You see, the proposition asserting the existence of the Mandelbrot
set is not only consistent, it is logically true, i.e. it follows
logically from the axioms of Zermelo-Fraenkel's set
theory, the truth of which we do not doubt, do we. So when you ask
whether the Mandelbrot set exists, the answer to your question would
have no relevance to the issue of whether "if something is logically
consistent does that makes it a part of the world?". Hence this
latter question is not *the* question, i.e. not the question we were
discussing, which is the question of the existence of such things as
the Mandelbrot set. (I sense a confusion between consistency and
logical necessity.)
> >I do think that the question "Does the Mandelbrot set exist?" needs
> >to be specified and refined. [...] and until you have explained what
> >that notion is, your question appears rather meaningless to me.
>
>
> You want a precise definition of "exist", I think that would be nice too but
> obviously I don't have one.
I did not say that a precise definition is a prerequisite for
fruitfully discussing the issue; I only said that the question needed
to be made more precise and unambigous than it is. It is a matter of
degree.
> As near as I can tell, Moravec thinks that a mind is the one thing that has
> it's own self consistent interpretation inherent within it; in fact that
> seems to be the definition of a mind, although you would still need an
> interpretation to make contact with it.
I have been eagerly awaiting this new book for over a year now. I
expect there to be clear signs when it finally is released, like
unusually shaped thunder bolts or snow in the middle of the summer.
------------------------------------------------
Nicholas Bostrom
bostrom@ndirect.co.uk
*Visit my transhumanist web site at*
http://www.hedweb.com/nickb