I think formalizing it in full will be a pretty nontrivial undertaking, but formalizing isolated components feels tractable, and is in fact where I’m currently directing a lot of my time and funding.
Great. Yes, I think that’s the thing to do. Start small! I (and presumably others) would update a lot from a new piece of actual formal mathematics from Chris’s work. Even if that work was, by itself, not very impressive.
(I would also want to check that that math had something to do with his earlier writings.)
My current understanding is that he believes that his current written work should be sufficient for modern mathematicians and scientists to understand his core ideas
Uh oh. The “formal grammar” that I checked used formal language, but was not even close to giving a precise definition. So Chris either (i) doesn’t realize that you need to be precise to communicate with mathematicians, or (ii) doesn’t understand how to be precise.
Please be prepared for the possibility that Chris is very smart and creative, and that he’s had some interesting ideas (e.g. Syndiffeonesis), but that his framework is more of a interlocked collection of ideas than anything mathematical (despite using terms from mathematics). Litany of Tarsky and all that.
Great. Yes, I think that’s the thing to do. Start small! I (and presumably others) would update a lot from a new piece of actual formal mathematics from Chris’s work. Even if that work was, by itself, not very impressive.
(I would also want to check that that math had something to do with his earlier writings.)
I think we’re on exactly the same page here.
Please be prepared for the possibility that Chris is very smart and creative, and that he’s had some interesting ideas (e.g. Syndiffeonesis), but that his framework is more of a interlocked collection of ideas than anything mathematical (despite using terms from mathematics). Litany of Tarsky and all that.
That’s certainly been a live hypothesis in my mind as well, that I don’t think can be ruled out before I personally see (or produce) a piece of formal math (that most mathematicians would consider formal, lol) that captures the core ideas of the CTMU.
So Chris either (i) doesn’t realize that you need to be precise to communicate with mathematicians, or (ii) doesn’t understand how to be precise.
While I agree that there isn’t very much explicit and precise mathematical formalism in the CTMU papers themselves, my best guess is that (iii) Chris does unambiguously gesture at a precise structure he has in mind, assuming a sufficiently thorough understanding of the background assumptions in his document (which I think is a false assumption for most mathematicians reading this document). By analogy, it seems plausible to me that Hegel was gesturing at something quite precise in some of his philosophical works, that only got mathematized nearly 200 years later by category theorists. (I don’t understand any Hegel myself, so take this with a grain of salt.)
Great. Yes, I think that’s the thing to do. Start small! I (and presumably others) would update a lot from a new piece of actual formal mathematics from Chris’s work. Even if that work was, by itself, not very impressive.
(I would also want to check that that math had something to do with his earlier writings.)
Uh oh. The “formal grammar” that I checked used formal language, but was not even close to giving a precise definition. So Chris either (i) doesn’t realize that you need to be precise to communicate with mathematicians, or (ii) doesn’t understand how to be precise.
Please be prepared for the possibility that Chris is very smart and creative, and that he’s had some interesting ideas (e.g. Syndiffeonesis), but that his framework is more of a interlocked collection of ideas than anything mathematical (despite using terms from mathematics). Litany of Tarsky and all that.
I think we’re on exactly the same page here.
That’s certainly been a live hypothesis in my mind as well, that I don’t think can be ruled out before I personally see (or produce) a piece of formal math (that most mathematicians would consider formal, lol) that captures the core ideas of the CTMU.
While I agree that there isn’t very much explicit and precise mathematical formalism in the CTMU papers themselves, my best guess is that (iii) Chris does unambiguously gesture at a precise structure he has in mind, assuming a sufficiently thorough understanding of the background assumptions in his document (which I think is a false assumption for most mathematicians reading this document). By analogy, it seems plausible to me that Hegel was gesturing at something quite precise in some of his philosophical works, that only got mathematized nearly 200 years later by category theorists. (I don’t understand any Hegel myself, so take this with a grain of salt.)