The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 17
... hence C C. Here the inference is seen to be obtained by sub- stituting a for b by virtue of their equality as ex- pressed in the first equation ab , the second equation b c being that in which substitution is C effected . One equation ...
... hence C C. Here the inference is seen to be obtained by sub- stituting a for b by virtue of their equality as ex- pressed in the first equation ab , the second equation b c being that in which substitution is C effected . One equation ...
Page 18
... 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 complete harmony with the affirmative form , except that , since it has only one equation to ...
... 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 complete harmony with the affirmative form , except that , since it has only one equation to ...
Page 19
... hence § C C. If in one case we take the sign as denoting that c is a multiple of b , it follows that it is a mul- tiple of a ; if it is the nth multiple of one , it is the nth multiple of the other ; if it is the nth submultiple , or ...
... hence § C C. If in one case we take the sign as denoting that c is a multiple of b , it follows that it is a mul- tiple of a ; if it is the nth multiple of one , it is the nth multiple of the other ; if it is the nth submultiple , or ...
Page 20
... hence a > c , a < b < c hence a < c , two valid modes of reasoning otherwise than by equations . But it is apparent , in the first 20 THE SUBSTITUTION OF SIMILARS ,
... hence a > c , a < b < c hence a < c , two valid modes of reasoning otherwise than by equations . But it is apparent , in the first 20 THE SUBSTITUTION OF SIMILARS ,
Page 24
... same relation A must stand to C. Or , using the sign to denote any possible or conceivable kind of relation , the formula A = B A § . hence § C C represents a self - evident inference . Thus , If 24 THE SUBSTITUTION OF SIMILARS ,
... same relation A must stand to C. Or , using the sign to denote any possible or conceivable kind of relation , the formula A = B A § . hence § C C represents a self - evident inference . Thus , If 24 THE SUBSTITUTION OF SIMILARS ,
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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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