Skarzenski

From A NON-ARISTOTELIAN SYSTEM
AND ITS NECESSITY FOR RIGOUR IN MATHEMATICS AND PHYSICS,
      by Alfred Korzybski, 1931.

Analysis finds that certain of the most important terms we use ; such as, 'yes', no', 'true', 'false', 'all', 'fact', 'reality', 'existence', definition', 'relation', 'structure', 'order' number', 'is', 'has', 'there is', 'variable', 'infinite', 'abstraction', 'property', 'meaning', 'value', 'love', 'have', knowing', 'doubt'., ., may apply to all verbal levels and in each particular case may have a different content or meanings and so in general no single content or meaning. I call such terms multiordinal terms (m.o). The definition of such terms is always given in other m.o terms preserving their fundamental multiordinality. In other words, a m.o term represents a man-valued term. If the many values are identified, or disregarded, or confused, we treat a fundamentally many-valued term as one-valued, and we must have every kind of paradox through such an identification. All known paradoxes in mathematics and life can be manufactured by the disregard of this fundamental multiordinality. Vice versa, by formulating the general semantic problem of multiordinality we gain means to discriminate between the many meanings and so assign a single meaning in a given context. A m.o term represents a variable in general, and becomes constant or one-valued in a given context, its value being given by that context. Here we find the main importance of the semantic fact established by Skarzenski,** that the 'logical' freedom from contradiction becomes a semantic problem of one-value.   (Etc).

 

      **Quoted by Chwistek in his Neue Grundlagen der Logic und Mathematik.

Supplement III, Science and Sanity 1933,
pp. 753-754