Does an actual infinte exist?

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Moving on…
So how does this affect the existence of God?
Honestly, I don’t think it does. God exists whether or not there is any type of infinity within the universe. However, our concepts about God may be affected by whether or not there exists such an infinity.

I think one of the main flaws with much of our approach to religion in general is that we often try to encapsulate God within our beliefs and concepts. God is beyond any beliefs or concepts we may have. Our concepts about God, as beautiful as they may be, are inevitably going to be incomplete, and hence wrong. The universe is infinitely more complex than any of our theories or ideas about it (and believe me, our ideas about it are pretty complex). And God, not to be trumped by His own creation, is even deeper and more mysterious than our universe.

It’s okay to have concepts of God, but when we elevate those concepts to the level of God, then we run the risk that when those concepts are disproved (and they will be disproved sooner or later, because all concepts are incomplete, in at least some sense), then we could potentially believe that it was God that was disproved.

In fact, when you listen to many (all) of the arguments put forth by atheists, what they are typically doing is disproving a particular concept about God, or a particular interpretation. None of them have ever launched an assault on God Himself, because it is impossible to contain God within the intellect.

Related to that, and also related to the theme of that essay, we also have the unfortunate tendency to reduce God to the residual in our equations. That’s statistical talk for saying “God must be the part of the universe that we can’t explain” (the “residual” is the part of the equation that is not explained by the theory or model).

For instance, one of the themes of this essay was “The universe cannot have come into being without a cause. We don’t know what that cause was. That cause must be God.” In a sense, this approach is no different from saying “The sun moves across the sky. We don’t know why it does that. Must be some God pulling it across with his chariot.”

Taking either of these approaches does no service to anyone. Many people become so wed to their concepts of God that they refuse to listen to any evidence to the contrary. There is a substantial proportion of people in the United States that believes the earth is only 5000 years old. There are other people who think that evolution is a hoax. When these people interact with well-educated people, they are perceived as backwards or unintelligent. This stereotype makes it difficult for many people to seriously investigate religion for themselves, because they have an image of religion as being a collection of fairy tales that are only believed by people that do not know any better.

Furthermore, the amount of the universe that can be explained by conventional science tends to increase over time. That means the residual is always growing smaller. Then many people look at this, and think “Oh, science is explaining so much, and that residual they call God is continually decreasing in importance. Eventually the residual will disappear. There must be no God.”

Other people explain part of the residual and think that they have explained away God. There is a very prominent scientist at Yale (I won’t mention his name), who would tell his students during class that because evolution was able to explain the creation of the various species, it was therefore impossible for God to exist.

You and I know that such a notion is ridiculous. The ability of the theory of evolution to explain certain aspects of nature has no bearing on the existence of God. Yet that poor professor was deceived because he thought God was nothing more than a residual.

Whenever we reduce God to a concept or a residual we make spirituality harder for everyone. Religion loses its credibility in the minds of everyone when such a concept is disproved or some of the residual is explained away. That makes it harder for many people to come to the Light.

Remember that when Jesus was asked, “What is Truth?”, He remained silent.

So, coming back to the point of that long-winded discussion, I don’t think that the density of black holes has any bearing at all on the existence of God. I really hope I didn’t insult you in any of this. I think philosophy is wonderful, but I just feel like it is emphasized a little too much in our traditional approaches to religion. We need a balanced approach. (I have a friend who is in the seminary, and I was just dumbfounded when he told me that they have them spend 4 years studying philosophy. I was like, “Why???” :confused: ) And I certainly don’t think that any argument or theory we can come up with will ever be able to disprove the existence of the Almighty God.
 
Coolduude,

There are two distinct questions.

First, whether an actual infinite may exist.

Second, whether the past series of events is an actual infinite.

Even if we answer in the affirmative regarding the first question, we still cannot conclude that the universe has a finite beginning in time. We must also affirm the second one.

Now, I’m not saying that there is no way to support this, but Craig’s almost automatic assumption that it must be is peculiarly modern. St. Thomas Aquinas famously held both that no actual infinite may exist, and that the past series of events was only an ‘accidental’ infinite, i.e., not a real, actual infinite.

Craig has some interesting reasons, and rarely is treated fairly by interlocutors, but he has a lot of work to do to ram through his argument here, in my opinion.

-Rob
If the question is whether an actual infinite may exist, there is nothing contrary to reason is saying that the universe has always existed, that it has existed from all eternity. Aquinas admits, for the sake of argument in the five proofs for the existence of God, that the universe has always existed. And it is only by Revelation that we know the universe had a beginning in time. A universe that has existed from eternity would still be a universe dependent on God for its existence. It would be sort of like an eternally created universe – a notion very difficult to grasp.

