Date: Feb 13, 2013 6:05 AM
Author: dan.ms.chaos@gmail.com
Subject: Re: infinity can't exist

I've had a look at the paper : there are at least  two objections to
it :
The first appeals to an idea popularity not considered as Leibnitzian,
although the truth on the matter is more complex :
the idea of ether , namely , for space , or space-time to have
reality , it must have "matrix style" unique and absolute coordinates
for every point . The spheres are distinguished by possessing
different coordinates .
The second , affirms a mode of 'esse est percipi' , namely, a universe
cannot be 'real' without at least one 'real observer' .Such an
observer will distinguish the spheres .
Even ignoring the above objections , to the extent that they can be
real without any observer or coordinates , they are either distinct ,
or are the same object . (in the same way members of the same
equivalence class in a group are the same in a factor group ) . That
object would be something along the lines of 'the potentiality of a
sphere to be to the left and/or to the right of an observer' .

The identity of indiscernibles can be formulated as simple principle
of second order logic applicable to every mathematical object :
?F(Fx ? Fy) ? x=y.
No one would dispute it's truth with regards to real numbers, for
example .
To apply it to reality , one needs an extra piece of info/assumption :
that is, the doctrine of the pythagoreans, that the universe is
mathematical at the deepest level :
"Number rules the universe" -Pythagoras