The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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... thing as a representative of another . The chief difficulty consists in showing that all the forms of the old logic , as well as the fundamental rules of mathematical reasoning , may be explained upon the same principle ; and it is to ...
... thing as a representative of another . The chief difficulty consists in showing that all the forms of the old logic , as well as the fundamental rules of mathematical reasoning , may be explained upon the same principle ; and it is to ...
Page 5
... things counter to general opinion : but it is a paradox which , like that of Copernicus , excited admiration from its first appearance . That the symbolic processes of algebra , invented as tools of numerical calculation , should be ...
... things counter to general opinion : but it is a paradox which , like that of Copernicus , excited admiration from its first appearance . That the symbolic processes of algebra , invented as tools of numerical calculation , should be ...
Page 15
... thing is true of its like . ? I must beg of the reader not to prejudge the value of this very evident axiom . It is derived from Aristotle's dictum by omitting the distinction ) of the subject and predicate ; and it may seem to have ...
... thing is true of its like . ? I must beg of the reader not to prejudge the value of this very evident axiom . It is derived from Aristotle's dictum by omitting the distinction ) of the subject and predicate ; and it may seem to have ...
Page 16
... Things equal to the same thing are equal to each other . In symbols , α = b = c gives a = c . Here two equations are apparently necessary in order that an inference may be evolved ; and there is something peculiar about the threefold ...
... Things equal to the same thing are equal to each other . In symbols , α = b = c gives a = c . Here two equations are apparently necessary in order that an inference may be evolved ; and there is something peculiar about the threefold ...
Page 17
... things be equal to the second , but the second be unequal to the 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 ...
... things be equal to the second , but the second be unequal to the 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 ...
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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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