Can There Be An Infinite Number Of Beings? I Don't Think Its Possible!

[MindOverMatter2]

When i speak of numbers here, i am speaking of numbers applied to potential objective reality. I am not speaking about mathematical number systems.

Here is my arguement.

1. You cannot count from the existence of one potential being to an infinite number of potential beings; or rather you cannot actualise an infinite number of potential beings. This is because no matter how far you count, and no matter how many times you actualise a being, you will always have a countable number that is definable as finite by the mere fact that you can count it or actualise it. If you can count it, then it is finite. You cannot reach a maximal number that is by definition infinite; but you can have a “potential infinite”, or an indefinite number of beings that continue forever. But you cannot count to an actual infinity; even if you count for ever, because forever and ever is never fully actual or complete. To put another way; if it is impossible to count to infinity from “1”, then it follows logically that potentially objective numbers can never make up an infinite.
2. It follows from this fact that an infinite number is nonsensical since premise one has demonstrated that it is impossible to have an infinite that has the value of a finite countable number or numbers in respect of potential reality.
3. Thus, an infinite cannot be made up of potential numbers.
4. Therefore there is no such thing as an infinite number of potential beings.
5. The universe is made of potential beings and events.
6. The universe is physical.
7. Therefore, it follows neccessarily that physical reality is finite in its existential duration.
8. This means that there hasn’t always been physical events and there cannot be an infinite number of physical beings.

 

[Jvrlns]

When i speak of numbers here, i am speaking of numbers applied to potential objective reality. I am not speaking about mathematical number systems.

Here is my arguement.

1. You cannot count from the existence of one potential being to an infinite number of potential beings; or rather you cannot actualise an infinite number of potential beings. This is because no matter how far you count, and no matter how many times you actualise a being, you will always have a countable number that is definable as finite by the mere fact that you can count it or actualise it. If you can count it, then it is finite. You cannot reach a maximal number that is by definition infinite; but you can have a “potential infinite”, or an indefinite number of beings that continue forever. But you cannot count to an actual infinity; even if you count for ever, because forever and ever is never fully actual or complete. To put another way; if it is impossible to count to infinity from “1”, then it follows logically that potentially objective numbers can never make up an infinite.
2. It follows from this fact that an infinite number is nonsensical since premise one has demonstrated that it is impossible to have an infinite that has the value of a finite countable number or numbers in respect of potential reality.
3. Thus, an infinite cannot be made up of potential numbers.
4. Therefore there is no such thing as an infinite number of potential beings.
5. The universe is made of potential beings and events.
6. The universe is physical.
7. Therefore, it follows neccessarily that physical reality is finite in its existential duration.
8. This means that there hasn’t always been physical events and there cannot be an infinite number of physical beings.

Hello MindOverMatter2,

I’m a bit confused by your argument, of course, I’m not the brightest person on earth

But couldn’t the consequence of an infinite number of beings existing be that it will take you forever to count them all and not that an infinite number of beings existing is impossible? I’m mean, Are you saying that the possibility of the existance of an infinite number of beings depends on our ability to count them and therefore if we can’t that means it’s impossible for them to exist?

 

[Leela]

When i speak of numbers here, i am speaking of numbers applied to potential objective reality. I am not speaking about mathematical number systems.

Here is my arguement.

1. You cannot count from the existence of one potential being to an infinite number of potential beings; or rather you cannot actualise an infinite number of potential beings. This is because no matter how far you count, and no matter how many times you actualise a being, you will always have a countable number that is definable as finite by the mere fact that you can count it or actualise it. If you can count it, then it is finite. You cannot reach a maximal number that is by definition infinite; but you can have a “potential infinite”, or an indefinite number of beings that continue forever. But you cannot count to an actual infinity; even if you count for ever, because forever and ever is never fully actual or complete. To put another way; if it is impossible to count to infinity from “1”, then it follows logically that potentially objective numbers can never make up an infinite.
2. It follows from this fact that an infinite number is nonsensical since premise one has demonstrated that it is impossible to have an infinite that has the value of a finite countable number or numbers in respect of potential reality.
3. Thus, an infinite cannot be made up of potential numbers.
4. Therefore there is no such thing as an infinite number of potential beings.
5. The universe is made of potential beings and events.
6. The universe is physical.
7. Therefore, it follows neccessarily that physical reality is finite in its existential duration.
8. This means that there hasn’t always been physical events and there cannot be an infinite number of physical beings.