So, depending on the meaning once attaches to “actual infinite” an actual infinite in the foregoing sense, could have been the case, but we know by Revelation that it is not.

Otherwise, we must admit, so it seems, only a potentially infinite, like numbers in which we can always add one more.
 
Infinity is a fascinating test for those who seek the Truth. It matters little to me whether or not it exists, but it is critical for the sake of argument.

Those who use science to explain that “The more mysteries science unravels, the closer we get to proving God doesn’t exist, which we will some day, it’s just a matter of time.” (take note of their hope and faith in THIS regard). The only way they can have ABSOLUTE faith in science to prove that God doesn’t exist is if they believe that ALL OF THE MYSTERIES OF THE UNIVERSE “CAN” BE REVEALED AND ALL TRUTHS “CAN” BE DISCOVERED BY SCIENCE. But, Infinity “CAN’T.”

Any person or scientist who seeks the TRUTH MUST place the TRUTH ahead of their own EGO, otherwise he/she is merely a hypocrite, filtering their own learning, and intentionally staying ignorant. This is where scientists must stop and admit that Infinity, by definition, is unknowable. Therefore, science CAN NOT unlock all the mysteries of the Universe, and science will always have at least one flaw, and, therefore, will always be imperfect, kinda like us sinners. Anyone who denies this is merely placing their own ego AHEAD of TRUTH, which is hypocrisy. Since science will always be imperfect, why do so many have such faith in something that can never be proven?

Once Truth-seekers admit that supreme knowledge of the universe through science is impossible, God vs. science becomes a 50/50, parallel, glass is half empty / half full choice. It’s each individual’s free will choice to make. DesCartes, the father of modern philosophy, chose Catholicism. Science has simply teased us a little since his time. I’m with him.
 
So, let me get this straight: If time had a beginning, then God started it, because any other “starter” would also exist infinitesimally, thereby forcing the Truth-seeker to adopt either God or Infinity. If time had no beginning (infinity), then the “science will solve all mysteries” believers must stop their silly beliefs, because Infinity will never be knowable. Sounds good to me. 👍
 
So, let me get this straight: If time had a beginning, then God started it, because any other “starter” would also exist infinitesimally, thereby forcing the Truth-seeker to adopt either God or Infinity. If time had no beginning (infinity), then the “science will solve all mysteries” believers must stop their silly beliefs, because Infinity will never be knowable. Sounds good to me. 👍
👍:cool:
 
Yes, I quoted myself :rolleyes:

Anyway, the way I see it is this:

The past cannot be infinite (see link)
Therefore, the universe had a beginning*, before which nothing existed.
Something (or should I say someone?) had to create the universe
Therefore, there is a God

*unlike one atheist I’ve heard, who rejected the idea the universe had a beginning. He said that the moment before the Big Bang could be divided into smaller and smaller segments, ad infinitum (sp?). :hmmm:

Also, I should add that the ‘branes’ theory is absurd (I think). Yeah, it’s cool to think about, but it cannot be tested (in true scientific manner) or proved in any way. It is merely speculative. I don’t think it holds much water.
 
Infinity on the small or large end may end up being not that interesting. You approach a limit and never reach it. The number where the limit is could be two; one of those important numbers. By way of analogy humans are in the middle as far as things large and small go. Maybe God isn’t that interested in the extemities. But God and nature seem to depend on those Golden Means and numbers like pi and e. all within that very small range between the square root of negative one and twenty. Maybe there is an endless void but why focus on it. I certainly wouldn’t be out in the vast cold infininte. One great mathematician, Gegor Cantor, went insane by focusing on the infininte.
 
How can you reason this statement? If time was paused at some time in the past, then something HAD to act upon time to get it to start. That “something” that started time must then exist infinitesimally.
I’m guessing that by suggesting time was “paused” you are simply referring to a timeline which has only a finite length into the past. However, regarding the rest, I have no idea what you mean. What are you talking about when you say that “something” can “act upon time to get it to start”? And what do you mean, “exist infinitesimally”?

It sounds to me like you’re assuming we know something about a larger context in which exists the universe and other hypothetical entities, but I for one have no such knowledge.
 
Actually you will never hit 0. You be infinitely away from 0, mathematically.

64/2: 32, 16, 8, 4, 2, 1, 1/2, 1/4, 1/8, 1/16 … 1/(2(m)) where m is the set of all real numbers.
To say that some concept can be divided, fractionated, or added to forever, only reveals a potential infinite. It does not give as an actual infinite.
At the moment, scientifically, this is true for the non-ethereal. How long would a soul exist though? Is it bound by current science? How about an apparition? At least in the concept of faith, infinity must exist right?
That depends on what you intend to mean by the word surely? It might be relatively infinite given a particular context; for example God is infinite because God has no finite boundary. But i don’t think that this is the kind of infinite that the OP had in mind.
 
