Why is infinite regression held to be impossible?

[TheTrueCentrist]

If an infinite amount of moments preceded a particular moment, the particular moment could never occur!

An infinite number of moments precede every particular moment. I still don’t see why that means they could never occur.

 

[ivebeenshown]

An infinite number of moments precede every particular moment.

This statement is problematic.

I still don’t see why that means they could never occur.

I’ll spell this out in premise/conclusion form. You just let me know if any of my premises are incorrect and why:

P1. Before any given moment may occur, every preceding moment must first occur
P2. If time has no beginning, an infinite quantity of moments must precede any given moment
P3. Infinite quantities do not deplete

Conclusion: If time has no beginning, any given moment can never occur because an infinite quantity of moments, which by definition does not deplete, must first pass.

 

[Cristiano]

An infinite number of moments precede every particular moment. I still don’t see why that means they could never occur.

This statement is problematic…

If time is a continuum you can always have an infinite number of moments that precede a particular moment. It would be similar to the paradoxes discussed by Zeno and Aristotle, but St Thomas and Bertrand Russell debated Aristotle by saying that there can be no motion in an instant that has no duration.

 

[JDaniel]

This statement is problematic.

I’ll spell this out in premise/conclusion form. You just let me know if any of my premises are incorrect and why:

P1. Before any given moment may occur, every preceding moment must first occur
P2. If time has no beginning, an infinite quantity of moments must precede any given moment
P3. Infinite quantities do not deplete

Conclusion: If time has no beginning, any given moment can never occur because an infinite quantity of moments, which by definition does not deplete, must first pass.

Crystal clear! The problem is, so many people understand infinity to be nothing more than a very large actualized number - which, of course, it isn’t.

God bless,
jd

 

[TheTrueCentrist]

For sure, the number of atoms in the universe is finite at 10[sup]80[/sup]. You cannot get an infinite value of anything from a finite value. No object surely can be of infinite dimension (mass, length, etc).
As to the non-observable universe: that is only a potential infinity, and not an actual infinity. We have no idea as to the extent of the reaches of the entire universe, and likely we never will. Your statement of “there could be infinite dimensions…” is completely hypothetical and not an assertion that it is, physically, the case.

But as you say, it is hypothetical. There is nothing immediately obvious about the hypothetical statement that would mean it is physically impossible. So far all you have offered are assertions that it is not the case.

 

[TheTrueCentrist]

This statement is problematic.

I’ll spell this out in premise/conclusion form. You just let me know if any of my premises are incorrect and why:

P1. Before any given moment may occur, every preceding moment must first occur
P2. If time has no beginning, an infinite quantity of moments must precede any given moment
P3. Infinite quantities do not deplete

Conclusion: If time has no beginning, any given moment can never occur because an infinite quantity of moments, which by definition does not deplete, must first pass.

That’s like saying you can’t count to 5 because there are an infinite number of numbers less than 5. However, counting implies a starting point, which we don’t have. Since an infinite timeline has no beginning, at any point in such a timeline an infinite amount of time has actually already passed.

 

[Cristiano]

That’s like saying you can’t count to 5 because there are an infinite number of numbers less than 5. However, counting implies a starting point, which we don’t have. Since an infinite timeline has no beginning, at any point in such a timeline an infinite amount of time has actually already passed.

I think that you are wrong here. An infinite number of points in time have passed but that does not imply that an infinite amount of time has passed. You are mixing two things: points in time and duration.

 

[ivebeenshown]

That’s like saying you can’t count to 5 because there are an infinite number of numbers less than 5. However, counting implies a starting point, which we don’t have.

Actually, it’s not like that. When we say ‘count to 5’ it is understood that we are counting from a particular point on an imagined number line – 0. However, time is much different than a number line, demonstrated by (premise 1):

“Before any given moment may occur, every preceding moment must first occur”

Now, to if there was a stipulation that before you could count to 5, you must count every integer which precedes it, it might be more similar.

Since an infinite timeline has no beginning, at any point in such a timeline an infinite amount of time has actually already passed.