Wy do you conclude that there haven’t always been physical events?

 

[reggieM]

Objective reality – cannot contain an infinite number of beings. The only way to prove that an infinite number exists is to actualize them sometime. If one cannot actualize (bound) the number of infinite beings, then in order to claim that this infinite number exists, we’d be forced to conclude that imaginary beings are the same as objectively real beings.

But since an infinite number of beings could never be bounded (or contained within what is objective), then we can conclude that an infinite number of beings could only exist in the way that non-existent things exist (e.g. it is impossible to observe them). If there is zero possibility of ever observing this infinite number of beings, then this is the same as saying that an infinite number of beings cannot possibly exist.

 

[Leela]

Objective reality – cannot contain an infinite number of beings. The only way to prove that an infinite number exists is to actualize them sometime. If one cannot actualize (bound) the number of infinite beings, then in order to claim that this infinite number exists, we’d be forced to conclude that imaginary beings are the same as objectively real beings.

But since an infinite number of beings could never be bounded (or contained within what is objective), then we can conclude that an infinite number of beings could only exist in the way that non-existent things exist (e.g. it is impossible to observe them). If there is zero possibility of ever observing this infinite number of beings, then this is the same as saying that an infinite number of beings cannot possibly exist.

Why is it important for you to say that an infinite number of beings cannot exist? Infinity isn’t even generally thought of as a number.

 

[reggieM]

Why is it important for you to say that an infinite number of beings cannot exist?

Because we’re discussing this topic?

 

[chrysostim83]

Hi MindOverMatter2,

I agree with Jvrlns that somewhere in your argument lurks an invalid transition from what is humanly possible to what is objectively possible. What is there to prevent an angel from having an infinite number of thoughts?

Leela hits on a good point too. Fans of mathematical logic, for example, know of a way to use a black hole to get a computer to do an infinite number of computations. At the very least, then, an infinite sequence of event is conceivable.

Of course, it could turn out that an infinite number is a metaphysical impossibility, its compatibility with thought and physical laws notwithstanding. My impression is, however, that no one has managed to provide an argument for this without begging the question. For instance, if I remember right, William Lane Craig relies on his intuition that Hilbert’s Hotel is physically impossible.

Peace.

 

[Leela]

Because we’re discussing this topic?

That doesn’t answer the question, which is basically, why are we discussing this topic? Why is it important for you to say that an infinite number of beings cannot exist? What follows from one position on the matter or the other?

 

[hatsoff]

When i speak of numbers here, i am speaking of numbers applied to potential objective reality. I am not speaking about mathematical number systems.

I’m curious: what is “potential objective reality”? Has it anything to do with Aristotelian or Thomist metaphysics? My ignorance here prevents me from engaging your argument.

 

[hatsoff]

That doesn’t answer the question, which is basically, why are we discussing this topic? Why is it important for you to say that an infinite number of beings cannot exist? What follows from one position on the matter or the other?

Well, denying the existence of a so-called actual infinite is a key component in Craig’s Kalam argument. Perhaps denying the existence of an infinite number (within the context of a “potential objective reality”) has something to do with Aquinas’ analogous prime mover argument.

 

[reggieM]

That doesn’t answer the question, which is basically, why are we discussing this topic? Why is it important for you to say that an infinite number of beings cannot exist? What follows from one position on the matter or the other?

Ok, I think that’s the purpose of a philosophical discussion, isn’t it? In other words, it’s best to engage the topic and come up with some kind of conclusion. After that, you need to determine what then follows from the conclusion you’ve reached.

As for what this argument proves – Well, first it means that it would be false to claim that an infinite number of beings can exist.

Why is that good to know? Well, obviously, it helps in any subsequent or different argument where someone might claim that an infinite number of beings can or do exist.

As for why MOM started the thread – I think it’s easy to guess that he’s very interested in philosophical topics and that’s what this thread is focused on.

 

[Leela]

Ok, I think that’s the purpose of a philosophical discussion, isn’t it? In other words, it’s best to engage the topic and come up with some kind of conclusion. After that, you need to determine what then follows from the conclusion you’ve reached.

As for what this argument proves – Well, first it means that it would be false to claim that an infinite number of beings can exist.

