Page 2 - Boundedness Revisited

I. The principle of boundedness
The principle of boundedness is that any inside is distinguished
1
from its outside by a fictional boundary. The criteria by which any
inside is nonfictional are irrelevant to the fictionality of its
boundary. Simply put, there cannot be anything between an inside
and its outside; the ascription of nonfictionality to a boundary (by
extension, for example) merely converts it to yet another inside
with its own boundary.

A. Aspects of boundedness

1. Any inside is continuous with its outside.
2
This aspect is first a restatement of the fictionality of
boundaries: an inside is not separated from its outside. A second,
more crucial meaning of continuity is that any inside has an
outside (and vice versa). An inside could “really end” only if it
were distinguished by a nonfictional boundary. Any supposed “last
point” of an inside, if given a nonfictional quality, loses its status
as a boundary-point by becoming either part of the original inside
or a separate inside by itself. Since their boundary is fictional, an
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inside cannot deny its outside.

1 This restates the “law of the excluded middle” in terms of referents for
proposed extensional objects rather than for pure abstractions. It does not
address any given attributes of an inside or outside other than extension. Like
Fichte, I am convinced that philosophy must be developed from “a single first
principle, but that it must then receive the self-evidence of geometry.”
2 A metaphysical implication of fictional boundaries is the necessity of monist
physical substance, owing to the impossibility of nonfictional boundaries (a
requirement of pluralism); that provides a basis for continuity or contiguity
without implications of discreteness. Physics has confirmed this in the equation
and conservation of that substance, mass-energy, and the universality of its
properties. See the section on metaphysics, below.
3 A critical qualification should be made here. Strict empiricism would deny the
necessity of every possible real-world inside having an outside (or outside
having an inside), as limits of perception at the microscopic and macroscopic
levels prevent such an a priori determination. Those empirical limits should not
be considered boundaries. This essay presents a case for accepting the
fictionality of all boundaries: the alternatives—real termini to insides; outsides
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