Re: Evil in bicategories

[Richard Garner <richard.garner@mq.edu.au>]

Two that spring to mind are "inflexible" (after Kelly) or "impersistent"
(after Paré).

On 13 September 2010 10:16, David Roberts <droberts@maths.adelaide.edu.au>wrote:

> Dear Jean,
>
> You wrote:
>> Maybe my english isn't so "beautiful", but in all cases where "evil" has
>> been used, what is wrong with "wrong" instead?
>
> I'm not so enamoured with the use of the word 'evil', but it seems to
> be more entrenched than perhaps it was intended, namely as a joke.
> Regardless of my personal convictions, I like to remain a mathematical
> agnostic, so 'wrong' seems to me to be too strong. In my everyday
> mathematical work I use choice and excluded middle and equality at
> will, but I know that these foundational ideas ('evil' in categories,
> constuctivism etc) exist and are useful and interesting.
>
> Unfortunately I don't have any decent alternatives to offer, but the
> philosophy boils down to, in my opinion, a structuralist view of
> foundations (as opposed to the standard ZF with 'member of'
> foundations) combined with (even a simple grasp of) type theory. The
> former is essentially the 'sets are bags of points' approach and the
> latter is the 'you can't ask: is \pi = (sin:R \to [-1,1])?' idea.
> Perhaps readers of this list with the inclination and an eye for
> nomenclature will suggest some words.
>
> Toby Bartels calls categories where one is not allowed to test for
> equality between arbitrary objects 'weak' and those where one can do
> so 'strict' (most often these latter are internal categories in some
> version of Set, or perhaps using universes). This reflects thinking
> about higher categories (and completely exemplified by Makkai's
> approach via FOLDS). This terminology takes the 'moral dimension' out
> of talking about serious foundational ideas. But we don't have a word
> that replaces 'evil' in this context that conveys the sort of mild
> disdain for attempting to make the naive mistake of trying to ask if a
> scalar is contained in a vector, as one can do in traditional
> foundations (note that the answer depends on how one defines tuples).
>
> That's my two cents, for what it's worth.
> David
>

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