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Thanks for writing this. I have added pointer to this from synthetic mathematics, and maybe it should be pointed to from orher places, too.
Is one of the to-do’s to insert a link to whatever Martin-Löf wrote?
Great to see you add some philosophy content! I have given the entry now the Philosophy floating context menu.
I know I should add more. But then every concept or thesis is so thoroughly contested. History of philosophy, as with this one, is more straightforward.
Right, but I suppose we have the magnificent option here to add an POV to the usual stories, point out – you do here – which philosophical positions are reflected (or not) in which piece of foundations of maths, type theory, physics, etc. That would be the additional value not found on any other sites.
Right, it should be a POV view which makes it quite a blank state. Extraordinary that 50 years on from Adjointness in Foundations, next to no philosopher could tell you that quantifiers are adjoints.
Yes, exactly. This would change if they found more philosophy discussed on the Lab.
My immediate target is via a book I’m finishing off for Oxford UP – Modal homotopy type theory: The new new logic for philosophy (a play on Russell’s ’new logic’ as in the quotation at analytic philosophy). Sorting out the index as we speak.
Unfortunately while there are plenty of pointers to the importance of modal HoTT for physics, there’s little content, but that’s perhaps another book.
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