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• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeJun 19th 2019

Jotted down some things. Leibniz should feature but perhaps another day.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeJun 20th 2019

Tweaked some more, and left some to do’s.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJun 20th 2019

Thanks for writing this. I have added pointer to this from synthetic mathematics, and maybe it should be pointed to from orher places, too.

• CommentRowNumber4.
• CommentAuthorTodd_Trimble
• CommentTimeJun 20th 2019

Is one of the to-do’s to insert a link to whatever Martin-Löf wrote?

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeJun 20th 2019

Re #4, yes. I’ve just added a brief paragraph along this line.

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeJun 25th 2019

Added a bit more of the story to show how to move from Descartes to Kant via Leibniz.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJun 26th 2019

Great to see you add some philosophy content! I have given the entry now the Philosophy floating context menu.

• CommentRowNumber8.
• CommentAuthorDavid_Corfield
• CommentTimeJun 26th 2019

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.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeJun 26th 2019

Right, but I suppose we have the magnificent option here to add an $n$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.

• CommentRowNumber10.
• CommentAuthorDavid_Corfield
• CommentTimeJun 26th 2019

Right, it should be a $n$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.

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeJun 26th 2019

Yes, exactly. This would change if they found more philosophy discussed on the $n$Lab.

• CommentRowNumber12.
• CommentAuthorDavid_Corfield
• CommentTimeJun 26th 2019

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.

• CommentRowNumber13.
• CommentAuthorDavid_Corfield
• CommentTimeAug 9th 2019

Added a quote from Kant employing terms in their original sense.