The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 14
... similar proposition , Iron the cheapest of the metals , we are easily enabled to infer that the cheapest of the metals the most useful of the metals , since by the dictum we know of iron that it is the cheapest of the metals ; and this ...
... similar proposition , Iron the cheapest of the metals , we are easily enabled to infer that the cheapest of the metals the most useful of the metals , since by the dictum we know of iron that it is the cheapest of the metals ; and this ...
Page 18
... similar act of reasoning in which b c is the active equation , as shown below : - = b = c hence ။ a a . My warrant for this view of the matter is to be found in the fact that the negative form of the axiom is now easily brought into ...
... similar act of reasoning in which b c is the active equation , as shown below : - = b = c hence ။ a a . My warrant for this view of the matter is to be found in the fact that the negative form of the axiom is now easily brought into ...
Page 23
... similar when compared with another . We have but to interpret the word equal in the older and wider sense of like or equivalent , in order to effect the long - desired union of logical and mathematical reasoning . For it is not ...
... similar when compared with another . We have but to interpret the word equal in the older and wider sense of like or equivalent , in order to effect the long - desired union of logical and mathematical reasoning . For it is not ...
Page 36
... evident that P of O = P of O , and substituting in the second member the descrip- tion of O we have P of OP of OQ . 1 Thomson's " Outline , " § 88 . 34. In an exactly similar manner we may solve a 36 THE SUBSTITUTION OF SIMILARS ,
... evident that P of O = P of O , and substituting in the second member the descrip- tion of O we have P of OP of OQ . 1 Thomson's " Outline , " § 88 . 34. In an exactly similar manner we may solve a 36 THE SUBSTITUTION OF SIMILARS ,
Page 37
... similar manner we may solve a common form of reasoning which the authors of the " Port Royal Logic " described as the Complex Syllogism , remarking how little attention logicians had in their day given to many common forms of reasoning ...
... similar manner we may solve a common form of reasoning which the authors of the " Port Royal Logic " described as the Complex Syllogism , remarking how little attention logicians had in their day given to many common forms of reasoning ...
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Common terms and phrases
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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