- The order of English, as an internal categorizational system, is mapped onto both the phonological order of English and the orthographical order. That is: The internal categorizational system is externalized into both its spoken and written counterparts.
- Analogously, the order of the physical world is mapped onto the auditory sensory order, the visual sensory order, and the tactile sensory order, along with the orders of the rest of the sensory modalities. In fact, epistemologically speaking we should, and do, actually go in the opposite direction: We compare the sensory orders of all of the different sensory modalities, looking for where there’s isomorphism.
- The thymological order, generalized into a (human-)universal description and explanation of the (human) mind; here we find another order, and we can theorize that order (i.e., the human-universal-generalized thymological order) to be in part isomorphic with the human-universal-generalized physical order of “the” brain and nervous system. That is, we can theorize that the mental patterns inherent to being human can be in part mapped onto certain physical patterns.
- George Boole in The Laws of Thought (1854) showed that the order of the symbolic system of arithmetic and algebra, including the order of its rote manipulation, is isomorphic not only to arithmetic and algebra but also to part of logic.
Isomorphism
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