Harold Walsby: Appendix to The Paradox Principle and Modular Systems Generally
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GEOMETRY |
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 |
Euclidean |
Non-Euclidian |
Aristotolean |
Non-Aristotolean |
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ELEMENTS |
lines and points |
classes and individuals |
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CRUCIAL ELEMENTS |
parallels |
opposites |
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GENERAL DESCRIPTION OF CRUCIAL ELEMENTS |
Eeuclidean parallels are special kinds of lines involving |
Aristotolian opposites are special kinds of classes |
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ESSENTIAL INTRINSIC PROPERTY OF CRUCIAL ELEMENTS |
they are rectilinear (one-dimensional) |
they are extensional (any-dimensional) |
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ESSENTIAL EXTRINSIC PROPERTY OF CRUCIAL ELEMENTS |
they are non-intersection |
they are non-intersecting |
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CRUCIAL POSTULATE |
Euclid’s Postulate of Parallels |
Aristotle’s Postulate of Opposites (i.e. Non-contradiction) |
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QUESTION SETTLED BY CRUCIAL POSTULATE |
the quantitative sum (number) of parallels to a given straight line (and through a fixed point) |
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 |
Euclid: 1 |
Lobachewsky: infinityRiemann: 0 |
Aristotle: 0 |
Walsby: 0, 1, infinity |
continue reading The Paradox Principle by Harold Walsby (1967):
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