[Haskell-cafe] type metaphysics

[Krzysztof Skrzętnicki]

Do they? Haskell is a programing language. Therefore legal Haskell types has
to be represented by some string. And there are countably many strings (of
which only a subset is legal type representation, but that's not
important).
All best

Christopher Skrzętnicki

On Mon, Feb 2, 2009 at 17:09, Gregg Reynolds <dev at mobileink.com> wrote:

> 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
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