Re: A Logical Model for Lists as Relations
Date: 12 May 2006 09:18:21 -0700
Message-ID: <1147450701.594373.183670_at_d71g2000cwd.googlegroups.com>
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 - 18:18:21 CEST