And this is exactly what the problem is. If there is no beginning to time, then an infinite set of moments precedes any given moment (premise 2) – and an infinite set by definition does not deplete (premise 3.) But as we established in (premise 1), a given moment can only occur once every moment which precedes it has occurred.

So considering that an infinite quantity of moments must occur before that given moment must occur, that moment will never occur because an infinite quantity of moments will never finish occurring.

Again, if you have a problem with any of the three premises, I would like to hear it.

 

[Alberti_Devoveo]

But as you say, it is hypothetical.

And that is exactly the point! It is not an actual infinity because it is only hypothetical.

There is nothing immediately obvious about the hypothetical statement that would mean it is physically impossible.

The hypothetical statement is only that: hypothetical. There is nothing physical about it. Thus, it is only a potential infinity and not a physical infinity.

So far all you have offered are assertions that it is not the case.

Au contraire, you are the one who offered assertions that are not the case. You are using the non-observable universe as an example of an actual infinity. I am trying to show you that this is not the case. There is nothing known about the non-observable universe (hence its name); any information about the non-observable universe is only hypothetical (potential) and not actual–this stems because we cannot observe the non-observable universe. Thus, it is logically a potential infinity, and not an actual infinity.

 

[TheTrueCentrist]

Actually, it’s not like that. When we say ‘count to 5’ it is understood that we are counting from a particular point on an imagined number line – 0. However, time is much different than a number line, demonstrated by (premise 1):

“Before any given moment may occur, every preceding moment must first occur”

Now, to if there was a stipulation that before you could count to 5, you must count every integer which precedes it, it might be more similar.

Indeed, I meant counting over the integers (not natural numbers.) In counting, before any number can be counted, the previous number must have been counted.

And this is exactly what the problem is. If there is no beginning to time, then an infinite set of moments precedes any given moment (premise 2) – and an infinite set by definition does not deplete (premise 3.) But as we established in (premise 1), a given moment can only occur once every moment which precedes it has occurred.

So considering that an infinite quantity of moments must occur before that given moment must occur, that moment will never occur because an infinite quantity of moments will never finish occurring.

Again, if you have a problem with any of the three premises, I would like to hear it.

However, there is an infinite amount of time for those infinite moments to deplete. In other words, premise 2 is incorrect. An infinite number of moments depletes in an infinite amount of time.

 

[JDaniel]

That’s like saying you can’t count to 5 because there are an infinite number of numbers less than 5. However, counting implies a starting point, which we don’t have. Since an infinite timeline has no beginning, at any point in such a timeline an infinite amount of time has actually already passed.

TTC:

But we do have a stopping point. “Infinite past time” is an oxymoron. It assumes that an infinity of time has passed. But, how could that be? We are now at this “Now,” and proceeding onward, into that which isn’t. Future time has yet to be and, as such, does not exist. For all intents and purposes, it is mere conjecture.

Think about the passage of infinite time. That does not, and cannot mean, that it had no beginning but has an end. That which is bounded - on either side - is finite.

God bless,
jd

 

[TheTrueCentrist]

TTC:

But we do have a stopping point. “Infinite past time” is an oxymoron. It assumes that an infinity of time has passed. But, how could that be? We are now at this “Now,” and proceeding onward, into that which isn’t. Future time has yet to be and, as such, does not exist. For all intents and purposes, it is mere conjecture.

Think about the passage of infinite time. That does not, and cannot mean, that it had no beginning but has an end. That which is bounded - on either side - is finite.

God bless,
jd

I would be careful with this line of reasoning. People have argued quite a bit about why we only observe time to be passing in one direction, and why we observe the particular time that we do. Indeed, while we have not yet observed the future, I don’t know that we can say for certain that it does not yet exist. Even if the future is not yet determined, time may still actually extend forward.

Even if we take our current time-position to be a boundary, it does not mean that time must therefore be finite. Consider the geometric concept of a ray:
en.wikipedia.org/wiki/Line_%28geometry%29#Ray

 

[JDaniel]

I would be careful with this line of reasoning. People have argued quite a bit about why we only observe time to be passing in one direction, and why we observe the particular time that we do. Indeed, while we have not yet observed the future, I don’t know that we can say for certain that it does not yet exist. Even if the future is not yet determined, time may still actually extend forward.

