754 |
SUPPLEMENT III |
||

problem of one-value. But for application we must have a four-dimensional,
non-el,, extensional system, based on structure . , and the complete elimination of identity. (28)U) That the disregard of multiordinality, orders of abstractions, may lead to identification and therefore false evaluation resulting in disagreement and maladjustment. (29)
V) From (25-29)it follows that identification or confusion of higher order abstractions must be eliminated. Because of (7, 9, 10, 25-29)
all identification must be eliminated. (30)W) The elimination of identification on all levels, or a complete and unconscious discrimination between different orders of abstractions, including as a special important case the multiordinality of terms, results in general consciousness of abstracting which in turn, solves the paradoxes of life and mathematics and leads to
generalized mathematics along the lines suggested by Chwistek. (31)X) The realization of the inherent multiordinality of some of the most important terms we have, gives us an enormous flexibility of language. It makes the number of our words indefinitely great. When both the writer and the reader recognize this multiordinality, and look for the meaning in the context and discriminate between the orders of abstractions, indicated by the context, confusion becomes impossible. (32)
Y) The test for multiordinality is simple. We take any statement and test it to see whether a given term applies to it. Then we make a statement about this statement and again test if this term applies to the new higher order statement. If it does, the given term must be considered multiordinal, because this procedure may be repeated indefinitely.
(33)Z)
The complete elimination of identification does not allow us to use the term 'is' of identity, and so we must use operational, functional, actional, behaviouristic . , languages, requiring new attitudes and new s.r, impossible without the formulation of a -system. (34)Zi) The
s.r of those who produced the general theory of relativity, the unified field theory, the new quantum mechanics, the new revision of the foundation of mathematics . , depend on new ., non-el, and non-identity, operational, actional. , attitudes. (35)Z2) As the -system is based on the general elimination of the 'is' of identity, or on 'is not', it is impossible to reject these premises without producing impossible data, and a theory of agreement 'in a finite period' then becomes a possibility. (36)
Z3) The old 'unknowable' becomes abolished and limited to the simple and natural fact that the objective levels
are not words. (37)Observation and experience, scientific and otherwise, show that in nature we find a definite order, which establishes a natural order; namely, that the sub-microscopic process, called the event or the scientific object, came first; only later abstracting organisms happened and objects which represent the results of abstracting by amoebas or men, came next. In the process of evolution |
|||