Why is that good to know? Well, obviously, it helps in any subsequent or different argument where someone might claim that an infinite number of beings can or do exist.

As for why MOM started the thread – I think it’s easy to guess that he’s very interested in philosophical topics and that’s what this thread is focused on.

It just seems to me that it is only interesting to disprove the claim that an infinite number of beings exists if someone actually makes that claim. Why would you want to disprove something that no one believes? I just can’t figure out why I would ever need to take a side on the matter.

 

[Leela]

Well, denying the existence of a so-called actual infinite is a key component in Craig’s Kalam argument. Perhaps denying the existence of an infinite number (within the context of a “potential objective reality”) has something to do with Aquinas’ analogous prime mover argument.

Ok, then. I’m willing to bite the bullet and accept that the number of physical things in the universe at any given moment is finite. Who would I be disagreeing with in saying so? What follows from my acceptance of this claim.

Best,
Leela

 

[reggieM]

I agree with Jvrlns that somewhere in your argument lurks an invalid transition from what is humanly possible to what is objectively possible.

I think the argument is oriented in a human perspective and within the physical universe.

What is there to prevent an angel from having an infinite number of thoughts?

This is a good question but we’d have to start with the knowledge that angels either could have the power to generate an infinite number of thoughts or they do not. Revelation doesn’t give us the full facts on that – but we’re no longer talking about the physcial universe in any case. Also, an infinite number of thoughts means having the maximum number possible (of thoughts). But angels cannot have the maximum number of thoughts, because angels began to exist with their creation and could not possess all possible thoughts about what happened prior to their existence. They could have a potentially infinite number of thoughts extending from their creation to the future – but that is not different from what we know about every human being. We all will have an infinite lifespan. (!!! It’s remarkable to consider that.)

But our eternal life (that we pray for) extends to an endless future and we’ll never fully “capture” that infinity. We could (I presume) always count back to the date of our birth, even after trillions of years in eternity. So, it’s infinite only in its potential.

Fans of mathematical logic, for example, know of a way to use a black hole to get a computer to do an infinite number of computations. At the very least, then, an infinite sequence of event is conceivable.

This is not an actual infinite set. It’s a potential infinite, but it cannot be “actualized”. Computers have a beginning in time. We could then think it is conceivable that they run forever – but again, we already know that human beings will live to infinity so this is not addressing the question of the physical universe and the beings in the universe as an actual infinite set of beings.

My impression is, however, that no one has managed to provide an argument for this without begging the question. For instance, if I remember right, William Lane Craig relies on his intuition that Hilbert’s Hotel is physically impossible.

I don’t recall him saying that it was intuition, but rather that reason tells us it is physically impossible for the simple reason that it violates any possible means of testing. It’s a logical absurdity and therefore not possible to actualize in the worldview that measures only physical effects from physical matter and processes.

 

[reggieM]

Ok, then. I’m willing to bite the bullet and accept that the number of physical things in the universe at any given moment is finite. Who would I be disagreeing with in saying so? What follows from my acceptance of this claim.

First of all, by accepting this argument you avoid many absurdities and contradictions. So, you have the benefit of a defensable position which follows from the facts which we know about the universe and reality.
Personally, anyone I’ve ever seen who would disagree with the view on this has come up with very weak and equally absurd opinions on how the contrary would be possible.
Basically, it’s indefensible as I see it.

 

[chrysostim83]

I think the argument is oriented in a human perspective and within the physical universe.

The problem Jvrlns and I see (or think we see) is that MindOverMatter2’s argument shows no more than this: if there is an infinite set of objects in space-time, then we human beings cannot possibility count all the objects in that set. This only rules out infinite numbers of physical objects if we humans can, in principle, count every collection of such objects. On the contrary, however, we can’t even do this for finite collections (proof: assuming a human could count 10 items in every second of a 120 year lifespan, the largest number anyone could reach is about 10^11; but there are about 10^21 stars in the universe). Put it this way: why doesn’t MOM2’s argument disprove the possibility of there being 10^(10^(10^(10^10))) physical objects in space-time?

About the angels, I’ve come not to like that point either. After all, angels are finite substances, so it’s unclear how they could have an infinite number of thoughts. (I can think of a possible line of defence, but let’s drop the subject.)

About the computers, let’s leave this alone too, even though I forgot to mention that the computer would carry out the infinitely many computations in a finite period of time with respect to an inertial frame of reference.

