Inquiry Into Inquiry

Re: Michael Harris • Language About Language

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

Perhaps it takes a number theorist to appreciate it …

Re: Michael Harris • Language About Language

And if we don’t [keep our stories straight], who puts us away?

One’s answer, or at least one’s initial response to that question will turn on how one feels about formal realities.  As I understand it, reality is that which persists in thumping us on the head until we get what it’s trying to tell us.  Are there formal realities, forms which drive us in that way?

Discussions like those tend to begin by supposing we can form a distinction between external and internal.  That is a formal hypothesis, not yet born out as a formal reality.  Are there formal realities which drive us to recognize them, to pick them out of a crowd of formal possibilities?

Re: Michael Harris • Language About Language

I compared mathematics to a “consensual hallucination,” like virtual reality, and I continue to believe that the aim is to get (consensually) to the point where that hallucination is a second nature.

I think that’s called coherentism, normally contrasted with or complementary to objectivism.  It’s the philosophy of a gang of co‑conspirators who think, “We’ll get off scot‑free so long as we all keep our stories straight.”

Re: Michael Harris • Language About Language

There is a language and a corresponding literature treating logic and mathematics as related species of communication and information gathering, namely, the pragmatic‑semiotic tradition transmitted through the lifelong efforts of C.S. Peirce.  It is by no means a dead language but it continues to fly beneath the radar of many trackers in logic and math today.  Nevertheless, the resource remains for those who wish to look into it.