Page 12 - Boundedness Revisited

D. Boundedness and metaphysics

Beyond empirical and logical questions there remain the
metaphysical. Since the former two issues have been subordinated
to the principle of boundedness, the latter reduces to an
examination of the unbounded. Any inside and its outside,
considered together, and no inside or outside, are the two cases or
alternatives of unboundedness. To be unbounded is not to be
within or without a boundary; thus anything reducible to an inside
or outside cannot be unbounded. However, since any inside is
continuous with its outside, their boundary can be extended
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indefinitely; together they are non-exclusive and unbounded,
regardless of the imputed qualities of the inside. The other case of
unboundedness is the absence of the first: no inside or outside.
This also satisfies the criterion of being neither within nor without
a boundary (it may, in fact, be considered as equivalent to a
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boundary); it is non-inclusive and unbounded, possessing no
ascribable quality of an inside (such as extension). Three
meaningful statements may be made about these cases. The first
two describe the unbounded per se; the third relates it to the
bounded.

1. Because one case is the absence of the other, only one
can be the case.

Since one case is fictional (no inside or outside), the mutual
preclusiveness of the cases of unboundedness reduces to the
necessity for either any inside and its outside to be the case, or no
nonfictionality at all. This aspect of unboundedness may also be
seen as denying the possibility of the two cases coexisting or
alternating; any hypothetical mixture of the two requires invalid
absolute nonfictional boundaries. Cosmologies which describe a
finite universe with no outside (coexistence) or a “something-
from-nothing” cosmic genesis (alternation) are committing such
errors. The case which is, is so without beginning or end.

17 Shown earlier as the necessary alternative to impossible dualism.
18 I.e., fictional, nothing.

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