The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 17
... hence C C. Here the inference is seen to be obtained by sub- stituting a for b by virtue of their equality as ex- pressed in the first equation ab , the second equation b c being that in which substitution is C effected . One equation ...
... hence C C. Here the inference is seen to be obtained by sub- stituting a for b by virtue of their equality as ex- pressed in the first equation ab , the second equation b c being that in which substitution is C effected . One equation ...
Page 18
... hence 11 a a . My warrant for this view of the matter is to be found in the fact that the negative form of the axiom is now easily brought into complete harmony with the affirmative form , except that , since it has only one equation to ...
... hence 11 a a . My warrant for this view of the matter is to be found in the fact that the negative form of the axiom is now easily brought into complete harmony with the affirmative form , except that , since it has only one equation to ...
Page 19
... hence § C C. If in one case we take the sign as denoting that c is a multiple of b , it follows that it is a mul- tiple of a ; if it is the nth multiple of one , it is the nth multiple of the other ; if it is the nth submultiple , or ...
... hence § C C. If in one case we take the sign as denoting that c is a multiple of b , it follows that it is a mul- tiple of a ; if it is the nth multiple of one , it is the nth multiple of the other ; if it is the nth submultiple , or ...
Page 20
... hence a > c , a < b < c hence a < c , two valid modes of reasoning otherwise than by equations . But it is apparent , in the first 20 THE SUBSTITUTION OF SIMILARS , INFERENCE BY INEQUALITIES.
... hence a > c , a < b < c hence a < c , two valid modes of reasoning otherwise than by equations . But it is apparent , in the first 20 THE SUBSTITUTION OF SIMILARS , INFERENCE BY INEQUALITIES.
Page 24
... or conceivable kind of relation , the formula A = B A § hence & C C represents a self - evident inference . Thus , If 24 THE SUBSTITUTION OF SIMILARS , SUBSTITUTION OF EQUALS OR SIMILARS GENERAL FORMULA OF LOGICAL INFERENCE.
... or conceivable kind of relation , the formula A = B A § hence & C C represents a self - evident inference . Thus , If 24 THE SUBSTITUTION OF SIMILARS , SUBSTITUTION OF EQUALS OR SIMILARS GENERAL FORMULA OF LOGICAL INFERENCE.
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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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