Signs Of Signs • 4
• https://inquiryintoinquiry.com/2025/03/20/signs-of-signs-4-a/

Re: Michael Harris • Language About Language
• https://mathematicswithoutapologies.wordpress.com/2015/05/23/language-about-language/comment-page-1/#comment-380

❝But then inevitably I find myself wondering whether a proof assistant, or even a formal system, can make the distinction between “technical” and “fundamental” questions. There seems to be no logical distinction. The formalist answer might involve algorithmic complexity, but I don't think that sheds any useful light on the question. The materialist answer (often? usually?) amounts to just‑so stories involving Darwin, and lions on the savannah, and maybe an elephant, or at least a mammoth. I don't find these very satisfying either and would prefer to find something in between, and I would feel vindicated if it could be proved (in I don't know what formal system) that the capacity to make such a distinction entails appreciation of music.❞

Peirce proposed a distinction between “corollarial” and “theorematic” reasoning in mathematics which strikes me as similar to the distinction Michael Harris seeks between “technical” and “fundamental” questions.

I can't say I have a lot of insight into how the distinction might be drawn but I recall a number of traditions pointing to the etymology of “theorem” as having to do with the observation of objects and practices whose depth of detail always escapes full accounting by any number of partial views.

On the subject of music, all I have is the following incidental —

🙞 Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

Perhaps it takes a number theorist to appreciate it …

Resource —

Higher Order Sign Relations
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations

#Peirce #Inquiry #Logic #Mathematics #Reflection
#Semiotics #SignRelations #HigherOrderSignRelations