Re: A Logical Model for Lists as Relations

vc wrote:
> Mikito Harakiri wrote:
> [...]
> > Don't you need ordered pair definition as well? I refuse to accept
> > Kuratovski set trick as ordered pair representation in terms of sets.
> >
>
> It sounds capricious. The pair does the required job, and besides
> there are alternative definitions of the ordered pair (Quine' for
> example).

Kuratowski and Quine' constructions are not definitions. The ordered pair definition is

    (x,y) = (a,b) if and only if x=a and y=b.

Any set construction that satisfies this property would do but, really, this a pointless exercise just for the sake of representing round brackets via curly ones.

OK, if an ordered pair is a set, then perhaps union and intersection of ordered pairs make sense. No? An ordered pair is not a set (although it can be considered as a set element, of course).

> > Alternatively, a sequence can be defined axiomatically via Kleene
> > algebra.
>
> Why proliferate unnecessarily the number of primitives ?

That was not the point. Reduction to the sets doesn't buy us anything (at least in case of ordered pair). A proposition "Everything is a set" is just as silly as "Everything is object". Received on Fri May 12 2006 - 11:18:21 CDT