Page 10 - Boundedness Revisited

nonfictional boundary: the axiom of choice. This attempted to
remove the “finite infinite” from the arena of logical combat by
giving it the status of an undisprovable axiom. On such a shaky
foundation are set theory and topology based, and schoolchildren
taught that infinity equals any number (a count of insides) divided
by zero (a point or other fiction). “Infinity” or “continuum”
simply cannot be bounded without setting up an invalid
nonfictional boundary; nor, for the same reason, is it valid to
speak of multiples or powers of “infinity.” Those portions of
mathematics which deny the principle of boundedness cannot be
consistent with the basic countable referent: a valid inside.

C. Boundedness and philosophy of science
The upper and lower limits of experience discovered in the
twentieth century have, in general, been misinterpreted by
theoretical scientists as absolute boundaries. Lacking a principle
higher than empirical verification, physicists and cosmologists
have sought to describe these limits as ultimate microcosm and
macrocosm. Boundary analysis exposes the errors in these
attempts and provides science with a means of self-criticism.

Microcosmic invalid boundaries formerly were couched in
terms of an “atom” or indivisible particle; since no further
distinctions could be made within such an entity, its edge would
have to be absolute. The results of modern physics have
eliminated such strong statements of ultimate microcosm. Instead,
the principle of indeterminacy in all experience has led to the
equally invalid notion of chance. While it is true that observation
of the means of observation (electromagnetic radiation) cannot be
distinctly accomplished, the conclusion cannot be drawn that
indeterminate events have no insides or antecedents. In this
respect, chance and free will are identical: they both deny the
continuity of an inside with its outside by requiring an absolute
nonfictional boundary. On the other hand, causality and natural
law, often seen as opposite to randomness, also violate the
principle of boundedness by requiring non-arbitrary, non-unique
insides distinguished by nonfictional boundaries. The principle of
boundedness indicates the impossibility of any common,

9