Even if we take our current time-position to be a boundary, it does not mean that time must therefore be finite. Consider the geometric concept of a ray:
en.wikipedia.org/wiki/Line_%28geometry%29#Ray

TTC:

Yes. Now I see the hypotheticality of it all.

God bless,
jd

 

[ivebeenshown]

Indeed, I meant counting over the integers (not natural numbers.) In counting, before any number can be counted, the previous number must have been counted.

Counting uses natural numbers. You could count integers, but you would be using natural numbers to count them. Now, if you wanted to begin counting integers starting with a particular integer, say -73, you could do that. But if you placed a stipulation on it, that before you can count an integer you must first count all preceding integers, then you could never count any integers because there would be an infinite regress of preceding integers.

However, there is an infinite amount of time for those infinite moments to deplete. In other words, premise 2 is incorrect. An infinite number of moments depletes in an infinite amount of time.

Premise 2 is this: “If time has no beginning, an infinite quantity of moments precedes any given moment” – so I am assuming you mean premise 3, “Infinite quantities do not deplete.”

Only finite quantities may deplete. This is at the very core of the difference between ‘finite’ and ‘infinite’. Consider an infinite set of moments which are yet to pass. If one of the moments in this set passes, there still remains an infinite quantity of moments yet to pass. No matter how many moments pass, the quantity of moments yet to pass remains infinite. Even if these moments keep passing and leaving the set for an infinite amount of time, the quantity of the moments yet to pass will remain infinite.

 

[kama3]

A set can be both countable and infinite. Regression only requires the set to be countable, i.e. that for each event P, we have the causing event, so that Q causes P. But since the preceding phrase uses the for each quantifier, it also applies to the causing event. Since every event is caused, then it results that the causal chain is infinite.

Consider a system which, at some chosen time t_0, has a state s_0. At the next time instant t_1, the system will have the state s_1, at t_2 it will have state s_2 and so on. Consider the function f which describes the next state of the system from its current state, i.e. f(s_n) = s_n+1.

Consider a system which comes into existence at time t_0 in corresponding state s_0. Most people will see no problem in counting future states of the system up to infinity.

They will also note, that time is closely related to the state of the system, and in fact, time is just a method of doing accounting of system states.

But, consider that the function f is reversible, i.e. there exists a function g=f^-1 such that g(s_n+1)=s_n . In other words, g will give you a previous state of the system. If you start from state s_0 at t_0, then you can calculate the past state at t_-1 as s_-1 = g(s0). In fact, you can calculate all the past states of the system just like you calculated all future states before – except that you are now counting down to -inf instead of up to +inf.

Next, consider that you have a system which exists in some state s_n. Without external information (not contained in the state of the system!) you cannot tell if the system has just been started (created) in state s_n, or evolved from the past state s_n-1. Even if you assume that the system indeed evolved from earlier state s_n-1, again, you cannot prove if the system was started in state s_n-1, or evolved from s_n-2. And so on.

This is the dreaded Last Thursday problem: you cannot prove that the universe was not created last Thursday in its corresponding state, your memories and all. All you can do is to infer the possible existence of last Wednesday from the evolution of the universe. Yet, most people find the notion of the universe being created last Thursday to be absurd.

By the same vein, you cannot disprove the existence of a pre-BigBang state, which resulted in a Big Bang. In other words, we can back-trace the state of the universe back to the state corresponding to the Big Bang. If someone proposes a state of the universe at t_-1 which would evolve to Big Bang (at t_0) then you cannot tell if the universe had been started in the state s_0, or evolved from s_-1. And again, if you determine that the universe indeed had the s_-1 state, then the question is out about the existence of s_-2. And so on.

Homework problems.

1. Consider a system which undergoes the following state transitions: s_0 → s_1 → s_2 → s_3 → s_4 → s_0. You observe the system in state s_2. What can you tell about past states of the system?
2. As before, but, consider that the state s_0 results in destruction of all information about the past states of the system.
3. Consider a system with the infinite state progression: s_0 → s_1 → s_2 → … in which the initial state s_0 can be caused by any of the three possible prior states: s_A, s_B and s_C, and, in which no information is preserved about the state prior to s_0. Can you tell which of the three states (s_A, s_B or s_C) predated s_0?