I’m guessing that by suggesting time was “paused” you are simply referring to a timeline which has only a finite length into the past. However, regarding the rest, I have no idea what you mean. What are you talking about when you say that “something” can “act upon time to get it to start”? And what do you mean, “exist infinitesimally”?

It sounds to me like you’re assuming we know something about a larger context in which exists the universe and other hypothetical entities, but I for one have no such knowledge.
Your quote #6 in this thread:
"I do not find Dr. Craig’s arguments against so-called actual infinities to be persuasive. To be sure, they challenge our intuitions about counting and measurement, but this is no reason to declare them impossible. So I disagree with Dr. Craig when he uses his own intuition to judge what is and is not possible regarding the length of time past.

That said, we neither have any reason to suppose that the past is infinite in length. That information is simply unknown.
"

I interpreted your “we neither have any reason to suppose that the past is infinite in length” to mean that you believe time began at a finite time. Without God’s existence to start time, there is no reason to believe that time would simply start without something acting upon it to start it. If you believe there was a godless beginning of time, then a godless something had to act upon paused time to get it to start. That godless “something” must then exist infinitesimally. If an actual infinity exists, then science is flawed and will never solve all the mysteries of the universe, imho.
 
I interpreted your “we neither have any reason to suppose that the past is infinite in length” to mean that you believe time began at a finite time.
Not exactly. I’m agnostic as to whether or not time had a beginning, although I tend to suspect that it did.
Without God’s existence to start time, there is no reason to believe that time would simply start without something acting upon it to start it. If you believe there was a godless beginning of time, then a godless something had to act upon paused time to get it to start.
It could be that time has a beginning as a brute fact, without explanation. Or it could be that there is some larger context under which we could, if only we knew about it, explain why time has a beginning. Or it could be that God is somehow responsible. We just don’t know.
That godless “something” must then exist infinitesimally.
Do you mean timelessly? I’m not sure what that would mean.
If an actual infinity exists, then science is flawed and will never solve all the mysteries of the universe, imho.
May I ask why you believe that?
 
It could be that time has a beginning as a brute fact, without explanation. Or it could be that there is some larger context under which we could, if only we knew about it, explain why time has a beginning. Or it could be that God is somehow responsible. We just don’t know.
I disagree that there can be no explanation. Either God did it, or something unknowable acted upon time to start it. If you agree that science will never, ever know the answer to this, then I’ll buy it. I’m happy with that answer as long as the seekers of the Truth via science admit that science is inherently and permanently flawed and it cannot be believed as an ideology. As long as scientists are cool with admitting that actual infinity is unknowable instead of claiming that science will eventually know ALL, I’m cool with it.

Quote:
That godless “something” must then exist infinitesimally.

Do you mean timelessly? I’m not sure what that would mean.
see above

Quote:
If an actual infinity exists, then science is flawed and will never solve all the mysteries of the universe, imho.

May I ask why you believe that? see above
 
I disagree that there can be no explanation. Either God did it, or something unknowable acted upon time to start it.
I don’t see why you’re ruling out the possibility that the universe exists as a brute fact (without explanation), or that the larger context is simply unknown (as opposed to unknowable). Perhaps that’s what your intuition tells you to do, but I don’t think we should trust our intuitions outside of our usual experience, if then.
 
To say that some concept can be divided, fractionated, or added to forever, only reveals a potential infinite. It does not give as an actual infinite.
My argument was that infinity is conceptually real. I figure its existence would be impossible to prove seeing as how we cannot observe the past or future. Lets pretend I find a small immovable and unbreakable sphere floating in space. I can state that the sphere is an eternity, having always existed in that shape at that place in the universe regardless of time and space. What would it take to prove such a claim?
That depends on what you intend to mean by the word surely? It might be relatively infinite given a particular context; for example God is infinite because God has no finite boundary. But i don’t think that this is the kind of infinite that the OP had in mind.
Assuming you believe in the ethereal, souls, ghosts, Gods, etc, and that these entities represent all properties that describe an infinity, then it follows that an infinity must exist albeit perhaps not on a physical plane of existence.
 
