The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 11
... manner , the postulate according to which the proposition is to be em- ployed ? Ought we not now to say that whatever is known of either term of the proposition is known and may be asserted of the other ? Does not the dictum , in short ...
... manner , the postulate according to which the proposition is to be em- ployed ? Ought we not now to say that whatever is known of either term of the proposition is known and may be asserted of the other ? Does not the dictum , in short ...
Page 18
... manner as before by the substitution of a for b , and the negative equation or difference b c is the part in which substitution takes place , but which has itself no substitutive power . Accord- ingly we shall in vain throw two ...
... manner as before by the substitution of a for b , and the negative equation or difference b c is the part in which substitution takes place , but which has itself no substitutive power . Accord- ingly we shall in vain throw two ...
Page 22
... manner of the conclusion a > c . On the other hand , the formula a > b < e would evidently lead to the equation in which a = e + p - r , is the excess of a over b , and the excess of e over b . Now this equation , taken in connexion ...
... manner of the conclusion a > c . On the other hand , the formula a > b < e would evidently lead to the equation in which a = e + p - r , is the excess of a over b , and the excess of e over b . Now this equation , taken in connexion ...
Page 29
... manner become , in a strictly logical form : - ( 1 ) Iron = metallic iron , ( 2 ) Metal = elementary metal . Now for metal or metallic in ( 1 ) we may substitute its equivalent in ( 2 ) and we obtain ( 3 ) Iron = elementary , metal ...
... manner become , in a strictly logical form : - ( 1 ) Iron = metallic iron , ( 2 ) Metal = elementary metal . Now for metal or metallic in ( 1 ) we may substitute its equivalent in ( 2 ) and we obtain ( 3 ) Iron = elementary , metal ...
Page 36
... 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 ,
... 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 ,
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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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