The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 46
... exists or docs not exist , or that everything either possesses a given attribute or does not possess it . Symbolically the law of duality is shown by A = AB Ab , in which the sign indicates alternation , and is equivalent to the true ...
... exists or docs not exist , or that everything either possesses a given attribute or does not possess it . Symbolically the law of duality is shown by A = AB Ab , in which the sign indicates alternation , and is equivalent to the true ...
Page 47
... exist , therefore , as a sun , and it conse- quently is not a sun . To represent this reasoning in symbols take A = sun . B = planet . C = self - luminous . Then the premises are ( 1 ) A = AC ( 2 ) B = Bc By the law of duality we have ...
... exist , therefore , as a sun , and it conse- quently is not a sun . To represent this reasoning in symbols take A = sun . B = planet . C = self - luminous . Then the premises are ( 1 ) A = AC ( 2 ) B = Bc By the law of duality we have ...
Page 53
... exist in the presence of B and the absence of both C and D. We ascertain also that D can only appear in the absence of both A and B , but that C may or may not be present with D. Where D is absent , C must also be absent , and so on ...
... exist in the presence of B and the absence of both C and D. We ascertain also that D can only appear in the absence of both A and B , but that C may or may not be present with D. Where D is absent , C must also be absent , and so on ...
Page 61
... exist , and more wide - ruling generalizations to be discoverable , than in the science of the laws of thought ; and I conceive that a prime object of any logical reform should be to reconcile the strict doc- trine with the looser forms ...
... exist , and more wide - ruling generalizations to be discoverable , than in the science of the laws of thought ; and I conceive that a prime object of any logical reform should be to reconcile the strict doc- trine with the looser forms ...
Page 29
... exists among all classes of intelligent readers for scientific literature which is not beyond the range of those who can read and think . In the " fresh fields and pastures new , " which scientific explorers are every year making ...
... exists among all classes of intelligent readers for scientific literature which is not beyond the range of those who can read and think . In the " fresh fields and pastures new , " which scientific explorers are every year making ...
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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
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