Why is infinite regression held to be impossible?

[Alberti_Devoveo]

But this is the problem. We are trying to determine why it is impossible. Assertions like yours have permeated that thread but don’t get us closer to an answer. The OP was curious why people believe actual infinity is impossible, and your answer was “because actual infinity is impossible.”

While we could talk about the limits of this universe, we can’t say anything (scientific (yet)) about universes outside our own. Unless you have a general reason why any actual infinity can’t exist, we have not really gotten anywhere.

I suspect that such a reason will not be given because the Christian conception of God is a being comprised of at least one actual infinity. Therefore, if there were a well articulated reason why a general actual infinity could not exist, it would also apply to God.

You cannot get infinite object from a finite one. That is the general reason as to why an actual infinity does not exist. Our observable universe is finite in size, so nothing in our observable universe is infinite in any dimension. The unobservable universe is complete conjecture and cannot be used as an example about an actual infinity because we literally cannot determine anything about it; thus it must be a potential infinity only.

 

[empther]

More hot air from the A-team: :hey_bud:

The OP was curious why people believe actual infinity is impossible, and your answer was “because actual infinity is impossible.”

A number specifies an exact number ( of real things ) as opposed to all other numbers. An “infinite number” doesn’t specify a number. It’s an oxymoron and a self-contradiction.

An amount specifies an exact amount ( of real stuff ). An “infinite amount” doesn’t specify an amount. It’s an oxymoron and a self-contradiction.

A distance specifies an exact distance ( of real dimensions ). An “infinite distance” doesn’t specify a distance. It’s an oxymoron and a self-contradiction.

And so on.

 

[1AugustSon7]

Now, I suppose the universe must be spatially infinite- otherwise there would be a ‘wall’ at some point marking the end of the universe, which would seem foolish (what would be on the other side of the wall?) Now, if causes can function in a spatial as well as a temporal medium (i.e. a cause can be synchronic with its effect), the spatial infinitude of the universe (if this is conceded) implies the possibility of an infinitude of synchronic causes?

[9] And when [Jesus] had said these things, while they looked on, he was raised up: and a cloud received him out of their sight. [10] And while they were beholding him going up to heaven, behold two men stood by them in white garments.

[11] Who also said: Ye men of Galilee, why stand you looking up to heaven? This Jesus who is taken up from you into heaven, shall so come, as you have seen him going into heaven.

According to Catholic theology, Heaven is an actual place. Our Lord is there with His Body. His Body in Heaven is what we consume here on earth in the Blessed Sacrament. This would necessarily require physical space. The Creed makes this plain also. I think certain protestant sects seize upon this to give the idea that it (heaven) is some planet somewhere- I of course do not agree with that conception.

The underlying danger I am objecting to is an idea that Christ somehow dissolved into a ghost or a spirit or something upon His Ascension, which for me seems to jeopardize the Ressurection or at least potentially its greater significance: indeed, it would seem to dissolve Christ (in the Hypostatic Union), which is the hallmark of Antichrist, according to the Apostle. The Scriptures (e.g. the Apocalypse) also seem to describe Heaven as an actual place. Traditionally I think it was thought to surround the extremity of the cosmos- but that it is and must be a physical place followed upon the fact that Our Lord is united with His Glorified Body in Heaven.

 

[Qoeleth]

You cannot get infinite object from a finite one. That is the general reason as to why an actual infinity does not exist. Our observable universe is finite in size, so nothing in our observable universe is infinite in any dimension. The unobservable universe is complete conjecture and cannot be used as an example about an actual infinity because we literally cannot determine anything about it; thus it must be a potential infinity only.

Of course, infinity is not obsdervable ("as the Psalmist says, “to count your thought I would have to be eternal like you”)- in that sense it exists ‘hypothetically’. But, the fact that it exists ‘hypoethtically’ does not mean it doesn’t also exist. I mean, Black Holes (and other crazy physics stuff) exist hypothetically- one could also say the soul and God are not observable, and therefore exist ‘hypothetically’.

Is there an edge, a wall, to the universe. The consensus seems to be at some point matter just runs out, and there is just space (or non-space). But if it is not space, what is it? But given these regions are unobservable, how do we no there is no matter- that absence of matter is itself no less ‘hypothetical’ than infinity.

 

[empther]

Now, I suppose the universe must be spatially infinite- otherwise there would be a ‘wall’ at some point marking the end of the universe, which would seem foolish (what would be on the other side of the wall?)

