| The Paradox Principle and Modular Systems Generally
Part Ten: Appendix by Harold Walsby (January 1967) |
Introduction | Dedication | Aristotle's Principle | The Role of Logic | Do Self-contradictions Exist? | Three Types of Contradictions | Meaningful Self-contradictions | Infinity and Self-Contradictions | Models for Self-contradiction | The Paradox Principle and Applications | Appendix
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GEOMETRY
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LOGIC
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CLASSICAL
(dominant 2,000 years) |
REVOLUTIONARY
(challenging the classical) |
CLASSICAL
(dominant 2,000 years) |
REVOLUTIONARY
(challenging the classical) |
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SYSTEM
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Euclidean
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Non-Euclidian
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Aristotolean
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Non-Aristotolean
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ELEMENTS
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lines and points
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classes and individuals
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CRUCIAL ELEMENTS
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parallels
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opposites
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GENERAL DESCRIPTION OF CRUCIAL ELEMENTS
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Eeuclidean parallels are special kinds of lines involving
at least two lines and an intervening boundary-space
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Aristotolian opposites are special kinds of classes
involving at least two classes and an intervening boundary line (barrier)
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ESSENTIAL INTRINSIC PROPERTY OF CRUCIAL ELEMENTS
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they are rectilinear (one-dimensional)
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they are extensional (any-dimensional)
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ESSENTIAL EXTRINSIC PROPERTY OF CRUCIAL ELEMENTS
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they are non-intersection
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they are non-intersecting
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CRUCIAL POSTULATE
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Euclid's Postulate of Parallels
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Aristotle's Postulate of Opposites (i.e. Non-contradiction)
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QUESTION SETTLED BY CRUCIAL POSTULATE
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the quantitative sum (number) of parallels to a given
straight line (and through a fixed point)
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the qualitative sum (intersection) of opposites of
a given extensional type (though a fixed internal barrier)
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ANSWER TO QUESTION GIVEN BY SYSTEM
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Euclid: 1
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Lobachewsky: infinity
Riemann: 0 |
Aristotle: 0
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Walsby: 0, 1, infinity
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Copyright © 1967 Harold Walsby