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Hmm, infinitary logic looks interesting (I'll read right through it later, but I'm not entirely sure it covers what I'm trying to do). As for Platonism, mathematical realism, and Tegmark, before discussing these things I'd like to check whether you've read on my version of Tegmark-like ideas? I'd rather not repeat all that bit by bit in conversation.
Have you looked into Univalent foundations at all? There was an a while ago and it seems as though it might be relevant to your pursuits.
I've read your post on Syntacticism and some of your replies to comments. I'm currently looking at the follow up piece (The Apparent Reality of Physics).