In Reply to: Hillbert's Hotel posted by MG on November 05, 2006 at 03:22:09:
MG:
Actually, I really WOULD like to read your own description of Hilbert's Hotel.
It IS a fascinating concept, that of infinity; is it not? All the way from "one plus one equals two" to the question of the "infinity" concept, we are still nagged by the begging of the question of, "Yes, but one "what"?", so that we are faced with the reality that math is a numerical metaphor for any reality it is attempting to enumerate and describe in some way, from simple arithmetical counting, through algebra and trigonometry to the calculii of differential equations and probability and statistics, including quanta projections.
Math itself, of course, is NEVER the actual "reality", only an "approach", to use a calculus term, towards a description of numerical "events" that may or may NOT have correspondents in space-time; right?.
Soviet atheists were famous for postulating that all matter and its measurable energy was both pre-existently "eternal" and would remain the same in a "steady state" towards any possible future. Then, they proceeded, data-free, to claim that postulate to be "absolutely true" (punishmenet for disagreement was the Gulag Archipelago!); all in the face of ALWAYS observable thermodynamic, and sub-nuclear entropy; measured conventionally, as well as by the probabilistic projection of quantum mechanics.
They lost their highly touted argument among the other less restricted scientists in the world; mostly Americans and Germans in the US working together after WWII. Heisenberg's Uncertainly Principle, Godel's work, and Eistein-Bose calculations shot the "eternality of matter" weak hypothesis down, as well, as did other observations.
So, to trot out a German story about an infinite hotel, is very humorous to me; personally, as a student of history, and a student of science and math with a degree to prove it.
Here is an interesting URL to consider, while contemplating the subject, form one of my favorite current-day analytical philosophers, William Lane Craig:
http://www.leaderu.com/truth/3truth11.html
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Here's just a taste of what he has to say on the subject og Hilbert's Hotel:
"If then it could be made plausible that the universe began to exist and is not therefore eternal, one would to that extent at least have shown the superiority of theism as a rational world view.
Now there is one form of the cosmological argument, much neglected today but of great historical importance, that aims precisely at the demonstration that the universe had a beginning in time.[9] Originating in the efforts of Christian theologians to refute the Greek doctrine of the eternity of matter, this argument was developed into sophisticated formulations by medieval Islamic and Jewish theologians, who in turn passed it back to the Latin West. The argument thus has a broad inter- sectarian appeal, having been defended by Muslims, Jews, and Christians both Catholic and Protestant.
This argument, which I have called the kalam cosmological argument, can be exhibited as follows:
1. Whatever begins to exist has a cause of its
existence.
2. The universe began to exist.
-2.1 Argument based on the impossibility of an
actual infinite.
--2.1.1 An actual infinite cannot exist.
--2.1.2 An infinite temporal regress of
events is an actual infinite.
--2.1.3 Therefore, an infinite temporal
regress of events cannot exist.
-2.2 Argument based on the impossibility of
the formation of an actual infinite by
successive addition.
--2.2.1 A collection formed by successive
addition cannot be actually infinite.
--2.2.2 The temporal series of past events
is a collection formed by successive
addition.
--2.2.3 Therefore, the temporal series of
past events cannot be actually
infinite.
3. Therefore, the universe has a cause of its
existence.
Let us examine this argument more closely."
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Historically, the Greeks, sans data, presupposed the eternality of matter FIRST, as Craig notes.
Arguments, of theists, countered the hypothesis, with both empirical data, as well as with elegant mathematical constructs.; one of which twas the Muslim theistic "Kalam argument".
In consideration of the logics of "cause and effect", there are really only so many possibilities. Few people realize that , after arriving at a necessary "first cause", that people like David Hume, BEFORE anyone postulated the "Big Bang" hypothesis (in its atheistic version, another quite fun topic!) that Humae assumed that an actual "Being" staus might be conferred on the Universe itselef, because of the philosophical considerations invloved.
Actually, the Hindus had that one first, and NOT modern pantheists, or panentheists.
The article is long, but worth the read; IMO!
Cheers!
OT2 (OldtimerToo)