H.H.

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Hilbert's Hotel refutes pure actuality?
« on: July 31, 2014, 03:54:24 am »
A hotel with a countably infinite number of rooms at full occupancy can still accommodate not only 1 more guest or ten more guests or a countably infinite number of new guests, but infinitely many coaches with infinitely many guests each. A veridical paradox that seems absurd on the face of it yet nevertheless is mathematically true.

Now my question is whether or not this principle of scaling, transcending infinities carries over to the Divine Infinite Essence? If so then wouldn't the concept of God as Pure Actuality be effectively refuted? We could still say that God is Infinite Actuality but because of this paradoxical aspect of infinity, God would also be infinite potentiality as well. Thus refuting the claim of pure actuality.

Also, does this strengthen the case for pantheism/panentheism? If there is anything to this line of thinking then it seems logical that it would indeed strengthen the case for these concepts considerably.

Maybe this is a silly question but as a good agnostic I have far more questions than answers and I'm sure most of them are silly. So please, any thoughts, criticisms, rebuttals are welcome and appreciated.
some dive into the sea, some toil upon the stone

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Bill McEnaney

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Re: Hilbert's Hotel refutes pure actuality?
« Reply #1 on: June 18, 2016, 06:57:41 pm »
Maybe two points will help.  First, Catholic theologians mean qualitative, non-quantitative  infinity when they say that God is infinite.  Second, in books I've read, Computability and Logic, for example, a countably infinite set is a finite one with too many members for anyone to count.

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Al Graham

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Re: Hilbert's Hotel refutes pure actuality?
« Reply #2 on: November 06, 2016, 12:46:34 pm »
A hotel with a countably infinite number of rooms at full occupancy can still accommodate not only 1 more guest or ten more guests or a countably infinite number of new guests, but infinitely many coaches with infinitely many guests each. A veridical paradox that seems absurd on the face of it yet nevertheless is mathematically true.

Now my question is whether or not this principle of scaling, transcending infinities carries over to the Divine Infinite Essence? If so then wouldn't the concept of God as Pure Actuality be effectively refuted? We could still say that God is Infinite Actuality but because of this paradoxical aspect of infinity, God would also be infinite potentiality as well. Thus refuting the claim of pure actuality.

Also, does this strengthen the case for pantheism/panentheism? If there is anything to this line of thinking then it seems logical that it would indeed strengthen the case for these concepts considerably.

Maybe this is a silly question but as a good agnostic I have far more questions than answers and I'm sure most of them are silly. So please, any thoughts, criticisms, rebuttals are welcome and appreciated.

For me the key question is: according to the analogy, is God's infinite essence represented by the hotel or by the actual and potential guests, whom the hotel accommodates?

If the former, then God is infinite actuality, and has the infinite capacity (let's say 'creativity') to accommodate an infinite number of 'others'.  If the latter, then what could the hotel represent?  Would it not stand in a superior position to God, thus undermining His status as the Supreme Being?

If the analogy is sound, then clearly God must be represented by the hotel, and thus the problem is solved.  The hotel is always 'actual'.
To understand that logic must be valid is to see at once that mind cannot be alien to the nature of the universe. Many people think this is due to the fact that Nature produced the mind. But on the assumption that Nature is herself mindless, this provides no explanation. CS Lewis (abridged)