> Nicholas Bostrom, <bostrom@mail.ndirect.co.uk>, writes:
> > No, that is not the question. Not many would say that
> > consistency guarantees existence (apart from David Lewis). The
> > snowman is a logically consistent notion but that does not mean that
> > the snowman exists.
> >
> > Now, obviously, if something is asserted to exist by a logically true
> > proposition, then it exists. So the questions are (1) Is the
> > proposition that the Mandelbrot exists logically true? (which boils
> > down to whether the notion of "logical truth" in the traditional
> > way really makes sense), and (2) Is this kind of existence somehow
> > fundamentally different from the existence of objects which cannot be
> > claimed to exist by any logically true proposition.
>
> Or as another example, with a definition of "reality" which classes the
> Mandelbrot set and the Virgo cluster as the same, can we reject any
> logically consistent but "actually" non-existent phenomena as "real"? Must
> we say that alien spaceships "really" are visiting the earth today,
> simply because there is no logical contradiction in doing so?
The obvious answer to this rethorical question is No. The existence
of the Mandelbrot set is provable in standard (ZF) set theory, but I
don't know of any plausible axioms from which one can derive the
existence of visiting alian spaceships.
------------------------------------------------
Nicholas Bostrom
bostrom@ndirect.co.uk
*Visit my transhumanist web site at*
http://www.hedweb.com/nickb