Re: Generic Package

[Markus E Leypold <development-2006-8ecbb5cc8aREMOVETHIS@ANDTHATm-e-leypold.de>]

Ray Blaak <rAYblaaK@STRIPCAPStelus.net> writes:

> Georg Bauhaus <bauhaus@futureapps.de> writes:
>> > > As you can see, there is some order again but I don't have to know
>> > > the order. (Finding a first book (and then the next book) is the
>> > > job of the librarian, not mine.)
>> > 
>> > Librarian is the interface. If it finds first book then that is a publicly
>> > ordered set = you _can_ know the order without breaking the abstraction.
>> 
>> ?
>> The first book might be determined by whatever order the librarian
>> thinks he should choose this time. Nothing I could determine beforehand.
>> The order(s), if any, isn't/aren't publicly known.
>
> Change it to:
>
>  As you can see, there is some order again but I don't have to know the
>  order. (Finding any book (and then another arbitrary book from the remainder)
>  is the job of the librarian, not mine.)
>
> And that should be precise enough for everyone here.
>
> There is no first book as such in the set. There is only the first one that
> was given to you, which is not knowable in advance.

There is considerable confusion about what "order" means here. An
order is a binary relation with certain properties defined on the set
of all elements (the base set). The sets we're talking about are
subsets of that set of all elements. Talking about the data type
'ordered set' means, I have to specify one constant order on the base
set before instantiating or implementing the ordered set type. The
fact that some ad-hoc ordering of a given subset occurs during
iteration does not mean that the data type suddenly becomes
ordered: This is just an artifact of sequential data processing in
languages the specifiy operations as occuring sequentially in time. My
impression is (from DKs axiom of choice argument and DKs uncoutable
set example) that he seems to argue that there are unorderable sets in
mathematics (sets for which no order could be provided), but this has
no bearing on iteration (see the real numbers: can be ordered, but
cannot be iterated over). Even worse: All that has no bearing on his
original statement "one cannot iterate over relational tables" (those
a finite) and his second implied statement that one cannot iterate
over sets (one can, but obviously not over all kind of sets like
algebraically expressed subsets of real numbers, but that has nothing
to do with order, only with countability).

I'm quite sure, DKs problem cannot be written down formally since it
doesn't even exists, except in the twilight between free associations,
hand waving arguments and exchanged all and existence quantors (see
the misunderstandings about order). 

It is much more difficult to argue against arguments and
misconceptions that have not been expressed exactly (because the
battle ground tends to shift) than any other false statement.

Regards -- Markus