List, Jon: On May 15, 2014, at 11:22 PM, Jon Awbrey wrote: "The ''structure'' that is preserved by a structure-preserving map is just the structure that we all know and love as a triadic relation. Very typically, it will be the type of triadic relation that defines the type of binary operation that obeys the rules of a mathematical structure that is known as a group, that is, a structure that satisfies the axioms for closure, associativity, identities, and inverses."
I continue to struggle with the foundational notions that you are seeking to communicate with your rhetoric. Your write: > The ''structure'' that is preserved by a structure-preserving map is just the > structure that we all know and love as a triadic relation. This assertion is generally denied by current mathematical thinking. Your are once again, as typically is the case in your expositions, conflating the notion of a triadic relation with the notion of a function. These are well-separated concepts in category theory. The adicity of a function may be any number you choice. If you have an alternative argument to my assertion, please bring it forward. Secondly, your introduction of the notion of "love" in this context is an overt attempt to appeal to social / political perspectives of the readers of this list. How do you introduce the concept of "love" into mathematics? (BTW, the notion of "love" is intrinsic to chemical thinking in the direct form of "nucelio-philic" and "electro-philic" reactions.) You further write: " Very typically, it will be the type of triadic relation that defines the type of binary operation that obeys the rules of a mathematical structure that is known as a group, that is, a structure that satisfies the axioms for closure, associativity, identities, and inverses." What do you mean by "very typically"? Certainly, mathematics is not merely about "very typical" inferences, or is this assertion foundational to your beliefs that mathematics is restricted to very typical inferences? If so, how would you frame this point of view in terms of group theory or any other structural theory of mathematics? Clearly, you are struggling to make your philosophy of mathematics clear. Perhaps it would be helpful is you formulated a sharp paragraph or page on your underlying philosophy of mathematics so that I could attempt to decipher your encodings of mathematical symbols. Cheers Jerry
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