[Haskell-cafe] type metaphysics

[Gregg Reynolds]

On Mon, Feb 2, 2009 at 10:05 AM, Andrew Butterfield
<Andrew.Butterfield at cs.tcd.ie> wrote:
> Martijn van Steenbergen wrote:
>>
>>> To my naive mind this sounds
>>> suspiciously like the set of all sets, so it's too big to be a set.
>>
>> Here you're probably thinking about the distinction between countable and
>> uncountable sets. See also:
>>
>> http://en.wikipedia.org/wiki/Countable_set
>
> No - it's even bigger than those !
>
> He is thinking of proper classes, not sets.
>
> http://en.wikipedia.org/wiki/Class_(set_theory)

Yes, that's my hypothesis:  type constructors take us outside of set
theory (ZF set theory, at least).  I just can't prove it.

Thanks,

g