FOM: Alice, Carol and Leibniz

Tue Apr 16 00:12:19 EDT 2002

<Dean Buckner wrote:>

>Well, first of all (to take a hackneyed example) we could have a
completely
>empty universe except for two atomic particles rotating round each
other.
>Couldn't they be qualitatively identical, but numerically different?

How can they be orbiting each other if they are identical?  To be
identical, they must ocupy the same space.  If they are orbiting each
other, that implies that they occupy different space.  Now, if we label
one of them A and the other B, then "occupies the same space as A"
plainly holds for A and not B. (this assumes point-type particles)

>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.

I'm not sure that's quite right.  Each electron is defined in quantum
mechanics by a certain kind of wave function.  A superposition of two
(obviously normalized) wave functions is a linear combination of them
that is also normalized.  In this sense, they do have distinct identies
inasmuch as the decomposition into "elementary" wave functions is
unique.  

<And earlier in the same message:>

>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.

You may not know exactly what your measurements will yield, but given
the wave functions, you do have a unique probability distribution.  

In any  case, if we move the size up to a non-quantum arena, then my
objection still stands.

<Back to Dean's stuff:>

>And  this information we get from language can be exactly as the
objection
>it cannot.  Here's some more information.  I just said I had an
anonymous
>correspondent, who made this Leibnizian objection.  Well, as it happens
I
>have another correspondent who made exactly the same objection.  

Yes, you say this, and I understand what you mean.  I can come to one of
two conclusions:
(1) You are not telling the truth (I only know for certain that you had
one such coorespondent)
(2) You are telling the truth.

If (2) is the case, then I know that you had two distinct people who
sent you letters of which you do not approve.  But what does this mean?
You wouldn't tell me they were different unless you had some way of
telling them apart!  If you couldn't distinguish them, then surely you
wouldn't have labeled them as two separate things.  If "both" your
coorespondents have my email address, identically worded letters sent at
the same time, and stored in the same place on your server, then you
would be crazy for calling them different coorespondents!

>I have just
>given you the information that there are two people, without supplying
any
>predicate U such that U the one and not U the other.  All I have said
is
>that they both made a certain objection.  They are, from your point of
view,
>indistinguishable.  Yet they are are different.

They are, from my point of view, indistinguishable.  If you are telling
the truth, then you must have some way of telling them apart.
Linguistically, it is possible to express inequality without specifying
a predicate which distinguishes two objects, but if people take what you
say in good faith, they assume you can tell objects apart.  I can say
for example, "there are two distinct French dictionaries on my desk".
This is a linguistic edifice which expresses the concept of inequality
to you without telling the technical details (i.e. that one is yellowed
and falling apart, and that I bought the other one new today).  

>It's no use arguing that in reality there must be characteristics
>distinguishing the things from one another.  Certainly, there will be.  

What kinds of things are you talking about?  Fictional objects are a
very different issue from real objects.  If you are talking about real
objects, then why is there no use in arguing this?

>But
>the propositions express that, do they?  Is that what we grasp, when we
>understand them?  And is that what, if the propositions are true, makes
the
>two sets of things different?  Rather than the simple assertion,
contained
>in the proposition, that they just are different?  I don't think so.

Could you clarify what you mean by this paragraph?  To what propositions
are you referring?

>In summary:  how do we know that two objects are not the same, if they
are
>said identical in every conceivable way?  Answer: because they are said
to
>be different.

Let W  & S be the predicates "rises in winter" and "rises in summer".
Plainly we have that the sun rises in winter and in summer, so W(sun)
and S(sun) are both true.  Now assume I belong to a religion which
believes that the sun is different in each season.  I can say that the
sun such that W(sun) and the sun such that S(sun) are distinct, and I
may even believe it, but does it make it so?  Of course not:  just
because I (or you) say something, doesn't make it true.

- Lucas Wiman