Re: x*x-1=0

Vadim Tropashko wrote:
> In article <958n31$4g2$1_at_news.tue.nl>,
> hidders_at_win.tue.nl (Jan Hidders) wrote:
> > Vadim Tropashko wrote:
> > > In article <94rr74$l4j$1_at_news.tue.nl>,
> > > hidders_at_win.tue.nl (Jan Hidders) wrote:
> > > > Vadim Tropashko wrote:
> > > > > Do tuples have *internal* structure in terms of set/bags theory?
> >
> > Yes, named tuples are defined as functions that map a name to a value.
>
> I'm OK with this definition.
>
> > And, as you probably know, functions can again be defined as a set of
> > pairs, and a pair can also be defined in terms of sets.
>
> Here, Reductionalism, again! A pair is defined in terms of sets as {a,
> {b}} or as {{a}, b}. This ambiguity indicates that the set construction
> is far from perfect. (At least, in programming ambiguity was never a
> good thing:-)

What!? Have I been talking all the time to a holist!? My God, I am doomed! What will become of me! Have I lost my reductionist purity for ever? How can I make amends?

:-)

But seriously. You are falling in the "is" trap that I already warned you about in previous postings. You are reading the "is defined as" as "is" but that is wrong, wrong, wrong. The claim is not that a pair <a,b> *is* {a,{b}} but that this constitutes a *model*. And it is hardly surprising that there are several models to choose from. That is always the case with models and it is not a bug but a feature. So nothing is being reduced here.

> > The expressive power becomes greater.
>
> For me this sounds pretty much like "If I rename variables in Maxwell
> equations, then they won't describe electromagnetic waves any more".

The column names are *observables*; you can point to them and see them. If you are going to ignore some observables in Maxwell's theory then the theory becomes a different theory, if not simply meaningless.

-- 
  Jan Hidders