Page 3 - Boundedness Revisited

2. Any inside is arbitrary.

Because boundaries are fictional, the size and location of
specific insides cannot be verified or determined. By convention,
the dimensions and positions of “things” are considered objective,
persistent, and repeatable. However, any non-arbitrary attributes
of insides depend upon nonfictional boundaries to establish the
termination of those attributes. Where and when, how large and
4
for how long, an inside is distinguished is arbitrary.

3. Any inside is closed.
This means that a distinction must be completely and
unequivocally made in order to be a distinction. A boundary
cannot have “breaks” that allow an inside to be indistinguishable
from its outside; neither can a boundary leave part of an inside
outside itself. In geometrical terms, finite extension in any possible
dimension can be made within any inside. (Dimensions are
mutually perpendicular extensions, of which there are no less than
four.) If a supposed inside lacks extension in some dimension(s), it
is fictional; a three-dimensional figure, for example, is such a
fiction until extension in a fourth dimension is given to it. If a
supposed inside is defined as having infinite extension in any
dimension, it obviously cannot be closed; thus it cannot be
5
considered an inside.

B. Boundary analysis
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creating one-sided edges with nothingness; or the contiguity of incompatible
physical realms—are impossible. See the section on metaphysics, below.
4 The intellectual error of reification is equivalent to belief in nonfictional
boundaries: useful as ad hoc descriptions of purported events or objects, but
logically insupportable. What is conventional remains arbitrary.
5 This is another way of stating that abstract insides cannot be considered real
(in the sense of physically possible) without proper fictional boundaries, and
that real insides must be subject to the same principle of boundedness as the
abstract. A two-dimensional triangle has no real possibility; a four-dimensional
pyramid persisting for a millisecond, although abstract, is properly bounded.
6 As will be seen, boundedness as an analytical tool resolves many issues
traditionally within the province of philosophy; but that resolution is in fact
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