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Saturday, 23 October 2021
A theory of types is needed to prevent unrestricted self-reference; the mapping of meta-theory into theory is possible only with restricted self-reference, actually only the appearance of self-reference when interpreted from a position that contains both the theory and the meta-theory but which otherwise is no, or need not be self-referential. Real self-reference is a circularity in the order of types which is just what we seem to experience as long as the loop include at least two distinct positions. Thus there is self-consciousness within the system but never in any one node of the system; the circuit must always go through an other. Also, where there can be one such loop there must be many loops, the loops are nested and the levels of nesting are again subject to circularity. Self-reference in such a system may be either a bad infinity or a good one, but if it is a good one it will lead you back to a non-circular hierarchy of types - the way out that you are always otherwise searching for.
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