There is a “wall”, in a manner of speaking. The “wall” is the curvature of space. Light, or anything, can only go where space is. The curvature of space forces everything back into limited space. There is no “other side”.

Can I explain this? No. Only theoretical physicists can explain it.
Of course, the A-team will use my lack of complete understanding of this idea to try to cast doubt in people’s minds with all kinds of mumbo-jumbo, like they always do.

 

[JDaniel]

But this is the problem. We are trying to determine why it is impossible. Assertions like yours have permeated that thread but don’t get us closer to an answer. The OP was curious why people believe actual infinity is impossible, and your answer was “because actual infinity is impossible.”

While we could talk about the limits of this universe, we can’t say anything (scientific (yet)) about universes outside our own. Unless you have a general reason why any actual infinity can’t exist, we have not really gotten anywhere.

I suspect that such a reason will not be given because the Christian conception of God is a being comprised of at least one actual infinity. Therefore, if there were a well articulated reason why a general actual infinity could not exist, it would also apply to God.

TTC:

As soon as a person correctly understands what “infinity” means, that person can come to the conclusion without outside help. “Infinity” means “ALL.” That is, “EVERYTHING.” A physical infinity would consume EVERYTHING. There is no edge to infinity. There is no beginning of infinity. There is no ending to infinity. An infinite plane is a mathematical concept, i.e., an abstraction. It signifies only what our minds can imagine limitedly, not what may, or does, actually exist. An infinite plane would be nothing more than an imaginary slice of the infinite magnitude. An actual infinity must be a magnitude. Any other use of the term is as a conceptual adjective. For example, an infinite set, or an infinite time.

We can limit the adjective to whatever physical things we want. But, such limiting is nothing more than us trying to understand it from the negative. (Do you see how difficult it is to envision it from the positive?) There’s no such thing as actual ‘infinite number’. In fact, there’s no such thing as ‘actual infinite physical magnitude’. And, there’s no such thing as a ‘composite infinity’, that is, an infinity consisting of parts. If there is space between the outer surface of one part and the outer surface of another part, no matter how small, then there is no infinite magnitude thing, because we have dis-included those spaces. A (potential) infinity of parts would also contain a (potential) infinity of space(s) - places where the thing does not exist.

In order to conceptualize “infinity” one must completely dis-abuse oneself of finite structures. It can only exist in that which is not material.

God bless,
jd

 

[ThinkingSapien]

Of course, infinity is not obsdervable ("as the Psalmist says, “to count your thought I would have to be eternal like you”)- in that sense it exists ‘hypothetically’. But, the fact that it exists ‘hypoethtically’ does not mean it doesn’t also exist.

It sounds like the “hypothetical infinity” of which you speak would be synonymous with the “potential infinity” (or conceptual infinity) that had been referenced in earlier comments. .

Is there an edge, a wall, to the universe.

That’s an unknown. So we can’t say that there is an edge or that there is no edge. In either case it seems that spacetime can expand faster than the speed of light or other electromagnetic radiation. So that may be something that is forever unknowable.

The consensus seems to be at some point matter just runs out, and there is just space (or non-space). But if it is not space, what is it?

It’s unknown as to what exists out in the unknown.

But given these regions are unobservable, how do we no there is no matter- that absence of matter is itself no less ‘hypothetical’ than infinity.

We don’t know anything about the unknown. We can’t say that there is matter beyond the unknown, or that there isn’t matter beyond the unknown. This unknown appears to be unknowable. It’s fun to construct conjectures of what may be out there, but we are stuck being agnostic on the matter.

 

[Alberti_Devoveo]

Of course, infinity is not obsdervable ("as the Psalmist says, “to count your thought I would have to be eternal like you”)- in that sense it exists ‘hypothetically’. But, the fact that it exists ‘hypoethtically’ does not mean it doesn’t also exist.

True, the hypothetical does not mean it does not exist. But it most certainly also means that it does exist. It means we do not know. And because we do not know, the hypothetical infinities must be included in the potential infinity group.

I mean, Black Holes (and other crazy physics stuff) exist hypothetically- one could also say the soul and God are not observable, and therefore exist ‘hypothetically’.

Black holes absolutely do exist. There is loads of empirical evidence for them, all of which stem from gravitational lensing effects. Obviously you cannot see a black hole, but you can tell it exists via alternative methods.
In a similar vein, proof of the existence of God and the soul are derived via alternative methods, and not on visual evidence.

