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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 8th 2020
    • (edited Dec 8th 2020)

    I have a student working on meta-metaphysics, which is where you reflect on how metaphysics is done, and part of the debate he’s describing has been governed over many centuries by responses to the opposition between the idea that Being is univocal and the idea that there are different modes of Being. There are objects, there are events, there are numbers, etc. Does the ’are’ refer to one concept Being, or should we think about different kinds of Being, Being an object, Being a number, etc.

    Looking to filter this through the framework of type theory, and in the spirit of the kind of unity of opposites we see in cohesion and set elements as “distinct, but indistinguishable”, described at Cohesive Toposes and Cantor’s “lauter Einsen”, I was wondering about what is the ’same’ in judgements a:Aa: A, b:Bb:B.

    I guess it’s that they sit above *:1\ast: 1. Any map x:1Xx: 1 \to X is composable with the terminal X1X \to 1 to give the map 111 \to 1.

    So there’s what we discuss as ’determinate being’, all types located in a cylinder, 0X10 \to X \to 1, and then the thought that any element of a type appears as an extension of *:1\ast: 1. Or something like that.

    By the way, I couldn’t get

        [[Cohesive Toposes and Cantor's "lauter Einsen"]] 
    

    to work properly.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 8th 2020

    Ok, so I guess one could speak of pointed types, and the terminal such.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 8th 2020

    Just to note that for pointed objects the terminal object is also initial, hence is a zero object, and so then the inclusion functor has coinciding left and right adjoint, which makes it an adjoint cylinder for “infinitesimal cohesion” or the like.