Is it metaphysically possible to have an actually infinite number of successive states? If not, what does that mean for heaven?

Is it metaphysically possible to have an actually infinite number of successive states? If not what does that mean for heaven?

Why wouldn’t it be?

Start counting up. Let me know when you get to the end.

The better question is, is it metaphysically possible to have an actually finite number of successive states? We exist along a continuum, so I would say no. Just like there are an uncountably infinite number of real numbers between any two real numbers, each person even by existing has already existed in an infinite number of successive states.

Infinity is not a true quantity. It transcends all finite distinctions and therefore cannot be defined or have as its constituents a finite quantity. There is no finite quantity that can add up to a number that by definition transcends finiteness as that would mean that you can complete a succession of ontological numbers. In reality a quantity of successive states is always potentially infinite, and so a quantity is always a finite number away from the first succession.

Are you speaking of numbers or actually existing substances or beings.? If the former, it has no relevance for Heaven one way or the other. Nor would the latter case have any relevance for Heaven. For Thomas has proven the existence of the Eternal God, and it must be assumed that Heaven is the state or condition of His existence. This would be speaking metaphysically.

And it is the Defined Dogma of the Church that Heaven exists. So whether an infinite number of numbers or beings actually existed would have no bearing on Heaven at all.

Linus2nd

I never said anything about the “existence” of heaven. I basically asked how do we understand heaven if an actual infinite number of successive states is impossible.

So if we think about heaven as a succession of states, all we need is that this number be arbitrarily large, and ever-increasing. Heaven isn’t a *bounded *infinity.

I don’t know if we *should *think about heaven as a succession of states, but I don’t see why this question would give us any reason not to.

An infinite set is not metaphysically impossible. It just means that any given element is followed by another element. Counting every element may not be possible, but it is possible to have a boundless quantity of elements.

An ever increasing number of successive states would mean that Gods knowledge of those states would be ever increasing.

What you ask is a variation upon a theme, one of the more well known being:

Schrödinger’s cat (click here)Schrödinger wrote:
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.
—Erwin Schrödinger, Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics), Naturwissenschaften
(translated by John D. Trimmer in Proceedings of the American Philosophical Society)

At some point in time, the cat is both equally alive and dead and until the box is opened, the state of the cat is in infinite flux. The same concepts allow physics to propose the infinite-reality-multiverse.

As for what this means for Heaven? Absolutely nothing.
Heaven transcends what the universe is about and what Science can or cannot say about the universe. Science tells us how the universe goes, and our faith tells us how to go within the universe. (Paraphrased from Galileo Galilei - during his inquisition I believe; however, some attribute this to a Cardinal of the Church at about the same time).

It depends by what you mean by an infinite set. I am talking about an actually infinite number of states, not a potentially infinite number of states.

Real scientists cannot possibly mean an actually infinite number. That is metaphysically impossible.

God’s knowledge does not exist in time, and it is unchanging.

If you are not assuming that Heaven exists, then I fail to see how the question has any relevance at all. Can you explain how it could have a relevance?

Could an actual infinate number of things or states exist? Thomas seemed to think so, as did the ancient Greeks. But we could not actually " see " such an infinity.

Linus2nd

Precisely. Hence the problem. If there is an potentially infinite number of events into the future, it contradicts the idea that God has a full actual knowledge of all events since there is always and forever one more to know about and one more that is yet to be actual. God does not know what does not exist and so his knowledge of that which is forever successive cannot be timeless…

In other words I think it is contradictory to have a timeless knowledge of a potential infinite that never ends and is forever becoming.

Why is this a problem for an infinite being?

This sentence is bounded by tense. Surely an author who holds in his head the entirety of his book can answer questions about this book correctly, even if the book is endless. To say that God is omniscient is not limited to the notion that God is omnipotent NOW.

In other words I think it is contradictory to have a timeless knowledge of a potential infinite that never ends and is forever becoming.

Please derive that contradiction, in an argument. Your argument cannot involve any premise such as “There exists a time t, such that God does not know P at t.”

I have just explained the problem. Why would it not be a problem? Why does saying the word “infinite being”, like it is a magic word, change anything I just said?

If God is by definition an actually infinite number, than I suppose that would be one solution. But God is not a number and neither is an actually infinite number logically possible.

You might have to disclose your definition of God for the class. I don’t think you are working with the assumption of the Christian God.

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