Is there an edge, a wall, to the universe. The consensus seems to be at some point matter just runs out, and there is just space (or non-space).

No, there is no edge, no boundary. The way to think of this is with spheres: if you exist (in 3D) on the surface of a sphere (which we pretend is also 3D), where is the wall? There is none, but the space on the surface where you live is certainly finite. This is much how our universe is.

But if it is not space, what is it?

No one knows. And, very likely, no one will ever know.

But given these regions are unobservable, how do we no there is no matter- that absence of matter is itself no less ‘hypothetical’ than infinity.

We do not know anything about ‘the other side’ (or ‘what the universe is expanding into’). Anything anyone claims about it is conjecture. It is as hypothetical as an actual infinity.

 

[empther]

Quote:
Originally Posted by Qoeleth

forums.catholic-questions.org/images/buttons_khaki/viewpost.gif
But if it is not space, what is it?

No one knows. And, very likely, no one will ever know.

Actually we do know.

Not only is there no space beyond the universe,
there is no “beyond” the universe.

You can’t get there from here.

So the scientists tell us. Don’t ask me to explain it. I can’t.

 

[TheTrueCentrist]

TTC:

As soon as a person correctly understands what “infinity” means, that person can come to the conclusion without outside help. “Infinity” means “ALL.” That is, “EVERYTHING.” A physical infinity would consume EVERYTHING. There is no edge to infinity. There is no beginning of infinity. There is no ending to infinity. An infinite plane is a mathematical concept, i.e., an abstraction. It signifies only what our minds can imagine limitedly, not what may, or does, actually exist. An infinite plane would be nothing more than an imaginary slice of the infinite magnitude. An actual infinity must be a magnitude. Any other use of the term is as a conceptual adjective. For example, an infinite set, or an infinite time.

That sounds an awful lot like: infinite regression is held to be impossible because infinite regression is impossible. Mathematics is one of the best ways to understand infinity, and just because mathematics are abstract does not mean what they describe is not real. Just because your understanding of infinity disallows a real infinity is not an argument. I could claim that the correct understanding of God indicates that it is impossible for God to exist, but that statement would not be convincing to anyone.

We can limit the adjective to whatever physical things we want. But, such limiting is nothing more than us trying to understand it from the negative. (Do you see how difficult it is to envision it from the positive?) There’s no such thing as actual ‘infinite number’. In fact, there’s no such thing as ‘actual infinite physical magnitude’. And, there’s no such thing as a ‘composite infinity’, that is, an infinity consisting of parts. If there is space between the outer surface of one part and the outer surface of another part, no matter how small, then there is no infinite magnitude thing, because we have dis-included those spaces. A (potential) infinity of parts would also contain a (potential) infinity of space(s) - places where the thing does not exist.

In order to conceptualize “infinity” one must completely dis-abuse oneself of finite structures. It can only exist in that which is not material.

The existence of a set of infinite dimensions does not make finite subsets (such as the observable universe) impossible.

 

[TheTrueCentrist]

If there is space between the outer surface of one part and the outer surface of another part, no matter how small, then there is no infinite magnitude thing, because we have dis-included those spaces. A (potential) infinity of parts would also contain a (potential) infinity of space(s) - places where the thing does not exist.

You are seem to be describing the Cantor Set which is an infinite set that has gaps between every element. There are no finite-length regions in a Cantor Set. However, this is not the only way to divide up an infinite region.

 

[JDaniel]

You are seem to be describing the Cantor Set which is an infinite set that has gaps between every element. There are no finite-length regions in a Cantor Set. However, this is not the only way to divide up an infinite region.

TTC:

Go outside, find and bring me a “Cantor Set.”

If you need any help lifting it, let me know.

God bless,
jd

 

[TheTrueCentrist]

TTC:

Go outside, find and bring me a “Cantor Set.”

If you need any help lifting it, let me know.

God bless,
jd

If that is the standard you wish to require for existence, then a prime mover is as impossible as an infinite regression.

 

[JDaniel]

If that is the standard you wish to require for existence, then a prime mover is as impossible as an infinite regression.

TTC:

How is that? We see motion brought about by efficient agency every day, all day. But, we never, ever see a completed infinite regression. Why? Because the latter is impossible! “Infinity” means unactualizability.

