DandelionSoul wrote: ↑Sat Jun 05, 2021 9:29 pm
To be honest... while I feel like I can follow the work of Kastrup (or others with similar perspectives like Freya Mathews or Philip Goff or Miri Albahari) pretty well, the discussion on intuitionism and formalism and the nature of language itself falls beyond the scope of my education so far, and I sorta feel like I'd need to expand my reading list somewhat to grasp what you're trying to say. Is there a place I can start with that? I hope that doesn't come across as dismissive, just that I've read that comment a few times in a row, slowly, and still can't get my head around what you're saying, and I assume the shortcoming here is on my end.
That's a good question and you're not the first to ask that. But sorry, no, there's no simple and quick introduction to what I'm speaking about, except perhaps most generally these about the foundational crisis of mathematics:
https://en.wikipedia.org/wiki/Brouwer%E ... ontroversy
https://personal.us.es/josef/pcmCrisis.pdf
More genarally, Wittgenstein's comment's on philosophy of mathematics were a turning point in my dance with mathematics.
Norman Wildberger's videoss, especially the foundations series, has been major influence and inspiration, on which my own approach has been building on from a complementary perspective. Which AFAIK is quite novel, and very much WIP and ongoing discussion. A main reason why I - a non-professional - try to talk math with other non-professionals - is to keep on learning how to speak math in more comprehensible and accessible way. But when we don't approach math simply as rule-following, following some set of rules by some supposed authority somewhere, but as creative and participatory process, the first task is to try to liberate from the expectations of rule-following. Foundational thinking is a free game, "rule following" from a foundational approach is not about "rules" as such, but about the ethics and esthetics of mathematical rigour, logical honesty and not least, communicability.
In a "rebel base" of more or less dissident math enthousiasts we've had also some discussions about relation of philosophy and foundations of mathematics and the general public. People are generally naive about math, not because they are stupid, but because they are not motivated to attend to mathematics beyond simple practicalities and/or indoctrination into the formalist-materialist academic dogma. To dig deeper in the foundational issues, generally you need loads of cold rage for the motivation, and loads of idle time to be practically able to do that.
Why so little motivation? The jargons of set theory mathematics, as well as financial capitalism etc etc are really difficult and confusing to get through, and that's by design. They are obnoxious and uninviting for the same function that medieval Monk Latin served.
I consider my own approach fanatically simple, and if we could genuinely start from a clean slate tabula rasa, perhaps it could appear so. But of course that's not the situation, there's the existing and established jargons to communicate with, as well as expectations created by the standard conditioning to tackle. And of course genuinely deep philosohical etc. questions to try to make sense of in a coherent and communicable way.