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

[Linusthe2nd]

First of all, when dealing with beings, or states, this involves more than simply counting. It involves the actualisation of potency.

Secondly if there is not a highest natural number, then it is in fact the case that God cannot know all quantity of natural numbers, because it is in fact meaningless to speak of “all” natural quantities since there is not an absolute natural quantity. Also there is a difference between conceptual numbers and ontological numbers. One natural number is not the same as “1 man”.

Thirdly, as I was saying in the first paragraph of this post, moving from potency to act is significantly different than counting natural numbers, and so your comparison simply does not apply.

God has a complete actual knowledge of “all” time. Therefore it follows necessarily from this that he cannot have timeless knowledge of a never ending potential infinite, since there will never be an end of all time.

If you are not speaking of an actual infinity ( as you told me ), then why all the above? Obviously, you didn’t mean what you told me. Sure looks like you were talking about an actual infinity to me.

Linus2nd

 

[Linux]

This is simply not true. If there is no conceivable natural number that God does not know, then God knows all of the natural numbers. God’s omniscience entails His knowing all that is conceivable (ie. all that is possible). Likewise, if there is no conceivable state which God does not know, then God actually knows all of the successive states.

This is a circular argument.

You don’t know that it is logically possible for God to know “all” quantity of natural numbers; you are just asserting that his omniscience logically entails this. Like I said there is no such thing as “all” natural numbers, for there is no highest quantity. So it is meaningless to say that God knows all natural numbers.

In any case your comparison of successive states with natural numbers is a red herring and a strawman. Its really irrelevant to my argument whether or not God can have actual complete knowledge of all natural numbers.

Can you please logically address the argument I made instead of this strawman that has been errected.

 

[Linux]

If the whole episode is a game then it is pointless. Why don’t you just invite eveyone to sit down a play a game of Old Maid?

If you don’t know the difference between an actual infinite number and a potentially infinite number, that is really not my problem.

 

[z_0101]

Linux,
It is the teaching of the Church that the Triune God is outside of time and space; thus, being outside of these constructs of MAN, God, is, by definition, not bound to them.

Attempting to limit God to your understanding of the time-space continuum is along the same lines as those that said that Christ was not divine in nature.

:banghead:Once again, all of your infinity talk has no bearing on Heaven. Period.
Read the Book of Revelation (this is a link to the Douay-Rheims version):

The Apocalypse Of Saint John (Revelation) (Click Here)(…) Behold, he cometh with the clouds, and every eye shall see him, and they also that pierced him. And all the tribes of the earth shall bewail themselves because of him. Even so. Amen. I am Alpha and Omega, the beginning and the end, saith the Lord God, who is, and who was, and who is to come, the Almighty.

[z(colour and emphasis mine)]

 

[z_0101]

oh … fine… just to finish your arguement as I see your circle of symantics coming again…

Because I know you will not go read the scripture yourself you can read it here:

The Apocalypse Of Saint John (Revelation) - Chapter 21 (click here)
The new Jerusalem described.

[1] And I saw a new heaven and a new earth. For the first heaven and the first earth was gone, and the sea is now no more. [2] And I John saw the holy city, the new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband. [3] And I heard a great voice from the throne, saying: Behold the tabernacle of God with men, and he will dwell with them. And they shall be his people; and God himself with them shall be their God. [4] And God shall wipe away all tears from their eyes: and death shall be no more, nor mourning, nor crying, nor sorrow shall be any more, for the former things are passed away. [5] And he that sat on the throne, said: Behold, I make all things new.

By our Lord’s own words, in the Gospel, Metaphysics has no bearing upon heaven for all that you think you know will cease and a new exsistance will replace it.

 

[polytropos]

This is a circular argument.

You don’t know that it is logically possible for God to know “all” quantity of natural numbers; you are just asserting that his omniscience logically entails this. Like I said there is no such thing as “all” natural numbers, for there is no highest quantity. So it is meaningless to say that God knows all natural numbers.

There is no circular reasoning here. What you are asserting is that if there is not a highest natural number, then one cannot speak of “all” natural numbers. This is false. God knows all of the natural numbers if there does not exist a natural number which God does not know. It doesn’t matter if the numbers are a potential or actual infinite. Likewise, God knows all successive states if there does not exist, at any time, a state which God does not know. If you refuse to view this as analogy, that is fine, because the principle holds on its own.

For something to be metaphysically impossible, it must be inconceivable. The burden is not on me to show that it is possible for God to know every state in time; the burden is on the person claiming that it is metaphysically impossible to demonstrate that it is metaphysically impossible, which you have not done.

If God knows a given state L, then it follows that God knows the succeeding state L+1; this holds for any state. It is inconceivable that this does not hold for any state, as it would violate divine omniscience. By mathematical induction, there exists no state which God does not know.

It is not an assertion that omniscience entails the knowledge of any potential infinite; God’s omniscience is generally taken to mean that He knows all that is possible, not just all that is actual.

In any case your comparison of successive states with natural numbers is a red herring and a strawman. Its really irrelevant to my argument whether or not God can have actual complete knowledge of all natural numbers.

