The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 17
... third , the first is unequal to the third . And again : - If two things be both unequal to a third common thing , they may or may not be equal to each other . 16. Reflection upon the force of these axioms and their relations to each ...
... third , the first is unequal to the third . And again : - If two things be both unequal to a third common thing , they may or may not be equal to each other . 16. Reflection upon the force of these axioms and their relations to each ...
Page 19
... third quantity c is related to one of them , in the same way it must be related to the other . If we take the sign to denote any conceivable kind of relation between one quantity and another , then the widest possible expression of a ...
... third quantity c is related to one of them , in the same way it must be related to the other . If we take the sign to denote any conceivable kind of relation between one quantity and another , then the widest possible expression of a ...
Page 24
... third thing C , in the 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 ...
... third thing C , in the 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 ...
Page 32
... third figure we may take Making ( 1 ) Oxygen is an element , ( 2 ) Oxygen is a gas , ( 3 ) . Some gas , therefore , is an element . A : = gas , B = oxygen , C = element , the premises become ( 1 ) B = BC , ( 2 ) B = BA . Hence , by ...
... third figure we may take Making ( 1 ) Oxygen is an element , ( 2 ) Oxygen is a gas , ( 3 ) . Some gas , therefore , is an element . A : = gas , B = oxygen , C = element , the premises become ( 1 ) B = BC , ( 2 ) B = BA . Hence , by ...
Page 46
... third law , that of excluded middle , or , as I prefer to call it , the LAW OF DUALITY , asserts the self - evident truth that a thing either exists or docs not exist , or that everything either possesses a given attribute or does not ...
... third law , that of excluded middle , or , as I prefer to call it , the LAW OF DUALITY , asserts the self - evident truth that a thing either exists or docs not exist , or that everything either possesses a given attribute or does not ...
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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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