 

[WesleyF]

WesleyF:

Your argument begs the question. It assumes that time could only have made passage to the present if there was a first term from which time made passage to the present.

That’s correct. Time could have made passage to the present only if there was a first term from which time made passage to the present. Didn’t you yourself quote Aquinas as saying - “passage is always understood as being from term to term”. Do you agree with this statement or not?

Time can be understood in three senses -

1. that which has already been actualized or achieved (past)
2. that which is being actualized or achieved (present)
3. that which is yet to be achieved (future)

Only the finite can be achieved. Infinity is that which cannot be achieved.

Whatever time has passed has been achieved. If it has been achieved then it must be finite, because only the finite can be achieved. If it is finite, then there are two endpoints. Therefore for time to pass, there must be a first term, or else passage is not possible.

This is how you’re able to say that if time regressed infinitely, an infinite amount of time must have been traversed to the present: you’re assuming there must be a first term. Of course we’ll get an absurdity from an infinitely regressing past if we assume this. But, it’s precisely this assumption that you’re being called to demonstrate; because we couldn’t make that assumption if the past did regress infinitely.

I hope my above comment clarifies my position.

 

[kama3]

What I failed to do, due to my being in a hurry to catch the bus, was extend this to the universe. The observable universe is of known, finite size

The operative word here is observable. Unobservable objects are the ones that the light from them did not reach us yet, due to finite speed of light and finite age of the universe.

You cannot get infinity from a finite value. Thus, a physical infinity does not exist.

At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite.[52] For a non-rotating black hole this region takes the shape of a single point and for a rotating black hole it is smeared out to form a ring singularity lying in the plane of rotation.[53] In both cases the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution.[54] The singular region can thus be thought of as having infinite density.

en.wikipedia.org/wiki/Black_hole#Singularity

Recall that the black hole, which includes the singularity, is finite in mass.

This is already starting to go bad. Citing a drawing by a guy who is famous for making physically impossible three-dimensional scenarios by drawing it in two dimensions as an example for infinity? Hardly plausible. Escher was able to do one thing very well: make optical illusions.

This is a fundamental misunderstanding of Escher. See this: ams.org/notices/201006/rtx100600706p.pdf

The image is finite in size, and nothing tends to infinity here. The smaller & smaller angels & demons can only shrink down to the size of the tip of the pencil point, which is several hundred thousand atoms big (definitely not infinitely small). The line is most certainly not infinite because it can be contained in the circle, which is measurable because it is of finite size.

This drawing is a projection of an infinite plane onto a finite surface. A projection done by scaling the objects according to their distance from the center.

 

[catholictiger]

philosophically I don’t know how to explain it but It think our basic observation of the universe shows that there was a beginning aka the big bang. This tells me there was a beginning.

 

[Alberti_Devoveo]

A set can be both countable and infinite. Regression only requires the set to be countable, i.e. that for each event P, we have the causing event, so that Q causes P. But since the preceding phrase uses the for each quantifier, it also applies to the causing event. Since every event is caused, then it results that the causal chain is infinite.

Consider a system which, at some chosen time t_0, has a state s_0. At the next time instant t_1, the system will have the state s_1, at t_2 it will have state s_2 and so on. Consider the function f which describes the next state of the system from its current state, i.e. f(s_n) = s_n+1.

Let’s just stop for a moment here. You are already beginning to confuse a potential infinity (allowing a set to be infinite) with an actual infinity (something tangible in our world as being infinite). The discussion had, so far, has been with the difference between physical infinity and potential infinity. We all accept potential infinities as permissible, but the physical infinities are what is for debate, not the potential infinity you are arguing here.

Consider a system which comes into existence at time t_0 in corresponding state s_0. Most people will see no problem in counting future states of the system up to infinity.

No! Quite the opposite! Most people see a problem with counting infinity because there is no meaning to infinity minus 5 or infinity minus a billion or infinity minus 10[sup]100000000000[/sup](something you must get to in order to count to infinity). There is no numeric value for either of those mathematical equations. People are comfortable with the concept of counting for an infinite time, but here we are using the term infinite to mean “long duration” and not an actual infinity which you are supposing are one and the same.

