Re: Eternity

On May 11, 9:11 pm, "Thomas" <some...@xxxxxxxxxxxxx> wrote:
[...]
The major laws of thermodynamics were formulated by Boltzman before the true
nature of the atom were understood. They are based on statistical
observations not physical ones - in particular the principle of
equi-partition. Even if god could invent a better circle (ie change the
laws of chemistry) then there is no reason to suppose that the laws of
thermodynamics would no longer apply. And any attempt to tinker with the
statistics (a la Maxwell's Deamon is also doomed to failure).

The derivation of the second law of thermodynamics relies on boundary
conditions, required to break time reversibility. For example,
Boltzmann's derivation of the H-theorem makes a crucial assumption of
"molecular chaos".

More to the point, the second law of thermodynamics applies to closed
systems. In say the steady state model, matter is being continuously
created in empty space (albeit at a very low rate).

(Think
of steady state cosmology for example - utterly ruled out by
observations yes, as far as our universe goes, but quite internally
valid as a model.)

I thought these were more or less ruled out by the Penrose-Hawking
singularity hypotheses,

The Penrose-Hawking singularity theorems are results of pure general
relativity. The steady state models postulate an extension of GR.

could you cite a peer reviewed paper which presents
an internally valid model of a steady state universe?

Hoyle (1948), "A New Model for the Expanding Universe", published in
Monthly Notices of the Royal Astronomical Society.

See also Weinberg's classic text: Gravitation and Cosmology (J.Wiley,
1972) for a nice explanation.

Besides, I never imagined that heaven would run according to laws of
physics - at least ones that are at all similar to what we're used to.
Heaven might be a purely spiritual realm.

People keep hiding behind this word spiritual, maybe you could explain what
it means.

I mean, we have the material world that we observe, the mental world that we
experience and the platonic world that we scratch the surface of. Surely
there's enough mystery in the way those known worlds operate and interact to
produce the human condition without throwing in another world for which
there seems to be absolutley no evidence and no need. Sounds very much like
the luminferous aether to me.

The issue is not whether there is evidence for a spiritual realm but
whether or not the idea is sound.

Eternality is most easily modelled by letting the time co-ordinate
range over the real number line. (Or perhaps the positive real number
line, if time is meant to have a beginning.) In fact all of the
purported paradoxes you mentioned would, if they actually were
paradoxes, prove that the real number line does not exist.

No they would only rule out the real number line as a physical object if it
were proposed that that line contained more than one infinity of
non-infinitessimals - which it doesn't.

Eh? I don't follow you here.

I am using the word paradox in the sense of a derivation of an actual
contradiction rather than just a conclusion that seems counter-
intuitive, since the former notion is what is relevant if one wants to
argue that something is logically unsound.

No, a paradox is a series of statements that leads to a contradiction.

Which is how I said I was using the term.

[...]
The paradox of the HH is that the Hotel is full and yet manages to
accommodate further guests - I'd describe those statements as contradictory
and hence paradoxical.

There are two possible meanings of the word full: (i) all spaces are
occupied, (ii) it's impossible to free up space by re-jigging. Now (i)
and (ii) are provably equivalent if there are finitely many spaces
(e.g. by induction on the number of spaces) but they are not
equivalent if there are infinitely many spaces. For example HH is full
in sense (i) but not in sense (ii). Unless you can show that (i) and
(ii) are equivalent without making the assumption of finiteness then
you haven't demonstrated a paradox.

Yes, the paradox is that on the one hand the cardinality of the days
spent
working is the same as the cardinality of the days spent playing and on
the
other hand, on any particular day N the elect will have spent millions of
more days partying than working.

Those two statements are not negations of each other and don't appear
to contradict each other in any way that I can see. If you think they
do then you need to explain why. If you manage then in addition to
having disproved eternal life you will also have shown that the set of
natural numbers does not exist.

Let the number of days of work = W and the number of days of play =P.
On the one hand we show that W == P and otoh we show that P = 10^6W
That sounds contradictory (aka paradoxical) to me.

Whether it *sounds* contradictory is not important - what is important
is whether it can be proved to be contradictory. It's easy to prove
those two equations are contradictory if W and P are positive naturals
(or reals). Can you prove it if W and P are (possibly infinite)
cardinals? If not, you have not demonstrated any paradox.

There is no such thing as the "end of the schedule" if the schedule is
eternal so what you're talking about would be not rejigging but
elimination. This is no more contradictory than if, in a finite
schedule, I try to "move" some task I don't like to the sqrt(-1)th day
or to the 30th of February.

It's not at all like referencing the sqrt(-1)th day - that would be a
straight category error.

Nor is it like referencing the 30th Feb since such a day does not exist -
all of the days in the schedule exist and a mechanism is available to
display the schedule for an arbitrary day N.

It's exactly like those two things, precisely because there's no such
thing as the end of the schedule. For example there is no last day of
the schedule.

[...]
Actually, purported paradoxes can never do that, as any object or
concept that lives in the Platonic realm must be just as free from
contradictions as one that exists physically.

Unsound systems can perfectly well exist and be examined in the Platonic
realm - they simply lead to contradictions. Physically unsound systems
cannot exist to be examined - in other words the nature of existence is very
different within the physical and platonic realms.

I think you mean inconsistent not unsound. Unsound has a different
meaning in logic. (A system has the property of soundness if and only
if anything that can be proven by its rules of inference is
semantically valid.)

Anyway: inconsistent theories certainly exist as sets of axioms but
they do not have models. This means that the objects they purport to
describe do not exist (either Platonically or physically). For example
if the HH "paradox" was really a paradox it would show that countably
infinite sets do not exist. In fact that's how mathematicians
generally go about showing that purported objects do not exist (even
mathematically): assume they do, and then show their would-be
properties lead to a contradiction.

Now, we can conceive of as many infinities sitting alongside each other in
the platonic realm as we like, but we can only propose a single temporal
infinity in which to exist. So whilst the platonic realm provides a way of
resolving our paradox (by providing a home for multiple sets of infinite
cardinality) the temporal realm does not. In this regard I also refer you
back to the difference between a physical real number line containing
multiple infinities of infinitiessimals and a platonic real number line
containing multiple infinities of indexes of equal order.

Sorry, you lost me again.

Michael


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