FOM: Alice, Carol and Leibniz

[Miguel A. Lerma]

 > From: kanovei at wmwap1.math.uni-wuppertal.de (Kanovei)
 > Date: Mon, 15 Apr 02 18:52:51 +0200
 >
 > > From: "Dean Buckner" <Dean.Buckner at btopenworld.com>
 > > Date: Sat, 13 Apr 2002 16:42:04 +0100
 >
 > > how do we know that two objects are not the same, if they are
 > > said identical in every conceivable way?
 >
 > Can you give any clear example of 
 > *two objects ... not the same [but] identical in every conceivable way* 
 > Or you only mean here nonexistent entities like Alice which 
 > you grant properties favorable for your theories?
 >
 > Examples like two electrons orbiting an atom of He 
 > are not convincing because while you don't look at the 
 > atom the fact that there is 2 orbiting electrons is nothing 
 > but a mathematical abstraction, what exists in reality is 
 > a certain field of some kind, 
 > anyway YOU DON'T KNOW is there still two or already 5 of them, 
 > but as soon as you deside to look at the atom in some microscop 
 > then the electrons become immediately distinguishable at this 
 > very moment because 
 > one of them is in the NW corner of the picture while the other 
 > is in the SE corner.  

However if you let them interact for a while and then look 
at them again, you may still see one electron in the NW corner
and another one in the SE corner, but you will be unable to 
determine whether the electron in the NW corner is the same
electron that was in the NW corner before or is the one that 
was in the SE corner. Electrons are indistinguishable particles,
at a given time it may seem that they can be distinguished by
their position in space by the value of some other physical 
observable, but depending on how much their wave functions
overlap they always have some probability of exchanging their
identities, so you lose track of which one is which one - it is
not that we are "unable" to determine their individual identities,
if Quantum Mechanics is right, they do not even have a well
defined individual identity.

In this regard identical particles behave like measure units,
for instance monetary units like dollars. If I have 2 dollars 
(I do not mean 2 dollar bills, but wealth for a value of 2 dollars), 
it does not make any sense trying to distinguish between one dollar
and another dollar, they are completely indistinguishable, and
however they add up to 2 dollars. The same can be said of
volts, meters, or other units of measure, except that most
measures we can think of are not discrete as elementary particles
are (there is no such a thing as one and a half electrons).

It seems that this supports the idea that "number" does not 
depends on the existence of distinguishable objects, all we 
need is that the objects can somehow be aggregated.


Miguel A. Lerma