They will also note, that time is closely related to the state of the system, and in fact, time is just a method of doing accounting of system states.

Okay…I somewhat disagree on the nature of time than how this is proposed, but I suppose that is a semi-viable definition.

But, consider that the function f is reversible, i.e. there exists a function g=f^-1 such that g(s_n+1)=s_n . In other words, g will give you a previous state of the system. If you start from state s_0 at t_0, then you can calculate the past state at t_-1 as s_-1 = g(s0). In fact, you can calculate all the past states of the system just like you calculated all future states before – except that you are now counting down to -inf instead of up to +inf.

RIght. You could also start at +infinity and count backwards to 0. Unfortunately, for the problem at hand, we are discussing as to whether it is physically possible to perform such an action (counting to/from infinity) rather than is it mathematically possible.

Next, consider that you have a system which exists in some state s_n. Without external information (not contained in the state of the system!) you cannot tell if the system has just been started (created) in state s_n, or evolved from the past state s_n-1. Even if you assume that the system indeed evolved from earlier state s_n-1, again, you cannot prove if the system was started in state s_n-1, or evolved from s_n-2. And so on.

This is the dreaded Last Thursday problem: you cannot prove that the universe was not created last Thursday in its corresponding state, your memories and all. All you can do is to infer the possible existence of last Wednesday from the evolution of the universe. Yet, most people find the notion of the universe being created last Thursday to be absurd.

The “Last Thursday” problem cannot be proven or disproven; bringing it up in conventional discussion on infinite regression is essentially moot. Actually, bringing it up at any point in time is essentially moot; it is a conversation stopper.

By the same vein, you cannot disprove the existence of a pre-BigBang state, which resulted in a Big Bang. In other words, we can back-trace the state of the universe back to the state corresponding to the Big Bang. If someone proposes a state of the universe at t_-1 which would evolve to Big Bang (at t_0) then you cannot tell if the universe had been started in the state s_0, or evolved from s_-1. And again, if you determine that the universe indeed had the s_-1 state, then the question is out about the existence of s_-2. And so on.

You need to spend some time with GR. Space & time are one and the same; when the big bang kicked off is when time began. Time index t[sub]-1[/sub] is completely and utterly meaningless.

Homework problems.

…I do not really have anything to say about this or the poorly stated questions asked (are we in the system, or just outside the system for (1)? If you suggest that a state starts at index 0, then nothing occurs before 0 for (2) or (3), in which case both questions are false dilemma questions).

 

[Alberti_Devoveo]

The operative word here is observable. Unobservable objects are the ones that the light from them did not reach us yet, due to finite speed of light and finite age of the universe.

I have stated several times that this is the point. We have no idea about anything of the non-observable universe, hence it can only logically be a potential infinity, and not an actual infinity.

en.wikipedia.org/wiki/Black_hole#Singularity

Recall that the black hole, which includes the singularity, is finite in mass.

You have no idea what you are talking about here. A black hole is a singularity, it is not actually infinite in density, it is just unknown because physics as we know it breaks down.

This is a fundamental misunderstanding of Escher. See this: ams.org/notices/201006/rtx100600706p.pdf

This drawing is a projection of an infinite plane onto a finite surface. A projection done by scaling the objects according to their distance from the center.

You’ve missed the point completely. Escher takes 3D images that are physically impossible and shows a 2D projection of that makes it appear to be physically possible; this does not mean we can build Escher’s waterfall.
Making the angels & demons appear smaller as you go outwards still does not make an actual infinity. Escher is still bound by the rules of our universe in which he can only draw as small as his pencil allows him and not any smaller. A pencil contains hundreds of thousands of atoms.

You absolutely need to determine the difference between an actual infinity (one that actually exists) and a potential infinity (one that, in theory, could exist but has no ontological analog). You are completely lost in the details of the entire thread and are arguing points that amount to nonsense. The debate is about why a potential infinity does not indicate an actual infinity, not more and more about a potential infinity that you are doing.