The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 21
... that all reasoning by inequalities can be represented with equal or superior clearness and precision in the form of equalities , while the con- " trary is by no means always true . Thus THE TRUE PRINCIPLE OF REASONING . 21.
... that all reasoning by inequalities can be represented with equal or superior clearness and precision in the form of equalities , while the con- " trary is by no means always true . Thus THE TRUE PRINCIPLE OF REASONING . 21.
Page 22
... represented by the equality ( 1 ) a = b + p , in which is any positive quantity greater than zero ; and the inequality b > c is similarly represented by the equality ( 2 ) b = c + q , in which q is again a positive quantity greater than ...
... represented by the equality ( 1 ) a = b + p , in which is any positive quantity greater than zero ; and the inequality b > c is similarly represented by the equality ( 2 ) b = c + q , in which q is again a positive quantity greater than ...
Page 23
... represented in the equations . But I can only assert my belief of this from the examina- tion of the process in my own mind , and I must submit to the reader's judgment whether there are exceptions or not to the rule , that we always ...
... represented in the equations . But I can only assert my belief of this from the examina- tion of the process in my own mind , and I must submit to the reader's judgment whether there are exceptions or not to the rule , that we always ...
Page 24
... represented by the indefinite terms or names A and B. Thus A may be taken in one case to mean Iron , when B might ... represents a self - evident inference . Thus , If 24 THE SUBSTITUTION OF SIMILARS , SUBSTITUTION OF EQUALS OR SIMILARS ...
... represented by the indefinite terms or names A and B. Thus A may be taken in one case to mean Iron , when B might ... represents a self - evident inference . Thus , If 24 THE SUBSTITUTION OF SIMILARS , SUBSTITUTION OF EQUALS OR SIMILARS ...
Page 25
... represents a self - evident inference . Thus , If C be the father of B , C is father of A ; If C be a compound of B , C is a compound of A ; If C be the absence of B , C is the absence of A ; If C be identical with B , C is identical ...
... represents a self - evident inference . Thus , If C be the father of B , C is father of A ; If C be a compound of B , C is a compound of A ; If C be the absence of B , C is the absence of A ; If C be identical with B , C is identical ...
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Common terms and phrases
A B C D abacus ABCD adjective affirmative proposition Algebra analogy Aristotle Aristotle's dictum assert axiom axiom of Euclid Boole Boole's BROOKE FOSS WESTCOTT calculus Cambridge canon cloth conclusion copula Crown 8vo differs Edward Thring ELEMENTARY TREATISE English equal equal-sided equivalent Euclid example expression Extra fcap fallacy Fcap follows form of inference forms of reasoning formula George Bentham Grammar Greek hence identity illustrated indefinite indirect inequalities infallible Iron J. S. Mill John's College late Fellow law of duality laws of thought ledge logicians means ments metals are elements method monarch negative proposition obtain ordinary oxygen planet pound weight premises PRINCIPLE OF REASONING principle of substitution proposition or equation quantification quantity reader REESE LIBRARY relation represented Schools Second Edition second member self-evident self-luminous slips substitution of similars syllogism symbols thing Third Edition tion triangle truth undecomposable substance
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