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

[Linux]

This sentence is bounded by tense.

I fail to understand what you mean; that is to say, I fail to understand why saying this refutes the argument.

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.”

The argument has been stated, I am waiting for you to address it rationally, rather than the strawman you just created.

 

[Linux]

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.

I don’t understand. Can you tell me why you think I am not working with the Christian notion of God?

 

[Prodigal_Son]

The argument has been stated, I am waiting for you to address it rationally, rather than the strawman you just created.

OK, here is your argument:

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…

There is “always and forever”, in my language, means “For all times, God does not know the events that are not yet actual.” And this is vacuously true, because God does not know anything at any time. God’s knowledge is timeless.

You say “God does not know what does not exist.” Either this means (a) he does not know it at some time, which I admit to be vacuously true, or it means (b) he does not know it timelessly. If (b), then timelessly, there is nothing that does not exist. All times are known to God, from “outside” time, no matter how arbitrarily many times there are.

This is why I said that you needed to state your argument in a way that does not rely on saying that there is some time when God does not know something. The point would have to be that God **never **knows the future.

Maybe I’m missing something?

(Please don’t accuse me of creating a strawman. I never attempted to restate your argument and so, by definition, I did not create a strawman. If I misunderstood your argument, it is either a matter of my stupidity, which I surely cannot be blamed for, or your lack of clarity.)

 

[Linux]

OK, here is your argument:

There is “always and forever”, in my language, means “For all times, God does not know the events that are not yet actual.” And this is vacuously true, because God does not know anything at any time. God’s knowledge is timeless.

You say “God does not know what does not exist.” Either this means (a) he does not know it at some time, which I admit to be vacuously true, or it means (b) he does not know it timelessly. If (b), then timelessly, there is nothing that does not exist. All times are known to God, from “outside” time, no matter how arbitrarily many times there are.

This is why I said that you needed to state your argument in a way that does not rely on saying that there is some time when God does not know something. The point would have to be that God **never **knows the future.

Maybe I’m missing something?

(Please don’t accuse me of creating a strawman. I never attempted to restate your argument and so, by definition, I did not create a strawman. If I misunderstood your argument, it is either a matter of my stupidity, which I surely cannot be blamed for, or your lack of clarity.)

Change involves an actualisation of potentiality. God actualises this potentiality. Gods knowledge is identical to his act. God timelessly knows all of time; that is to say all that has ever happened is timelessly actual to God all at once as a complete unchanging whole. There are no time indexes in God’s knowledge if his knowledge is truly timeless. But a potential infinite that never ends is never all of time(that is to say it is never complete), and so evidently it is not possible that God has actual knowledge of a potential infinite that never ends for there is always one more thing to become actual in Gods knowledge. Gods knowledge of time cannot be timelessly complete if time is never complete.

 

[Prodigal_Son]

Change involves an actualisation of potentiality. God actualises this potentiality. Gods knowledge is identical to his act. God timelessly knows all of time; that is to say all that has ever happened is timelessly actual to God all at once as a complete unchanging whole. There are no time indexes in God’s knowledge if his knowledge is truly timeless. But a potential infinite that never ends is never all of time(that is to say it is never complete), and so evidently it is not possible that God has actual knowledge of a potential infinite that never ends for there is always one more thing to become actual in Gods knowledge. Gods knowledge of time cannot be timelessly complete if time is never complete.

I don’t understand the idea of something becoming actual in God’s knowledge. This is a change-statement, since a becoming is an event (a change) and God is not liable to change. There is a formal connection between some real event and God’s knowledge of it: the event is *logically prior *to God’s knowledge, but the event is not temporally prior. (I’m not saying you’re denying any of this, I’m just trying to get clear on a few things.)

The problem that I have with your description is that you speak of logical priority as if it is temporal priority: for example, you say, “there is always one more thing to become actual.” This sounds like a problem, with the temporal language attached. But to say that “the existence of an infinite number of events means that God contains an infinite amount of knowledge” does not sound like a problem. Can you express what you are trying to say without temporally bounded metaphors?

Note: I’m not sure I follow you in defining a change as an actualization of a potentiality. This doesn’t seem to capture motion, for example, unless we simply say that an object’s location is a quality of that object, which simply seems false. But I don’t know if this matters.

 

[z_0101]

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

Thank you, yes they (Real scientists) do. I am such a “real scientist” with a background and degree in Chemistry, Mathematics, and Physics. The concept of Infinite is one of the most difficult to define let alone understand. It is like attempting to Define Heaven… or God’s love for humanity.

Metaphysics is such an old school of philosophy that it is difficult to pin it down, however, it attempts to define the universe in the broadest terms possible. Respectfully, perhaps you should look up the term. Wiki has a, albeit naive, definition that most laymen can handle: en.wikipedia.org/wiki/Metaphysics

IN any case, the question has neither bearing nor effect upon Heaven: Read Revelation.

 

[Linusthe2nd]

Linux

" Change involves an actualisation of potentiality. God actualises this potentiality. Gods knowledge is identical to his act. God timelessly knows all of time; that is to say all that has ever happened is timelessly actual to God all at once as a complete unchanging whole. There are no time indexes in God’s knowledge if his knowledge is truly timeless. But a potential infinite that never ends is never all of time(that is to say it is never complete), and so evidently it is not possible that God has actual knowledge of a potential infinite that never ends for there is always one more thing to become actual in Gods knowledge. Gods knowledge of time cannot be timelessly complete if time is never complete. "

This would not be the case. An actual infinity of events, moving from potentiality to actuality in an incidential manner such as an infinite number of ancestors and progeny, would be known by the Eternal Now of the Divine. His knowledge is Infinite, so it could know an actually existing infinity of things. His knowledge is at least coextensive with whatever actually exists.

