[CG] Re: Higher Order Sign Relations

Cf: Higher Order Sign Relations • 6 http://inquiryintoinquiry.com/2022/08/14/higher-order-sign-relations-6/ Re: Cybernetics ( https://groups.google.com/g/cybcom/c/UwInmSnuv0c ) ::: Cliff Joslyn ( https://groups.google.com/g/cybcom/c/UwInmSnuv0c/m/w9ncBWKUAAAJ ) Cliff Joslyn recommended the following books. • Spivak, David I. (2014), Category Theory for the Sciences ( https://www.amazon.com/Category-Theory-Sciences-MIT-Press/dp/0262028131 ) • Fong, Brendan, and Spivak, David I. (2019), An Invitation to Applied Category Theory : Seven Sketches in Compositionality ( https://www.amazon.com/Invitation-Applied-Category-Theory-Compositionality/… ) Dear Cliff, All, The following Survey page gives a hint of the tack I've been taking with category theory since the early days but definitely moving into higher gear during my year at Illinois in the mid 1980s. John Gray taught a course joint between math and computer science on the Applications of Lambda Calculus and David Plaisted taught a course on Resolution-Unification Theorem Proving, both of which I took and followed up with independent studies. I spent a heady year making the circuit between math, computer science, and psychology departments and a lot of what I work on today goes back to issues raised in those days. • Survey of Precursors Of Category Theory ( https://inquiryintoinquiry.com/2020/09/20/survey-of-precursors-of-category-… ) I know that Survey from a couple years ago still looks a little sketchy but I'll be working to make it less so as time goes by, especially if I ever get around to unpacking my notes from the basement boxes. I have managed to sample contemporary approaches to categories at sundry sites around the web over the last couple of decades — John Baez, nCafe, nLab, Zulip Category Chat, Topos Group, etc. As great as all that is there's a reason why it bears but tangentially on the issues I've been pursuing. That has to do with the Peirce Factor and how far a given line of inquiry takes account of it. As luck would have it, one of the texts John Gray used for his course, Lambek and Scott's “Introduction to Higher Order Categorical Logic”, resonated strongly with themes I knew from Peirce and that led me to many adventures of ideas still in progress. The following set of excerpts I shared with the Standard Upper Ontology Group back in the day may suggest the character of that work. • Lambek, J. and Scott, P.J. (1986), Introduction To Higher Order Categorical Logic • Excerpts ( https://oeis.org/wiki/User:Jon_Awbrey/Mathematical_Notes#HOC ) • Discussion ( https://oeis.org/wiki/User:Jon_Awbrey/Mathematical_Notes#HOC_Discuss ) There's a lot more to say, but that's all I have time for today … Regards, Jon