The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 15
... illustrated in the first place by looking at it in its mathematical aspect . 15. The axiom indeed with which Euclid begins to build presents at first sight little or no resem- blance to the modified dictum . The axiom asserts that UNIVARS.
... illustrated in the first place by looking at it in its mathematical aspect . 15. The axiom indeed with which Euclid begins to build presents at first sight little or no resem- blance to the modified dictum . The axiom asserts that UNIVARS.
Page 33
... illustrated : - ( 1 ) Some metals are inflammable , ( 2 ) All metals are elements , ( 3 ) Some elements are inflammable . -- Taking A = elements , C = inflammable , B = metals , D = some , we may represent the premises in the forms ( 1 ) ...
... illustrated : - ( 1 ) Some metals are inflammable , ( 2 ) All metals are elements , ( 3 ) Some elements are inflammable . -- Taking A = elements , C = inflammable , B = metals , D = some , we may represent the premises in the forms ( 1 ) ...
Page 42
... illustrated by such examples as happy contented , = hence unhappy = not - contented ; or again , triangle = three - sided rectilinear figure , hence what is not a triangle = what is not a three- sided rectilinear figure . The new ...
... illustrated by such examples as happy contented , = hence unhappy = not - contented ; or again , triangle = three - sided rectilinear figure , hence what is not a triangle = what is not a three- sided rectilinear figure . The new ...
Page 47
... illustrated : - ( 1 ) A sun is self - luminous , ( 2 ) A planet is not self - luminous , ( 3 ) A planet , therefore , is not a sun . Now it is apparent that a planet is either a sun or it is not a sun , by the law of duality . But if it ...
... illustrated : - ( 1 ) A sun is self - luminous , ( 2 ) A planet is not self - luminous , ( 3 ) A planet , therefore , is not a sun . Now it is apparent that a planet is either a sun or it is not a sun , by the law of duality . But if it ...
Page 48
... illustrated by the following example : — M ( 1 ) All monarchs are human beings , ( 2 ) No human beings are infallible , ( 3 ) No infallible beings , therefore , are monarchs . This is proved by considering that every infal- lible being ...
... illustrated by the following example : — M ( 1 ) All monarchs are human beings , ( 2 ) No human beings are infallible , ( 3 ) No infallible beings , therefore , are monarchs . This is proved by considering that every infal- lible being ...
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Common terms and phrases
A B C D abacus ABCD adjective affirmative proposition Algebra analogy Aristotle Aristotle's dictum assert axiom axiom of Euclid Boole Boole's BROOKE FOSS WESTCOTT calculus Cambridge canon cloth conclusion copula Crown 8vo differs Edward Thring ELEMENTARY TREATISE English equal equal-sided equivalent Euclid example expression Extra fcap fallacy Fcap follows form of inference forms of reasoning formula George Bentham Grammar Greek hence identity illustrated indefinite indirect inequalities infallible Iron J. S. Mill John's College late Fellow law of duality laws of thought ledge logicians means ments metals are elements method monarch negative proposition obtain ordinary oxygen planet pound weight premises PRINCIPLE OF REASONING principle of substitution proposition or equation quantification quantity reader REESE LIBRARY relation represented Schools Second Edition second member self-evident self-luminous slips substitution of similars syllogism symbols thing Third Edition tion triangle truth undecomposable substance
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