Page 8 - Boundedness Revisited

contradiction) and implication hold true whether elephants, rocks
or letters of the alphabet are the referents of logical propositions.
These relations, however, require some referents; analysis reveals
that the basic requirement for an analytic symbol is boundedness.
Logical relations do not work unless insides with fictional
boundaries are plugged in. At their most formalized, logical rules
are no more than elaborations of the principle of boundedness
13
and refinements of the method of boundary analysis.
Determination of equivalence (same inside) and implication
(relative containment of insides) require no specific information
about what is referred to; the referent insides, however, must be
validly bounded.
Once the duality of logical empiricism has been resolved by the
principle of boundedness, ontological and epistemological
problems disappear. The question, “what is a thing?” is
meaningless because “things,’ whether considered in terms of their
experienced content (synthetically) or simply as unspecified insides
(analytically), are the result of fictional boundaries. Any inside, if
properly bounded, is a “thing.” The question, “how is a thing
known?” is meaningless because the boundary between subject
and object, or knower and known, is fictional. “Knowing,” as a
distinction between an inside and its outside, is no less arbitrary
than any other distinction. Any inside, if properly bounded, can be
“known.” The statement “I know X” reduces to “X is a valid
inside,” regardless of the specific qualities ascribed to X.
Empiricism and logic both depend upon the principle of
boundedness: the unification and simplification of analytic
philosophy achieved by this reduction permits the elimination of
ontological and epistemological duality and uncertainty. Further
application of the principle of boundedness to the problems of
logic and empiricism is made in the following two sections.

B. Boundedness and metamathematics

13 This is a broad claim, and I do not now believe I knew enough to make it so
unequivocally. I would be glad to learn of a logical truth not reducing to a
tautology involving valid insides and outsides.
7