On Craig’s views, I was going off this article where he abruptly ends a nice discussion of Hilbert’s Hotel by asking rhetorically, “Can anyone sincerely believe that such a hotel could exist in reality?” Unless he means that his pure, transcendentally valid intuitions rule out the possibility of such a hotel, then all I can say to his argument at that point is, “Well, one could sincerely believe it if and only if one could sincerely believe there could be infinitely many physical objects in space-time.” He might as well have outlawed infinite numbers from the beginning: it comes to precisely the same thing.

Note, incidentally, that if Craig’s question is not taken rhetorically, then the answer is simply “yes.” The philosopher of science, Hartry Field, is famous for arguing that there are an infinite number of points in real, physical space-time.

 

[reggieM]

The problem Jvrlns and I see (or think we see) is that MindOverMatter2’s argument shows no more than this: if there is an infinite set of objects in space-time, then we human beings cannot possibility count all the objects in that set. This only rules out infinite numbers of physical objects if we humans can, in principle, count every collection of such objects. On the contrary, however, we can’t even do this for finite collections (proof: assuming a human could count 10 items in every second of a 120 year lifespan, the largest number anyone could reach is about 10^11; but there are about 10^21 stars in the universe). Put it this way: why doesn’t MOM2’s argument disprove the possibility of there being 10^(10^(10^(10^10))) physical objects in space-time?

The way I understood his argument was not that a single human being was considered, but the sum total of all human beings – if humanity continued to exist even for an infinite period of time. It would still be impossible to count the infinite set of objects. Whereas, your hypothetical number of objects could, eventually, be counted over a period of whatever trillions of years (if humans lived that long). It’s a finite number and therefore falls within the range of possibility.
An infinite number, by its nature, would be forever impossible to circumscribe by counting or measuring. So, (in my interpretation of the argument), when we have a group of physical objects that could never indicate an objective, actualized existence – even by searching for it in an infinite amount of time … then we have to conclude that it is impossible for those physical objects to exist.

On Craig’s views, I was going off this article where he abruptly ends a nice discussion of Hilbert’s Hotel by asking rhetorically, “Can anyone sincerely believe that such a hotel could exist in reality?” Unless he means that his pure, transcendentally valid intuitions rule out the possibility of such a hotel, then all I can say to his argument at that point is, “Well, one could sincerely believe it if and only if one could sincerely believe there could be infinitely many physical objects in space-time.” He might as well have outlawed infinite numbers from the beginning: it comes to precisely the same thing.

It does seem like he’s referring to intuition here (thanks for that link) but I also think that he made the distinction between an actual infinite and a potential infinite – and with that, he rules out the existence of an actual infinite. I’m not familar enough with how that might relate to infinite numbers, but I think the argument is also directed to a physical-universe model and not intellectual abstractions (numbers are symbols that may not reflect an actual, physical reality).

Note, incidentally, that if Craig’s question is not taken rhetorically, then the answer is simply “yes.” The philosopher of science, Hartry Field, is famous for arguing that there are an infinite number of points in real, physical space-time.

I’m in no position to argue against most philosophers, but for whatever its worth – the arguments I’ve encountered which seek to prove that there are an infinite number of “points” anywhere run into the first problem in providing some measurements for what is meant by a “point”. What are the dimensions of a point? If a point is not a physical object, then the argument is referring to symbolic entities, like numbers. It would be like saying “there is an infinite quantity of numbers in the universe”. It’s true that we could never “name” all of the numbers in an infinite set, but in simple terms the quantity of numbers is not limited by anything. There is no biggest possible number, etc.

But once we are dealing with physical objects, then we have some physical properties to deal with – and those properties have an impact on objective reality.

This argument has probably been answered somehow but I haven’t seen it, myself.

 

[Leela]

I’m in no position to argue against most philosophers, but for whatever its worth – the arguments I’ve encountered which seek to prove that there are an infinite number of “points” anywhere run into the first problem in providing some measurements for what is meant by a “point”. What are the dimensions of a point? If a point is not a physical object, then the argument is referring to symbolic entities, like numbers. It would be like saying “there is an infinite quantity of numbers in the universe”. It’s true that we could never “name” all of the numbers in an infinite set, but in simple terms the quantity of numbers is not limited by anything. There is no biggest possible number, etc.

