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 THE ...
... 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 THE ...
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 , hence what is not a triangle triangle = three - sided rectilinear figure , = what is not a three- sided rectilinear figure . The new ...
... illustrated by such examples as = happy contented , hence unhappy = not - contented ; or again , hence what is not a triangle triangle = three - sided rectilinear figure , = 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 ...
... 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 ...
Page 48
... illustrated by the following example : — ( 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 is ...
... illustrated by the following example : — ( 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 is ...
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Common terms and phrases
A B C D abacus ABCD adjective affirmative proposition analogy appear apply Aristotle Aristotle's dictum assert axiom axiom of Euclid Boole Boole's calculus Cambridge canon cloth conclusion consists copula corresponding Crown 8vo differs Diseases ELEMENTARY TREATISE equal equal-sided equivalent expression fallacy fcap follows form of inference forms of reasoning formula George Bentham hence identity indefinite indirect inequalities infallible Iron J. S. Mill law of duality laws of thought Lectures ledge logicians mathematical reasoning means ment metals are elements method mind monarch nature negative proposition obtained Owens College oxygen Philosophy pound weight premises principle of substitution Professor proposition or equation quantification quantity relation represented Royal scientific Second Edition second member self-evident self-luminous Sir William Hamilton slips subject and predicate substitution of similars syllogism symbols term element THEORY Thomson tion triangle true truth undecomposable substance University University of Cambridge
Popular passages
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