In order for “infinity” to become actualized it would have to be actualized within a finite, or aggregative structure. The actualization of a finite structure into an infinity means that there is no space, i.e., room, left for the addition, or subtraction, of anything else. For aggregative structures, such as Time, it means that all of Time is complete. We clearly see that neither of these situations is the case. (Why do you think that the representation of a Cantorian Set consists of a finite number of real numbers, followed by commas or dots, surrounded by finite brackets? And, then, to make it negative, the student merely writes a minus sign!)

Is a potential infinity possible? Possibly. One might be able to make a case for the continuous counting of real numbers, by successive people doing the counting, that goes on and on until, at some point in the unintelligible future, someone says, “We’re done; we have, Ladies and Gentlemen, reached infinity!” Can you conceive that this could occur? Unfortunately, until that point is reached, we have a type of “finity” that we give the name, potential infinity, to.

Many of us switch on a TV set when we want to watch an enticing show. The instant that the set’s electrical impetus un-blocked, its parts-in-series activate. Electrons becoming excited from part to part, and copper wire, does move a bit slower than a photon, but, for our purposes, what we are looking at is a prime mover, of sorts. So, by this small demonstration, we see the electrons flowing after the utilization of the first electron for work. This is a series of efficient causes, each causing the electron before it (or after it) to move along, as we say. Physical matter is all part and parcel of a very large framework of discrete space, that has been called by Yppop, the s-frame. Whether or not motion, per se, truly exists, is a matter of contention among some physicists. But, even if motion is only an illusion to us and other creatures, there must be a singular, intelligent author of the algorithm that gives impetus to the change of configuration of the s-points within the s-frame that provides this illusion. We Christians call this Initial Impetus, “God.”

God bless,
jd

 

[TheTrueCentrist]

How is that? We see motion brought about by efficient agency every day, all day. But, we never, ever see a completed infinite regression. Why? Because the latter is impossible! “Infinity” means unactualizability.

Lets work on your terms then. I will agree for now that something that is infinite is unactualizable. That does not mean it cannot exist. You would agree that God is infinite and unactualizable, but that God exists. Therefore, I claim that an infinite timeline is likewise infinite and unactualizable, as well as existing.

Is a potential infinity possible? Possibly. One might be able to make a case for the continuous counting of real numbers, by successive people doing the counting, that goes on and on until, at some point in the unintelligible future, someone says, “We’re done; we have, Ladies and Gentlemen, reached infinity!” Can you conceive that this could occur? Unfortunately, until that point is reached, we have a type of “finity” that we give the name, potential infinity, to.

This discussion of potential infinity continues to be a distraction and indicates an incomplete understanding of infinity. The question is whether or not an actual infinite regression could exist. The fact that we can not observe an actual infinity in its entirety is not sufficient to reject the possibility of its existence. If it were, we would also have to reject the “God” hypothesis.

You have again been treating an infinite timeline as though it had a beginning, which I claim it does not. The only serious issue that has been raised against the possibility of an infinite timeline so far is that the existence of an infinite amount of time preceding the present time. The argument is that it would therefore be impossible to arrive at the current time, since the time required to do so would be infinite. While this is conceptually very difficult, I believe that the existence of an infinite timeline allows such an arrangement and that it is not paradoxical. Ultimately, it is an insufficient reason to reject the possibility of an actual infinity.

 

[Qoeleth]

If I may throw something in- time is not an actual substance, like water or air. So, while it is true (experientially supported) that there can’t be an infinite quantity of a substance, can the same principle be applied to time.

I mean, we have never actually encountered an ‘end’ or boundary of time. Does it even have ‘ends’ or ‘edges’? In this sense, do we have any meaningful reason for saying time could be finite?

 

[danserr]

Lets work on your terms then. I will agree for now that something that is infinite is unactualizable. That does not mean it cannot exist. You would agree that God is infinite and unactualizable, but that God exists. Therefore, I claim that an infinite timeline is likewise infinite and unactualizable, as well as existing.

This discussion of potential infinity continues to be a distraction and indicates an incomplete understanding of infinity. The question is whether or not an actual infinite regression could exist. The fact that we can not observe an actual infinity in its entirety is not sufficient to reject the possibility of its existence. If it were, we would also have to reject the “God” hypothesis.

You have again been treating an infinite timeline as though it had a beginning, which I claim it does not. The only serious issue that has been raised against the possibility of an infinite timeline so far is that the existence of an infinite amount of time preceding the present time. The argument is that it would therefore be impossible to arrive at the current time, since the time required to do so would be infinite. While this is conceptually very difficult, I believe that the existence of an infinite timeline allows such an arrangement and that it is not paradoxical. Ultimately, it is an insufficient reason to reject the possibility of an actual infinity.

