List: > On Apr 29, 2017, at 10:41 PM, John F Sowa <s...@bestweb.net> wrote: > > Re mathematical category theory: Many mathematicians believe that > the term 'category theory' was a poor choice. The focus of category > theory is on the mappings or morphisms. The things that are mapped > could be mathematical structures of any kind. Some mathematicians > call it a "theory of arrows" -- the symbols that represent the maps.
John’s assertions here are spot on. If anything, these assertions are rather weak relative to what could be said. And, I will add a simple example to John’s semantic framework. Pure mathematics is an artificial idealization of symbols constructed by human minds. Such mathematical symbols must be free of any encumbering significations of nature because the scientific (real) significations of nature are antecedent to natural consequences of nature. And, I will add a simple caveat to John’s assertion that: > The things that are mapped > could be mathematical structures of any kind. The mappings may represent a vast range of mathematical structures and be constrained to oriented graphs. Cheers jerry
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