My argument was that infinity is conceptually real.
Its evident to me that we can have an idea of what it means for something to be an actually infinite number by adding the concepts of infinity, actuality, and number, together; but that doesn’t mean that the concept is coherent. One has yet to know if it is anything more then a linguistic addition that is fundamentally meaningless. We can certainly have the concept of a square triangle, with out being able to imagining it, by adding the words square and triangle together. But if by adding those words together they are found to be necessarily contradictory because of their individual natures, or rather if their incomprehensibility cannot be shown to follow necessarily from the natural act of reality, then we cannot claim that it has a possible existence in actual reality. So the question is, does the words “actual”, “infinite”, and “number”, add up to something that is logically consistent with the act of reality. I don’t think it does. Perhaps you can play word games and create an actual infinite by first assuming its consistency. But in terms of potentiality (strictly one finite number following the other) i don’t think that it is even “conceptually” possible.

You can demonstrate this to yourself by simply asking how many numbers does it take to have an actual infinity. Once you understand that there is no logically possible amount or quantity of numbers that can meaningfully attain an actual infinity of numbers, you will realize that the idea is conceptually flawed; that is once you have a proper understanding of what an actually infinite “quantity” of “numbers” actually entails.
I figure its existence would be impossible to prove seeing as how we cannot observe the past or future.
Its possible to “disprove”, once you accept that the past and the future is definable as one finite measurable moment following the next; or rather, “change” is made up of potential measurable moments.
Lets pretend I find a small immovable and unbreakable sphere floating in space. I can state that the sphere is an eternity, having always existed in that shape at that place in the universe regardless of time and space. What would it take to prove such a claim?
The claim is self contradictory; if one is saying that the sphere exists by proceeding from one potential finite moment to the next.
then it follows that an infinity must exist albeit perhaps not on a physical plane of existence.
That’s the point. “God” is not made up of “quantifiable numbers” or states of change, and thus when one speaks of infinity in regards to God, one means that God has no quantifiable boundaries or physical limits. God is a completely immaterial and timeless expression of being (i use expression here not in the sense of time, but rather in the sense of “nature”). Thus to say that God is an actual infinite is not the same as saying that God is an actually infinite “number”.
 
I don’t see why you’re ruling out the possibility that the universe exists as a brute fact (without explanation).
Because that is the same as saying that reality is fundamentally irrational.

Logic dictates that a thing is either self explanatory (self existent by the intrinsic act of its own nature), or has its explanation in something else.
 
So the question is, does the words “actual”, “infinite”, and “number”, add up to something that is logically consistent with the act of reality.
Is that necessary for a concept? Concepts can exist outside of reality as long as they contain a complete definition.
Perhaps you can play word games and create an actual infinite by first assuming its consistency.
Which is fine, i’m still just playing the what if game here. There is no physical justification supporting or refuting the tangible nature of an infinity.
But in terms of potentiality (strictly one finite number following the other) i don’t think that it is even “conceptually” possible.
I define it, therefore it is a concept. answers.com/topic/infinity It seems like a sound concept to me.
You can demonstrate this to yourself by simply asking how many numbers does it take to have an actual infinity. Once you understand that there is no logically possible amount or quantity of numbers that can meaningfully attain an actual infinity of numbers, you will realize that the idea is conceptually flawed; that is once you have a proper understanding of what an actually infinite “quantity” of “numbers” actually entails.
The numbers and results do not define the infinity. When I gave my example of taking a non zero number and dividing by 2, I was talking about the time it takes to get to absolute 0, which is infinitely long according to how we have defined mathematics.
Its possible to “disprove”, once you accept that the past and the future is definable as one finite measurable moment following the next; or rather, “change” is made up of potential measurable moments.
Your assumption is that time is already predefined. Again, not being able to observe the past and the future I find this a difficult claim to support.
The claim is self contradictory; if one is saying that the sphere exists by proceeding from one potential finite moment to the next.
Given what I stated was an assumption of truth, the claim itself cannot be contradictory.
Thus to say that God is an actual infinite is not the same as saying that God is an actually infinite “number”.
There is no such thing as an infinite number.
 
Because that is the same as saying that reality is fundamentally irrational.

Logic dictates that a thing is either self explanatory (self existent by the intrinsic act of its own nature), or has its explanation in something else.
Unless you’re referring to axioms (which are true because we declare them to be true), then I really have no idea what you mean by “self explanatory” or “self existent by the intrinsic act of its own nature.” However, I can tell you that logic concerns inferential rules, and does not tell us anything directly about whether or not facts must have explanations.
 
There is no such thing as an infinite number.
I used to say that too, but it’s technically incorrect. Indeed, there are infinite numbers, e.g. infinite cardinals and ordinals, and the endpoints of the extended reals. However, you can still say things like this: “Infinity isn’t a number in the traditional sense.” Usually that is a suitable substitute.
 
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