Just a quick note since I don’t have time to jump into the whole discussion. There is an important difference between God’s infinity and the infinity of an infinite regress.

When we say that infinite regress cannot occur, we mean that an actually infinite numer of things cannot exist. (A quantitative infinite).

When we say that God is infinite, we are referring to a qualitative infinite. To say that God is infinite is not to say that He is made of an infinite number of things, but that he is morally perfect, metaphysically necessary, omnipotent, omniscient, etc.

 

[TheTrueCentrist]

Just a quick note since I don’t have time to jump into the whole discussion. There is an important difference between God’s infinity and the infinity of an infinite regress.

When we say that infinite regress cannot occur, we mean that an actually infinite numer of things cannot exist. (A quantitative infinite).

When we say that God is infinite, we are referring to a qualitative infinite. To say that God is infinite is not to say that He is made of an infinite number of things, but that he is morally perfect, metaphysically necessary, omnipotent, omniscient, etc.

An infinite number of things wouldn’t have to exist simultaneously. An infinite number of things might have existed though. An infinite regress is a property of an infinite timeline and so is the historical existence of an infinite number of objects. There is no reason for an infinite number of things to exist at any given point in time though.

 

[empther]

An infinite number of things wouldn’t have to exist simultaneously. An infinite number of things might have existed though. An infinite regress is a property of an infinite timeline and so is the historical existence of an infinite number of objects. There is no reason for an infinite number of things to exist at any given point in time though.

So now there could have been an infinite number of things over time.
So I guess since we’ve already reached infinity, there could not be one more thing?

I thought I’d seen the limits of ridiculousness from the A-team,
but apparently they’re not finished yet. It’s still coming.

 

[JDaniel]

Lets work on your terms then. I will agree for now that something that is infinite is unactualizable. That does not mean it cannot exist.

TTC:

Are you sure you want to say that? Are you really, really sure? If a thing cannot be actualized, it cannot, per definitionem, EVER exist. Period. Only a thing that is actualizable can possibly exist - even if it doesn’t exist at this present moment.

You would agree that God is infinite and unactualizable, but that God exists.

No, I absolutely would not agree with something like that!

Therefore, I claim that an infinite timeline is likewise infinite and unactualizable, as well as existing.

Well, you’re probably young enough to live it over.

This discussion of potential infinity continues to be a distraction and indicates an incomplete understanding of infinity.

The discussion of potential infinity only seems to affect non-theists, that theists outnumber 10 to 1 (ah, those pesky numbers again!) Anyway, I’m in good company.

The question is whether or not an actual infinite regression could exist. The fact that we can not observe an actual infinity in its entirety is not sufficient to reject the possibility of its existence.

That may - allow me to repeat: MAY be true. But, the odds against it being true are astronomical.

If it were, we would also have to reject the “God” hypothesis.

Absurd. The substance of God is either spiritual substance, or continuous space. If it is either, it is actually infinite by virtue of logic and science. The axiom is, no lesser being can create a greater being. So, the worst case scenario is that God is potentially infinite, since everyone admits that He is creating the potentially infinite.

You have again been treating an infinite timeline as though it had a beginning, which I claim it does not.

Not so. I treat it as through it has an end - which is the here and Now. A thing is not infinite if it has any bounds. Eternal, maybe, but not infinite! If you think that it does, then you confirm that it is you that truly has no idea of what infinity is.

The only serious issue that has been raised against the possibility of an infinite timeline so far is that the existence of an infinite amount of time preceding the present time.

Hmmm?

The argument is that it would therefore be impossible to arrive at the current time, since the time required to do so would be infinite. While this is conceptually very difficult, I believe that the existence of an infinite timeline allows such an arrangement and that it is not paradoxical.

That is an excellent example of a bald-faced, unfounded assertion. If a so called timeline ends at the most current Now, it is finite, not infinite. It does not matter when said hypothetical timeline began. It stopped (for reasons unknown to any observer) - therefore more time can be added. I think you the only person out there that does not understand this?

Ultimately, it is an insufficient reason to reject the possibility of an actual infinity.

I recognize that the subject of “infinity” is daunting to someone as wet behind the ears as you seem to be, but, I hope and pray that some day in the near future a light will flick on in your head, that you have an "Ah, ha! moment.

God bless,
jd