Re: Eternity

(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.)

"Thomas" wrote:

I have no problem with people championing a cause, but
it's strange to see that a failed model of a real universe
should now be presented in support of an eternal one.

Not in support of an eternal universe; rather, in support of the idea
that there is nothing physically (or logically) incoherent about an
eternal universe, even if it is ruled out empirically.

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.

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? :-)

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.)

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.

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".)

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

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.

Since the statements necessarily follow from the assumption that there
exists a world containing infinite days then I cannot use the same
assumption to prove that the statements are contradictory,

Your logic is broken. The whole point of inconsistent theories is that
the same set of assumptions may be used to derive mutually
contradictory propositions.

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.

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.

--
Gareth McCaughan
sig under construc


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