The Infinite. Part 11. Mormon Troubles with the Infinite.

Here is the previous part. All parts may be found here. Apologies to the huge cadre of readers who have been waiting on the edges of their collective seats for this for over a year. I just forgot to post it at the time–and then went off on other adventures. You’re welcome. To catch up with what’s here, I recommend subjecting yourself to the pain of following the link above (and similar links in it and its predecessors until you reach the “beginning”).For you, Brad.

One of the axioms of Mormonism is the existence of an infinite supply of matter. This follows from various statements like “this is my work and my glory, to bring to pass the immortality and eternal life of man.” (Moses 1:39.) This process, which many Mormon thinkers have seen as not only the life of God but the life of every exalted person, implies that spirits will never run out. That is, there is either an infinite supply so that the process may continue, or there is an infinite supply of material from which spirits and their corresponding bodies may be “organized.” (Sorry, ex nihilo not allowed.)
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The Infinite. Part 10. The Axiom of Regularity, Theological Tag-alongs, Mormonism.

[Here is part 9. Here’s a page with all parts.]

I’m being very brief here and I don’t want anyone to get the impression that I take lightly the work of sincere people who have thought long and hard over important questions. I leave that to Brad.

Christians (along with Muslims and Jews) have a historically mediated anxiety to *prove* that their God exists. Various attempts abound through history, and some still have followings/advocates. Two that play into Mormonism are the Ontological Argument (OA) and the Cosmological Argument (CA). The OA is often associated with St. Anselm and consists in arguing that the “being than which nothing greater can be conceived” must indeed exist (necessarily).[1]
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The Infinite. Part 9. Abraham, Omega, and Doing Things In Order.

[Here is part 8. All parts may be found here.]

What does it mean for one thing to be less than another? We are natural “orderers” aren’t we? We have ordering intuitions about size, strength, speed, beauty, importance, riches, standard of living, loudness, height, and other stuff. Some of this is reasonably quantifiable, some not so much. As a schoolboy, I learned the hard truth from a sixth grade seat mate, Susan Ortiz: the girls ranked guys on a handsome scale (that wasn’t the only scale, but it was one). Are some people (or animals) more “intelligent” that others? As Mormons we are familiar with this sort of ordering by Deity:
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The Infinite. Part 8. Trouble in Paradise. The good, the bad and the peculiar.

[Part 7 is here. Probably it’s worth reviewing before reading this. All parts may be found here.]

I’ll begin with the Peculiar, or let’s say, Unsettling, or Cautionary. Cantor allowed that “sets” could be defined by any well-formed logical statement. As it happened, this was not precise enough. And by that I mean, you can describe collections of things by well-formed logical statements which are somehow, too large or strange. A first sign of trouble came from British mathematician and philosopher Bertrand Russell, in the form of a paradox. This is not one of those namby-pamby literary/political/economic/theological/legal things where it seems some assumption or other leads to an outlandish or uncomfortable conclusion. No. This is a genuine fault in the system, FULL STOP.

Trouble in paradise.

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The Infinite. Part 7. Paradise.

[All parts may be found here.]
Last time, I briefly introduced you to Georg Cantor (1845-1918), a Russian-born Jewish Christian who became a well-known and in some quarters infamous, mathematician. Cantor systematized much of what perviously was just mystical respect for the infinite.
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The Infinite. Part 6. Mathematics, Physics and Religion in the 19th Century

[See part 5 here. All parts may be found here.]

The Intrigues of the Infinite are coming to play. Whether you are confused by the infinite or have some logical grasp of it, I’m going to take you on a ride through a few of those intrigues of the past. Hold on to your logical pants.
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The Infinite. Part 5. Is there anything infinite?

[All parts may be found here.]
In part 4 I looked at some “large” stuff. Now let’s think a little about the possibility that infinite things may exist.

Depending on the physics or metaphysics you subscribe to, infinite or eternal may be reality. In the physical universe we may live behind an “event horizon.” It’s possible there is a secret universe hiding behind some information barrier (inflation).[1] Think of the universe as existing on the surface of a ballon. There is an horizon.

M31. One of my favorite galaxies. It's bigger than our island.

Someone is blowing up this ballon. As it gets larger, the surface stretches and points formerly close together become further and further apart. There isn’t a real “center” of the universe, but everything is getting further from everything else. Space itself is expanding. Another interesting thing is going on: the further stuff is from you, the faster it is moving away from you.[2] Space is expanding locally, not into some extra dimension and not by pushing out some “edge.”[3]
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The Infinite. Part 4. Or What Makes the Federal Debt Look Tiny.

[All parts may be found here.]
Journalists and pop science writers have a little fun trying to make large numbers “real” to us.[1] For example, a billion dollars in one hundred dollar denomination bills would require about ten standard storage pallets in your garage, stacked 5 feet high or so. A trillion dollars in one hundred dollar bills would occupy a warehouse with 10,000 such pallets. I don’t know what you’d spend it on, but if you spent a million dollars every day since the time of Moses, until now, you may have used up the trillion dollars. Spendthrift! Stacking up a hundred million trillion one dollar bills will get you out a bit more than one light year from earth. (Making that many dollar bills would require more than the mass of the earth – and it would take too long – not to mention the ink.)
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The Infinite. Part 3. The Unexamined Life er, Speech

[Part 1, Part 2. All parts may be found here.]

Last time we agreed that scriptural references to the infinite should be approached with caution and often are not to be taken seriously as pointers to the “actual” infinite. Didn’t we?
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The Infinite. Part 2. Large.

[Here is part 1. All parts may be found here.]

Humans do not deal directly with the infinite and there has been considerable debate on whether the idea makes sense at all. Imprecision is the name of the game where infinity is concerned.

If that isn't Mormon, I don't know what is.

Eventually we will see that trying to codify the idea is difficult and puzzling. It is as much a problem with intuition as logic. But first let’s look at a related discursive family: The Very Large.[1]
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The Infinite. Part 1: The Finite.

This series examines, from a somewhat naive point of view, the meaning of “infinite” in a number of contexts. Joseph Smith delves deeply into the infinite, and in particular in funeral sermons, even though he does not engage it with rigor. (Parts of this series appeared elsewhere. All parts of this series may be found here.)

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