These are baseless assertions. I gave the reason, “God is external to time. To Him, all states in time are as actual as the natural numbers.” You have fallaciously called this a red herring and a straw man.

If you require a demonstration: Consider the set of infinite successive states. Assign a natural number to each state. We can now discuss the infinity of successive states in terms of the natural numbers.

 

[Linux]

There is no circular reasoning here. What you are asserting is that if there is not a highest natural number, then one cannot speak of “all” natural numbers. This is false.

We are talking about knowledge not speaking. Of course I can say all the “natural numbers”, but not in a literal quantitative sense or context. I cannot say there is a distinct quantity that is all natural numbers. Much less this does not imply that one can know all the natural numbers for the simple reason that there is no such thing as all natural numbers, since that would imply that natural numbers can be completed, which they cannot.

All is meaningless in that which is successively limitless.

 

[Linux]

It is not an assertion that omniscience entails the knowledge of any potential infinite; God’s omniscience is generally taken to mean that He knows all that is possible, not just all that is actual.

You haven’t shown me that it is possible to know all natural numbers. You are just asserting it.

 

[polytropos]

We are talking about knowledge not speaking. Of course I can say all the “natural numbers”, but not in a literal quantitative sense or context. I cannot say there is a distinct quantity that is all natural numbers. Much less this does not imply that one can know all the natural numbers for the simple reason that there is no such thing as all natural numbers, since that would imply that natural numbers can be completed, which they cannot.

We evidently have very different understandings of “all,” but our differences in that realm seem to be semantic. As you note in #5, infinity is not a quantity anyway, just a way of expressing boundlessness. The point is that in a “potential infinite” of successive states, every state is conceivably actual. God’s knowledge is, by definition, infinite (and so boundless), and no less boundless than any sequence of successive states. Hence, there is no state of which God does not know.

There does not seem to me to be any conflict here. Could you flesh out what you think the implications of this are for heaven (or anything else)? Perhaps then we could then move beyond the definition of “all.”

You haven’t shown me that it is possible to know all natural numbers. You are just asserting it.

No, we’re both asserting different definitions of “all.” You are (correct me if I am wrong) saying that “God knows all states” to have no meaning if there is no final state. I am taking it to mean that there is no state which God does not know, whether there is a final state or not.

But as this discussion demonstrates, “all” is just a word too, so you’ll have to clarify what the relevance is the statement “God knows all states” being undefined.

 

[z_0101]

<…>But as this discussion demonstrates, “all” is just a word too, so you’ll have to clarify what the relevance is the statement “God knows all states” being undefined.

This is already done in the case of God by the Lords on words: Post #43 and the following post in #44

 

[Linusthe2nd]

If you don’t know the difference between an actual infinite number and a potentially infinite number, that is really not my problem.

Oh, taking the high road again, I see. I would have thought the person who posted the thread would have made it clear in what sense these things are regarded. Now if the idea is just to play a game, just to do some mathematics he should have made it clear. On the other hand, if he is developing a theoretical argument from which some extrapolation will be made which will have application to realities outside of mathematics, then he should have informed the reader.

To carry on a discussion of mathematics and then, at a future point, it is sprung on the other participants that they have just proven that the Moon is made of green cheese, is a practice in the art of deception, it is to be disingenious.

Linus2nd

 

[Aloysium]

God is omniscient: whether something happened, is happening or will happen in relation to the moment in eternity that I happen to be in, God knows it.
An infinite series of numbers is a construct of the human mind. He knows we think like that.
This does not make sense to you. It makes perfect sense to me. Surrendering one’s mind to God, making use of one’s gifts of the Holy Spirit helps understand these things.

 

[inocente]

It doesn’t seem like Linux is objecting to the number of possible states. I think he is saying that God’s knowledge must be actual, and although an infinite number of successive states is possible, it will never be actual. So can God’s knowledge of an infinite number of successive states be actual?

A potential infinite (as opposed to an actual infinite) number of successes state will never end (and will never be actually infinite), and so there will always be a state that has not yet become actual; in other-words it will never be complete; that is to say there will never be an end to its becoming.

In Gods eternal knowledge, all time is complete ,unchanging, and actual, and thus there is not one more thing to be come actual from God perspective.

Hence there is a contradiction between Gods complete and actual knowledge of time, and an ever changing potential infinite.

Zeno’s paradox tries to have us believe that the race is an inifinite number of states, whereas in reality those states are superfluous since the race is also a single continuum. The states only exist as snapshots in time, and we don’t need to know them, we can know what happens at every instant by using the equations of motion. God is the law maker and knows the math, He knows the continuum and can’t be fooled into thinking it is an infinite number of states.

The lesson behind the paradox is that it’s a mistake to reify concepts such as states, potentiality and actuality, they don’t dictate reality but are just how some philosophers chose to analyze the world.

 

[polytropos]

The lesson behind the paradox is that it’s a mistake to reify concepts such as states, potentiality and actuality, they don’t dictate reality but are just how some philosophers chose to analyze the world.

I agree. Both time and God’s knowledge of states in time increase without bound, and I see the potential/actual distinction as trivial if there is no state of which God cannot know.

