordinary oxygen predicate premises problem quantification quantity reader represented Schools Second Edition self-evident SHILLING BOOK slips student substitution of similars syllogism symbols System of Logic thing Third Edition tion triangle true undecomposable substance
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