A. KORZYBSKI's "map territory" metaphor is fundamental to the understanding of homomorphisms and isomorphisms in General Systems Research.
KORZYBSKI stated: "Two important characteristics of maps should be noticed. A map is not the territory it represents but, if correct, it has a similar structure to the territory, which accounts for its usefulness" (1933, p.58).
Thereafter, KORZYBSKI transfers this understanding to languages: "If we reflect upon our languages, we find that at best they must be considered only as maps. A word is not the object it represents; and languages exhibit also this peculiar self-reflexiveness, that we can analyse languages by linguistic means. This self-reflexiveness of languages introduces serious complexities, which can be solved only by the theory of multiordinality" (Ibid).
That the word is not the object is made perfectly clear by G. BATESON's example: "The word 'cat' cannot scratch us" (1973, p.153) and also from the following humorous A.N. WHITEHEAD"s comment, quoted by KORZYBSKI: "The appeal to a class to perform the services of a proper entity is exactly analogous to an appeal to an imaginary terrier to kill a real rat" (1933, p.247).
As to theory of multiordinality, it is quite close to RUSSELL's theory of logical types.
Confounding the "map" with the "territory" leads generally to dire consequences, as well as using an incorrectly structured "map", whether geographic, linguistic or conceptual. The subject has also been reworked by H.von FOERSTER through his Cybernetics of 2d order (1981).
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