Why is infinite regression held to be impossible?

[empther]

So easy to knock down the A-team. It took me three and a half minutes to research this.

Quote:
Originally Posted by empther

forums.catholic-questions.org/images/buttons_khaki/viewpost.gif
Entropy is not statistical phenomenon. It goes in one direction.
With three college degrees in the sciences, I could write thousands of words on this point, but never mind.

It is statistical:
en.wikipedia.org/wiki/Entropy…rmodynamics%29
_____ “isolated systems”, energy can’t get in or out__________:smiley:

There is a non-zero probability that it can be violated:
en.wikipedia.org/wiki/Fluctuation_theorem
"isolated sytems" again__:smiley:

The second law has been observed to be violated on small scales (from Scientific American):
scientificamerican.com/ar…of-thermodynam
____ “when the system is sufficiently smalll”____________:smiley:

None of this applies to the universe. Or even our human bodies.

 

[TheTrueCentrist]

So easy to knock down the A-team. It took me three and a half minutes to research this.

None of this applies to the universe. Or even our human bodies.

The universe is typically taken to be a closed (isolated) system in thermodynamics, so these things do apply. There are theories that allow the universe to be an open system, but if the system is open then entropy could be reversed simply due to its interaction with things outside the universe. What those things might be is again the subject of speculation.

Violations of the 2nd law can only be observed on small scales, because violation on large scales is astronomically improbable. Astronomically improbable does not mean impossible, and when talking about the timescales involved in the heat death (10^1000 years) things that are highly improbable become likely.

 

[Iron_Donkey]

TheTrueCentrist:

Indeed, we would claim that the infinite regression exists as is. If it is possible for God to exist without beginning, then it is also possible for regression to exist without beginning. What you seem to want to do is create two sets of logic, one of which applies to God, and the other to infinite regression. “Normal” logic applies to material things, but we get to waive certain complications when it comes to “immaterial” things.

Perhaps I will simplify things this way: whatever property God has that you believe allows him to exist without beginning, I claim is also possessed by the infinite regression.

I think we are missing what infinite regression is.

Think of it in terms of an argument with a two year old. Every time you give him an answer, he asks “why?”

Infinite regression is then an argument where you keep giving answers to infinity, with none of them being proven or known to be true before you say them. So every time the two year old asks why, you just give another unproven assertion.

It’s not that it must necessarily give wrong information, it’s that it doesn’t explain anything. Here’s an example:

I claim that 0=1. Why? Because 1=2. Why? Because 2=3. Why? because 3=4. etc

0=1 does follow from 1=2, which does follow from 2=3, etc. None of the implications are bad. They all work. But the argument is bogus, because there is no foundation.

And that’s why infinite regressions fails, not because infinite chains of causation are necessarily impossible, but because by themselves they do not in fact explain anything.

A finite chain of reasoning works because the truth of first premise together with the implications gives that the final claim is true. Infinite regress loses the truth of the first premise since there is no first premise, and does not have the truth known of any of the middle ones (otherwise you’d have a finite regression from that premise). There must be some such truth statement for the implications to yield truth.

So for an infinite chain of physical causes: a priori, this could happen. We don’t know. But it wouldn’t explain why things occured, the question we asked - why is there a universe - would be unanswered by the claim that the universe is as it is now because of how it was a second ago and it was that way because of how it was 2 seconds ago, etc. That could possibly be true, but it doesn’t answer why there is anything.

I’m refraining, with difficulty, from talking about infinite ordinals, but if you’re a mathy person, you might want to check those out.

 

[TheTrueCentrist]

I think we are missing what infinite regression is.

Think of it in terms of an argument with a two year old. Every time you give him an answer, he asks “why?”

Infinite regression is then an argument where you keep giving answers to infinity, with none of them being proven or known to be true before you say them. So every time the two year old asks why, you just give another unproven assertion.

Except in our case the first term is “We exist and were caused by events immediately prior to us.” If you want to argue that we do not exist, that seems like a topic for another thread. Based on this first premise, we conclude that the events prior to us were caused by events prior to them, and so on for an infinitely long series.

 

[Iron_Donkey]

Except in our case the first term is “We exist and were caused by events immediately prior to us.” If you want to argue that we do not exist, that seems like a topic for another thread. Based on this first premise, we conclude that the events prior to us were caused by events prior to them, and so on for an infinitely long series.

The whole point though, is that we’re asking why we exist, not if we exist (or you could say we’re asking for a proof that we exist despite the fact that we know that we do, and where our own experience is not considered as a fundamental answer - that is, I can say know I exist because I think, then you can say fair enough, but why do you think? the why isn’t in fact answered). So if we accept the regress based on the fact that we’re already here, it’s like saying we exist because we exist. Again, if you take any given step in the infinite regress as a given then it’s not an infinite regress at all and there’s no reason to argue about it.

