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An Introduction To Non-aristotelian Systems And General Semantics.

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term by himself without any difficulty. The main point about all such m.o terms is that, in general, they are ambiguous, and that all arguments about them, 'in general', lead only to identification of orders of abstractions and semantic disturbances, and nowhere else. Multiordinal terms have only definite meanings on a given level and in a given context. Before we can argue about them, we must fix their orders, whereupon the issues become simple and lead to agreement. As to 'orders of abstraction', we have no possibility of ascertaining the 'absolute' order of an abstraction; besides, we never need it. In human semantic difficulties, in science, as well as in private life, usually no more than three, perhaps even two, neighbouring levels require consideration. When it comes to a serious discussion of some problem, errors, ambiguity, confusion, and disagreement follow from confusing or identifying the neighbouring levels. In practice, it becomes extremely simple to settle these three (or two) levels and to keep them separated, provided we are conscious of abstracting, but not otherwise.
For a theory of sanity, these issues seem important and structurally essential. In identifications, delusions, illusions, and hallucinations, we have found a confusion between the orders of abstractions or a false evaluation expressed as a reversal of the natural order.
One of the symptoms of this confusion manifests itself as 'false beliefs', which again imply comparison of statements about 'facts' and 'reality', and involve such terms as 'yes', 'no', 'true', 'false',. As all these terms are multiordinal, and, therefore, ambiguous, 'general' 'philosophical' rigmaroles should be avoided. With the consciousness of abstracting, and, therefore, with a feel for this peculiar stratification of 'human knowledge', all semantic problems involved can be settled simply.
The avoidance of m.o terms is impossible and undesirable. Systematic ambiguity of the most important terms follows systematic analogy. They appear as a direct result and condition of our powers of abstracting in different orders, and allow us to apply one chain of oo-valued reasoning to an endless array of different one-valued facts, all of which are different and become manageable only through our abstracting powers.
For further details about the theory of types, the reader is referred to the literature on the subject and Supplement II*; here I shall give only a few examples of the complexities and difficulties inherent in language, and show how simply they become solved by the aid of A general semantics and the resulting 'consciousness of abstracting'.
As an example, I quote Russell's analysis of the 'simple' statement 'I am lying', as given in the Principia. 'The oldest contradiction of the