But once we are dealing with physical objects, then we have some physical properties to deal with – and those properties have an impact on objective reality.

This argument has probably been answered somehow but I haven’t seen it, myself.

A point just refers to a specific location in space. Not only are there an uncountable infinity of points in space, there are infinitely many points (also uncountable) on a line segment. This means that for any two locations that are not the same location, there are infinitely many points in between the two locations.

Best,
Leela

 

[chrysostim83]

The way I understood his argument was not that a single human being was considered, but the sum total of all human beings – if humanity continued to exist even for an infinite period of time. It would still be impossible to count the infinite set of objects. Whereas, your hypothetical number of objects could, eventually, be counted over a period of whatever trillions of years (if humans lived that long). It’s a finite number and therefore falls within the range of possibility.
An infinite number, by its nature, would be forever impossible to circumscribe by counting or measuring.

We need to be cautious at this point, because it’s not at all certain that an immortal being couldn’t count an infinite collection. The small amount of set theory I know suggests two ways this could happen.

So, (in my interpretation of the argument), when we have a group of physical objects that could never indicate an objective, actualized existence – even by searching for it in an infinite amount of time … then we have to conclude that it is impossible for those physical objects to exist.

It’s certain that counting over a finite period of time could never furnish us with evidence that an infinite set of physical objects actually exists. But if there were such a set of objects, all that follows is that we could not have direct, inductive evidence that there was. Along these lines, the only way to rule out the possibility of such a set is to claim that we can know everything there is to know about the physical world. Is there any reason to buy that claim?

What are the dimensions of a point?

Must a physical object have dimensions?

But once we are dealing with physical objects, then we have some physical properties to deal with – and those properties have an impact on objective reality.

This is the beginning of good argument against the idea of an infinite collection of physical objects. The only difficulty is working out precisely which properties inherent in physicality exclude the concept of infinity.

 

[reggieM]

We need to be cautious at this point, because it’s not at all certain that an immortal being couldn’t count an infinite collection. The small amount of set theory I know suggests two ways this could happen.

I don’t see how that could be possible, but I’m sure I know an even smaller amount of set theory. Could you explain?

It’s certain that counting over a finite period of time could never furnish us with evidence that an infinite set of physical objects actually exists. But if there were such a set of objects, all that follows is that we could not have direct, inductive evidence that there was. Along these lines, the only way to rule out the possibility of such a set is to claim that we can know everything there is to know about the physical world. Is there any reason to buy that claim?

I like the direction you’re heading in with this because if we could answer, definitely, that it is impossible for us to know everything about the physical world, that would be a major point to build on. So, even with an immortal existence, we could never possibly know all of the physical world, that says a lot. Faith, for example, would be a necessity. The idea of God’s creation could never be ruled out, and science could never possibly answer all of the questions. It would prove that science is inadequate even for knowing the physical world.

We’d have to then ask how it could be proven that it is impossible for us to ever know (with an infinite amount of time), the physical universe. The assumption is that a study of physical laws and materials is not obscured or impenetrable to human reason.

But this is also how we define “objective reality” or “actual things” or “physical universe”. If something cannot ever possibly be verified or actualized through physical means, can we say that it is part of objective-physical-material reality?

For me, this is the good part. Why not consider angels to be part of the objective-actual reality of the universe? The claim is, “we can never scientifically validate the existence of angels”. Ok, but if we conclude that science cannot ever possibly know all of the physical universe – but at the same time, we assert that those physical-but-forever-unobserved things exist, then we can do the same for angels (and for God Himself).

Must a physical object have dimensions?

For the sake of this argument, I think we’re talking about “physical objects that have dimensions and which it is not impossible for their existence to be verified”. So, they have physical properties and take up some space in the universe and could possibly be observed.

If we said that they can only be observed indirectly, then why can’t we say the same thing about evidence for the existence of God?

This is the beginning of good argument against the idea of an infinite collection of physical objects. The only difficulty is working out precisely which properties inherent in physicality exclude the concept of infinity.

I agree that more has to be worked out, and thanks for some excellent challenges on this.

Another important factor is what we mean when we say something “exists”.
In the materialist view, the origin of everything has to be traced to matter and natural laws. So, thoughts are “physical things”. There can be no non-material things at all.

Numbers, supposedly, would all need to be assigned to specific parts of the human brain and could only represent material things and not abstract concepts.