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 become ...
... 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 become ...
Page 16
... Things equal to the same thing are equal to each other . In symbols , a = 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 , a = 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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