About Logic - Is Mathematics a Story?

They're threatening to do this weekly, ...

My comment: 

Looking forward to the Dana Scott interview! Maybe there's not time to do this before then, but I would like to hear a discussion about the different views people have about models. I sometimes think that Computer scientists look for models in the zoo of mathematical theories, because they feel like this the only possible source of their legitimacy: they say something like "Well, this type system is sound because if it wasn't then ZFC would be inconsistent and you would have much bigger things to worry about than the soundness of my little type system!" But then serious mathematicians who have Fields medals come along and say "Well actually, I have these proofs that I've done in Higher Homotopy theory and I seriously doubt anyone has checked them as carefully as I did, and I am not sure that I haven't made a mistake somewhere, ..." and then they find a type system that a computer scientist cooked up out of some left-over intuitionistic logic he found somewhere and the Fields medalists start formalising proofs in it, relying on the soundness of the type system, ... So it seems very clear that if you want to use a "fiction as a model of meaning" interpretation of mathematics, then mathematicians are like characters in the story that are writing that very story themselves. When I have written stories and it's gone well, I have often felt like it was the characters in the story who were writing it, and what happened next followed almost inevitably from a sort of internal logic. Lawvere's idea of functorial semantics then starts to seem like the only hope! 

[So is a Functor a metaphor for metaphor or is it just isomorphic to one, like a simile?] 

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