 

[Linusthe2nd]

If you don’t know the difference between an actual infinite number and a potentially infinite number, that is really not my problem.

And again :

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

First of all your O.P. stated an actual infinite number of successives states. I don’t know what you mean by " metaphysically " possible but I don’t see how a metaphysica actual would differ from an actual actual?

The point is, you were not talking about just numbers and you were not talking about, some imaginary condition.

Linus2nd

 

[Ben_Quincy]

Let’s keep this thread civil.

Otherwise, it will be closed and infractions will be issued.

 

[z_0101]

that’s it.
you two want to argue in circles that’s fine; I however have had enough of the double talk and the continual attempts at redefining the word and concept of infinity.

Therefore, let us use what “Real Scientists” use and let us put this question of how to define infinites to bed with:

Starting with an nibble from the Britannica

Metaphysical infinities - britannica.com (Click Here)Metaphysical infinities
Perhaps the most familiar context for discussing infinity is in metaphysics and theology. Cantor originated the distinction between the infinities of mathematics, physics, and metaphysics. Although Plato thought of the Absolute as finite, all theologians and metaphysicians from Plotinus (ad 205–270) on have supposed the Absolute to be infinite. What is meant by “the Absolute” depends, of course, upon the philosopher in question; it might be taken to mean God, an overarching universal mind, or simply the class of all possible thoughts.

The Bohemian mathematician Bernard Bolzano (1781–1848) formulated an argument for the infinitude of the class of … (Z: the article continues with some 2000 words)

However, that is not near enough I think to quelling this distraction from the original question so maybe something from our more learned and “Real Scientists” in a compact form?

Aristotle’s Potential-Actual Distinction of Infinity (princeton.edu) (click here)

Aristotle handled the topic of infinity in Physics and in Metaphysics. Aristotle distinguished between infinity in respect to addition and in respect to division.

Aristotle also distinguished between actual and potential infinities. An actual infinity is something which is completed and definite and consists of infinitely many elements, and according to Aristotle, a paradoxical idea, both in theory and in nature. In respect to addition, a potentially infinite sequence or a series is potentially endless; being a potentially endless series means that one element can always be added to the series after another, and this process of adding elements is never exhausted.

As an example of a potentially infinite series in respect to increase, one number can always be added after another in the series that starts 1,2,3,… but the process of adding more and more numbers cannot be exhausted or completed, because there is no end to the process.

In respect to division, a potentially infinite series of divisions is e.g. the one that starts as 1, 0.5, 0.25, 0.125, 0.0625. According to Aristotle, the process of division never comes to an end, and the limit value 0 is never reached, although the division can be continued as long as one wants. This is a crucial difference to the transfinitists, who start with the very notion that the limit value exists and is reached (this is not to say that 0 would not exist; zero is at our disposal).

In contrast to the potential infinity, all the elements of an actually infinite (= transfinite) set are assumed to exist together simultaneously as a completed totality. The term ‘transfinite’ ought to be used instead of ‘actually infinite’ to denote the transfinite sets, because the set-theoretical notion of actual infinity has got nothing to do with actualization in nature.

Opposition from the Intuitionist school
The mathematical meaning of the term “actual” in actual infinity is synonymous with definite, completed, extended or existential[1], but not to be mistaken for physically existing. The question of whether natural or real numbers form definite sets is therefore independent of the question of whether infinite things exist physically in nature.

Proponents of intuitionism, from Kronecker onwards, reject the claim that there are actually infinite mathematical objects or sets. (Also, according to Aristotle, a completed infinity cannot exist even as an idea in the mind of a human.) Consequently, they reconstruct the foundations of mathematics in a way that does not assume the existence of actual infinities. On the other hand, constructive analysis does accept the existence of the completed infinity of the integers.(z: note, there is another link to the full article or no small length!)

We now have what the Peers in Science, especially those working with Metaphysics, have to say and how they define the terms.

So with all of this highbrow (mind you, I did mention that I have a background in Chemistry, Mathematics, and Physics ) jibber-jabber and how it relates to the original question, before this splitting of hairs and walking of Moebius Strips (find the end to that walk, I dare you :hypno: ).

I gave you the answer to the OP not only once but three times (that last time from Gods own words from scripture): post #43 and 44.

Nothing in this existence has any bearing on what Heaven is (or will be from our time perspective).

I say it again; all of this talk about infinite states means nothing as given to us by scripture in the Holy Bible in the Book of Revelation:
For GOD said:

(…) I am Alpha and Omega, the beginning and the end, saith the Lord God, who is, and who was, and who is to come, the Almighty. (…) (…) And he that sat on the throne, said: Behold, I make all things new.

With that, I humbly bow out of what has become a inane thread of circles.
:tiphat:

 

[openmind77]

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

According to Hinduism, the Universe (any Universe) lasts about 311.04 trillion years. After that the physical universe, heaven, hell everything that exists is destroyed, even the Trinity - the three main Gods dissolve into nothingness. Only the very basis of existence (Brahman) remains and survives - this is only really eternal One.

That is a pretty long time with a lot of possible states, but perhaps still not infinite.