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The Bathtub and Infinity

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While in the bathtub tonight I finally understood what Stanley Jaki meant when he said (more than once) that the universe can not be infinite, for an infinite quantity can never be realized.

That never really sank in until I saw it ... right there in the tub as the water was sinking down the drain.  It is the nature of infinity that it has no limit.  Its very definition means it is indefinite - in-de-finite; it can not be real, composed of things.  It can only be conceptual.  There is no such thing as "an infinite number of things" for infinity is, in one sense, not a "number" (you can never count "up to" infinity), and "things" are always "realized".  By its nature infinity can not be "realized", composed of actual things.

Jaki saw this and saw that this was the fundamental philosophical and mathematic reason that the universe was finite; there were empirical reasons as well.  And if the universe is finite, then materialistic atheists who deify Chance have a big big problem.

Anyway, if you don't get it, maybe some day you will.  It took me several years and a nice hot bath.

Stanley Jaki, OSB (1924-2009)

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Tom Leith said…
I'd read something about this once. The question is "Since the universe is (evidently) expanding, what's it expanding into? What exactly is meant by 'universe'?" One answer is that it expands into [undefined] -- until the universe expands into [undefined] it is no-thing. At least no-thing we can say or know anything about. Since the distances within the universe are finite, we can say the universe is not infinite. But it can (apparently) expand infinitely. Here Frequently Asked Questions in Cosmology.
September 26, 2013 at 6:51 AM
Kevin O'Brien said…
I don't know enough about the current thinking on the expanding universe to comment, Tom - but Jaki used to ask, "Is there a universe?" Here's his proof for it, and it includes the conclusion that the universe is finite. From a commenter on another blog ...

Here is Fr. Jaki’s proof on the reality of the “universe,” I can' remember if it is from A Mind's Matter or one of his other works:

Premise 1: There exists material entities.

Premise 2: All material entities contain quantitatively determinable, measurable properties, in the sense that they can be counted.

Premise 3: Therefore, those entities constitute a coherent system insofar as its parts reveal some basic quantitative properties whereby they can be counted.

Conclusion: And if they can be counted, the universe has to be finite and so the universe must be the strict totality of interacting things.
September 26, 2013 at 10:23 PM
Tom Leith said…
And there's another answer -- the space between the interacting things isn't part of the universe. OK. So maybe the Infinite Improbability Drive will work after all, but not for the reasons we thought. Of course, as much as I like sushi, I really don't want to be turned into a penguin mainly because it would interfere with more important things like getting drunk and dancing with girls. So I should avoid space travel. Probably.
September 27, 2013 at 12:33 PM
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