>>Philosopher Nozick mentions the following argument in one of his
>>books (Philosophical Explanations 1981): There are infinitely many
>>ways for there to be something, but only one way for there to be
>>nothing. Therefore, assuming each way is equally probable, the
>>probability that there is something equals 1.
>I would like to comment the following about Mr. Nozick's affirmation:
>
>First: an infinite set of *discrete* events, can never be equiprobable,
>since sum(p)=1. So any individual p=1/n >>> when n=oo...p=0...and
>sum(p)=0... (obvious contradiction...)
Infinities tend to cause problems in many places in probability
theory. In this case, maybe we can fix the problem by
introducing infinitesimals. So each of the infinitely many events
would not have p(e)=0, but p(e)=i, where i is defined by i*oo=1.
>( I always laugh a lot with certain
>philosophical questions... just based on NOZICK's affirmative, such
>question has no sense... )
Yes, it is of course problematic whether it makes sense at all to
attribute an a priori probability of the world being in a certain
way. Hmm... Inductive inferences, the rationality of which we can't
doubt, implicitly presuppose that all sorts of things have
conditional a priori probabilities; this seems to translate into an a
priori probability assignment to all possible worlds... (I'm sorry
I'm cryptic here; I just got an idea.)
_____________________________________________________
Nick Bostrom
London School of Economics
Department of Philosophy, Logic and Scientific Method
n.bostrom@lse.ac.uk
http://www.hedweb.com/nickb