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This is a work in progress - all rights reserved.
Copyright © 2006-2008 Tony Giovia
CHAPTER 13 - A New Definition of Physical Existence v2.0
13.1 - A mathematical point has no dimensions. (Definition)
a) A point has no width, length, or depth. (Definition)
13.2 - A mathematical line has one dimension. A line has the dimension of length, but no width or depth. (Definition)
13.3 - A mathematical plane has two dimensions. A plane has length and width, but no depth. (Definition)
13.4 – The definition of points, lines and planes are perceivable by a mind. (Construction)
13.5 - Objects perceivable by a mind are mental objects. (Definition)
13.6 – Definitions are contexts. (Construction)
13.7 – Contexts are objects. (Construction)
13.8 - Perceivable objects exist. (Definition)
13.9 - Objects that exist are composed of energy. (Construction)
13.10 - Energy exists in a relationship with matter. (Construction)
13.11 - Points, lines and planes are mental objects that exist in a relationship with matter. (Construction)
13.12 - Mental objects are Ideas. (Definition)
13.13 - Points, lines and planes are Ideas with a mathematical, logical and physical existence. (Definition)
Traditionally, physical objects are considered to have at least three dimensions – length, width and height. Here we are using common mathematical concepts to clarify our definition of physical existence. Points, lines and planes exist at least to the extent that they are used in calculations to describe the characteristics of matter. Because they exist, they are composed of energy. And because energy is a form of matter and vice versa, ideas are a form of matter and have a physical existence.
Mathematics and logic are equivalent disciplines – each uses exactly the same rules as the other in their applications. Both can use the same terminology, as in Symbolic Logic, or different terminologies, as in numeric formulas and syllogisms. Clearly defined, precise definitions are required by both to achieve reproducible results.
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