Re: Eternity


"Gareth McCaughan" <Gareth.McCaughan@xxxxxxxxx> wrote in message
news:87zldbb9df.fsf@xxxxxxxxxxxxxxxxxxxxx
(First of all, a general note to Thomas: I know who Michael D. is
in real life; he knows rather a lot of mathematics and physics, and
if you find yourself thinking that he has made an elementary error
in either domain then you should consider very seriously the possibility
that the error is yours.)

Thanks. I'm sure he is a more than competent mathematician and I don't
believe I have so far suggested he has made any mathematical errors. But I
do think he misuses the word paradox since by his usage the word would have
little if any meaning - ie a paradox with a resolution would not be a
paradox.

Anyway, sorry if the attributions go awry in what follows, hopefully it
won't cause any great confusion.

To demonstrate that this supports such an idea you'd need to provide
evidence for the type of process that is supposed to drive this
universe.

Er, no. Michael is not claiming that the steady state theory is
likely to be correct. He's claiming that it's not internally
incoherent: that there *could be* such a world, even though it
seems pretty clear that our world isn't one.

Hoyles model contains a mechanism which continuously conjures up real
observable matter from nothing. The model might be consistent with the
Eistein's feld equations but it is certainly not consistent with any quantum
field models that I'm familiar with. To demonstrate a physically sound
theory that could support a mental world you also need to exhibit a model
which can support discrete states. Can you do this?



But there's another type of problem with this type of steady state
universe - it has infinite mass and structure (at least in the limit).
So,
if we accept that the mental supervenes on the material then you have a
likelihood (if not a certainty) that there will be multiple copies of
each
elect. Which copy will correspond to the one who existed on earth, how
would
they know, would the rest be souless zombies? It looks like some more
tinkering is needed to add some laws or conditions which prevent these
unfortuate duplications.

It's not obvious to me that they would be unfortunate. If being
resurrected once into a perfect world is a blessing, how much
better to be resurrected infinitely many times into a perfect
world? :-)

It's an interesting idea which strikes at the heart of what personal
identity really means.

If we accept that the mental supervenes on the material (ie that two systems
which are materially identical must possess the same mental worlds) then we
do have to accept that mental states may not be unique - even within our
finite universe. Whilst it might be unlikely that two brains might ever be
materially identical, it doesn't seem beyond the bounds of possibility that
at some level of granularity two thoughts (or whatever thoughts decompose
into) might be materially identical.

It seems quite plausible that other minds that are not significantly
different from our own and those of our loved ones might exist in other
world which are either entirely separated from our own or which have
decohered from our own (I'm thinking multi-verse). Such a thought seems to
offer little comfort however either to our anxietes about our own deaths or
the sadness we feel when we lose others.

Questions of identity and continuity arise - if this world contains just one
of me then which one of the infinite set of alternative me's will I
associate with in an infinite eternal after-life? having said that I'm
reminded of the very very strange feelings I've had when waking up from
general anaesthetic - where was I during those operations?

But as I've said elsewhere, there are enough mysteries concerning the manner
in which the the mental, material and platonic interact without introducing
other worlds for which there seems to be no evidence and no need.



You misunderstand. What I'm saying is that a zero length interval exists
(and as you say is required for consistency) in the platonic realm but it
does not exist (by the definition of physical existence) in the physical
realm.

I don't think we know this. (I agree that it seems plausible.)

Do you have a view on the nature of the platonic realm and it's realtionship
and distinction from the material world?


There is a clear difference bewteen the real line in the platonic
realm and any physical instantiation of it in the physical realm. In the
platonic realm the real line maps to the closed interval +/-[0,oo]
whereas
in the physcal realm the interval cannot exceed the open interval
+/-(0,oo)
{ok, I slipped the right bracket in}

The real numbers, as generally conceived in pure mathematics, do not
include points at infinity. I don't know why you should insist that
"in the platonic realm" the real line should include infinities.

I think the real line is commonly conceived of as the set of points on an
infinitely long line. The addition of specific points at infinity seems to
me to be a convenience for use in projective geometries or set theories.


Now you are pulling yourself up by your bootlaces. The whole point of
the
HH paradox was to illustrate a significant difference between a finite
set
and an infinite set.

Is that supposed to be a paradox? That significantly different things
(finite sets and infinite sets) have significant differences?

The paradox confirms and highlights the fact that finite and infinite
sets
are fundamentally different objects.

What does "fundamentally" mean here? (I think "fundamental" is a word
often used with no definite meaning, like "spiritual".)

It means deeply - as opposed to superficially. In other words, an infinite
set is not a simple extension of a finite set.


There are many things that are true of finite sets and false of
infinite sets. What's paradoxical about that?

Paradoxes arise when a set of statements seemingly give rise to a
contradiction - the paradox drives us to discover the root of the
contradiction. In this case we see that for infinite sets we need to revisit
the equivalence of "there are no vacant rooms" and "no more guests can be
accomodated in their own rooms".


At the very least it warns us
against
assuming that we can treat them in the same way and I suspect that many
of
your fellow Christians have not fully understood that - based on my
experience of discussing these matters face to face.

Michael is no more a Christian than I am. And I am extremely sure
that his understanding of the mathematics of infinite sets is
pretty good.

Apologies if I made the wrong assumption, however this shouldn't be too
relevant to any particular argument.


As you yourself say, consitency comes at the expense of accepting that
"full" is not the same as "unable to accommodate any more guests".

That doesn't seem like a particularly severe expense. It doesn't
even contradict ordinary physical intuition; a vessel can be full
of some gas but still able to accommodate more.


No, I don't think that that is using full in at all the same sense.

If you want to talk about gases then you first need to talk about whether
you mean a gas of identical bosons or fermions and then you need to define a
phase space volume. For bosons the volume can never be full whilst for
fermions it can - hence the different thermodynamic properties of those
types of gas at near absolute zero.


The
only
way I can reinstate the contradiction is by reinstating the equivalence
of
these two statements - which you expressly forbade.

I would put this differently: There is no contradiction, only an
erroneous assumption that two statements are equivalent when they
(1) are not logically equivalent and (2) are not even extensionally
equivalent when applied to physical things.


In a finite world the statements; "there are no vacant rooms" and "no more
guests can be accomodated in their own rooms" are certainly logically
equivalent. Since an hotel is a physical thing, (2) is false.

Thanks
Thomas









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