Maybe I should re-emphasise the caveat at the top of the post: “I will provide informal hints on how surreal numbers could help us solve some of these paradoxes, although the focus on this post is primarily categorisation, so please don’t mistake these for formal proofs. I’m also aware that simply noting that a formalisation provides a satisfactory solution doesn’t philosophically justify its use, but this is also not the focus of this post.”
You wrote that I “made the entirely arbitrary choice that you are only prepared to understand it in terms of surreal numbers”. This choice isn’t arbitrary. I’ve given some hints as to why I am taking this approach, but a full justification won’t occur until future posts.
Maybe I should re-emphasise the caveat at the top of the post: “I will provide informal hints on how surreal numbers could help us solve some of these paradoxes, although the focus on this post is primarily categorisation, so please don’t mistake these for formal proofs. I’m also aware that simply noting that a formalisation provides a satisfactory solution doesn’t philosophically justify its use, but this is also not the focus of this post.”
You wrote that I “made the entirely arbitrary choice that you are only prepared to understand it in terms of surreal numbers”. This choice isn’t arbitrary. I’ve given some hints as to why I am taking this approach, but a full justification won’t occur until future posts.
OK! I’ll look forward to those future posts.
(I’m a big surreal number fan, despite the skeptical tone of my comments here, and I will be extremely interested to see what you’re proposing.)