Linus2nd

 

[Viola_Incognita]

I don’t understand. Can you tell me why you think I am not working with the Christian notion of God?

This may be why…

…]Gods knowledge of time cannot be timelessly complete if time is never complete.

Time will be complete. The world will end. There will be a new heaven and a new earth. To accept these truths as God has revealed them is part of the “Christian notion of God.”

As said here:

IN any case, the question has neither bearing nor effect upon Heaven: Read Revelation.

May Christ’s peace be with you.

 

[Linux]

Thank you, yes they (Real scientists) do. I am such a “real scientist” with a background and degree in Chemistry, Mathematics, and Physics. The concept of Infinite is one of the most difficult to define let alone understand. It is like attempting to Define Heaven… or God’s love for humanity.

Metaphysics is such an old school of philosophy that it is difficult to pin it down, however, it attempts to define the universe in the broadest terms possible. Respectfully, perhaps you should look up the term. Wiki has a, albeit naive, definition that most laymen can handle: en.wikipedia.org/wiki/Metaphysics

IN any case, the question has neither bearing nor effect upon Heaven: Read Revelation.

An infinite number of universes is not measurable, so it is simply false to claim that there is a peer review accepted scientific theory that there is an infinite number of universes.

I don’t care who you claim to be.

 

[Linusthe2nd]

An infinite number of universes is not measurable, so it is simply false to claim that there is a peer review accepted scientific theory that there is an infinite number of universes.

I don’t care who you claim to be.

I’m really glad to hear you say that, it shows the situation is not impossible. But your logic is horrible, what is the difference between an infinite number of successive states and infinite number of universes? I know the answer, do you?

Linus2nd

 

[Prodigal_Son]

I’m really glad to hear you say that, it shows the situation is not impossible. But your logic is horrible, what is the difference between an infinite number of successive states and infinite number of universes? I know the answer, do you?

Linus2nd

Linus, he seems to be saying that an infinite number of universes is not measurable, so is not subject to scientific theory. If that’s what he means, I’m not sure if he’s correct about the science (why can’t science hypothesize infinities?), but it certainly doesn’t imply either that there could *not *be an infinite number of successive states or an infinite number of universes.

 

[inocente]

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

I think you’re giving Zeno’s Achilles and the Tortoise dilemma in another form. Achilles must cross an infinite series of distances to catch the tortoise but of course this doesn’t stop him overtaking. The number of possible states doesn’t depend on an observer’s counting abilities.

 

[Linux]

Linux

This would not be the case. An actual infinity of events, moving from potentiality to actuality in an incidential manner such as an infinite number of ancestors and progeny, would be known by the Eternal Now of the Divine. His knowledge is Infinite, so it could know an actually existing infinity of things. His knowledge is at least coextensive with whatever actually exists.

Linus2nd

I didn’t speak of an actual infinity of events in the post you quoted.

 

[polytropos]

I think you’re giving Zeno’s Achilles and the Tortoise dilemma in another form. Achilles must cross an infinite series of distances to catch the tortoise but of course this doesn’t stop him overtaking. The number of possible states doesn’t depend on an observer’s counting abilities.

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?

To me this does not seem problematic, because it would be impossible to conceive of a state of which God does not know.

 

[Linux]

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?

To me this does not seem problematic, because it would be impossible to conceive of a state of which God does not know.

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.

 

[polytropos]

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

No there isn’t. God can know all the natural numbers even though it is metaphysically impossible to be able to count all of the natural numbers. The fact that time is never actually complete does not prevent God from knowing all of time.

 

[Prodigal_Son]

Linux,

Any response to my latest comments, above? In the terms Polytropos used above, I do not think that there is any possibility of God having merely potential knowledge, so I don’t think there is any necessity of that knowledge “becoming” actual. Actualizing knowledge is something that happens in time.

(Of course, I’m not sure of the notion of actualizing knowledge, at all).

 

[Linux]

No there isn’t. God can know all the natural numbers even though it is metaphysically impossible to be able to count all of the natural numbers. The fact that time is never actually complete does not prevent God from knowing all of time.

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.

 

[polytropos]

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.

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.

An analogy is the way we define limits in mathematics. A limit L exists if, for any specified degree of tolerance ε > 0, there exists some X such that for all x > X, |L - f(x)| < ε. In other words, you must first specify the degree of tolerance and then see if there is a sufficiently large x such that all subsequent values bring the function closer to L than the degree of tolerance. The limit only does not exist if you can find some degree of tolerance for which there does not exist a sufficiently large x. You can always come up with a smaller degree of tolerance, but then you can always find a larger X.

Likewise, God only lacks actual knowledge if you can specify a natural number (or state) which he does not know about. If God knows about any natural number (or state) that is conceivable, then he has actual knowledge of every state. Saying that God cannot have actual knowledge of a potential infinite sequence of states because the sequence is potentially infinite is analogous to specifying a degree of tolerance of ε = 0 and saying that the function never equals L so the limit doesn’t exist.

Note the analogy here is in the way we determine limits, not in what the limits represent.

Another way to state this: If God does not have knowledge of all states of time, then there is a bound or limit on His knowledge of states in time. This requires that it it is conceivable that there is a state of which God does not know. That in itself is incomprehensible.

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.

I disagree. God is external to time. To Him, all states in time are as actual as the natural numbers. The principle holds, in my opinion.

 

[Linusthe2nd]

I didn’t speak of an actual infinity of events in the post you quoted.

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?