Or, to put it another way, we know that we exist, but knowing that we exist doesn’t explain why. If we ask why we exist, and we say because the universe immediately prior to us was in such a state that we would come to exist soon, that’s fine as far as it goes. But then we’d have ask why that was so, or we haven’t answered the question yet.

And if you say that that is so because the universe prior to that state was in a state that would make it so that the universe must enter into the state that must then produce us, that’s also fine, so far as it goes. But the question still isn’t answered because I don’t know why the universe was in that state. You can repeat this as often as you like, but it won’t ever actually answer the question, even if each causal link is valid, and even if each posited state of the universe actually occurred. It’s not that you’re saying anything wrong, just that the question hasn’t been answered, and asking it an infinite number of times doesn’t make it any more answered. And the question won’t be answered until you get to something that simply must be true.

If you never stop asking why, or if you never step outside of the infinite regress and say “and this infinite series of events happened because ____”, then all you’ve done is given a sequence of implications that doesn’t explain anything because it is fundamentally unexplained. We’re in the 0=1 because 1=2 case again - the implications are fine, and we know that if any one of the things we propose were true then 0 would in fact equal 1, but since we haven’t show that we haven’t shown that 0=1.

Or maybe, we’re in the 3=3 because 4=4 because … because 10^10=10^10 because 0=1 because 1=2 because 2=3 because … case (and the implications there also work). That is, maybe the first so many propositions actually are true and the last couple (well, last infinity) aren’t, but *from this argument *we have no way of knowing that, simply because the argument never bothers to (and indeed can’t) check.

Also, the point you make has the implication arrows going the wrong way. The infinite regression argument says:

now <= before now <= before that <= before that <= before that …

Asking why we exist implies that we are not taking “now” as a given, otherwise, as said, we could say “we exist because we exist.” But even if we did take now as a given, and we showed that now must follow from some hypothetical “before now” stage, that doesn’t directly mean that the before now stage actually happened. And even if it did (but we no longer took “now” as a given since we’re essentially asking “why now”), it wouldn’t make much difference: instead of an infinite chain of implications, we’d have an infinite chain of equivalences, which basically means that we’ve said “if we know why anything in this infinite chain is true then we know why everything else is”. But that’s no better because as soon as we can answer that question for one of the things, we’re no longer in the infinite regress case (so either we haven’t answered the question, or we eventually do but it’s not an infinite regress answer).

 

[empther]

I was hoping TrueCentrist would say this nonsense by the time I got back home tonight, and he didn’t disappoint me.

Quote:
Originally Posted by empther

forums.catholic-questions.org/images/buttons_khaki/viewpost.gif
*So easy to knock down the A-team. It took me three and a half minutes to research this. *

None of this applies to the universe. Or even our human bodies.

The universe is typically taken to be a closed (isolated) system in thermodynamics, so these things do apply.

:extrahappy:

The universe is a closed system in the sense that there is nothing outside to supply energy to it or take energy from it,
but the universe is not a closed system in being trapped inside itself, or being trapped within a fixed space, or in being limited in any way like that.
The universe is always expanding, everything is escaping its previous location, and everything is spreading out more and more diffused ( thinly distributed ) forever with nothing to ever bring it all back together.
That’s entropy.*** Irreversible entropy***.

There are theories that allow the universe to be an open system, but if the system is open then entropy could be reversed simply due to its interaction with things outside the universe. What those things might be is again the subject of speculation.

There is nothing outside the universe. There isn’t even an "outside of " the universe because space is where matter is, as I’ve already quoted scientists as saying. I’m not interested in ridiculous A-team theories.

Violations of the 2nd law can only be observed on small scales, because violation on large scales is astronomically improbable. Astronomically improbable does not mean impossible, and when talking about the timescales involved in the heat death (10^1000 years) things that are highly improbable become likely.

As I’ve already indicated,
everything will fly ever apart more thinly dispersed forever. There is no briinging it all back together.

And this topic is dead. Everything possible has already been said.

 

[Iron_Donkey]

I’ve think I’ve managed to say a fair amount about why the infinite regress doesn’t work to prove things, but I think I failed to ever concisely make the primary point:

Infinite regress cannot be a valid way of proving things because if it were, it would prove things that are false. The 0=1 because 1=2 because 2=3 case is the easiest example.

(Where a “valid way of proving things” is a method which can only spit out statements that are true if any initial (name removed by moderator)uts are true (and infinite regress doesn’t have any (name removed by moderator)uts - neither the conclusion nor the infinite number of preceding steps count, since each is supposed to logically follow from something else within the method of infinite regress) .)

Everything else I said is supposed to be explanation about why it fails, since a counter example doesn’t explain much by itself, but the counter example is enough to show that infinite regress does not, in fact, work.

 

[TheTrueCentrist]

The whole point though, is that we’re asking why we exist, not if we exist

Correct, that is what I was saying. The fact that we currently do exist forms an induction basis. We cannot immediately conclude from that fact that the universe is an infinite regression, but neither can we immediately rule out the possibility.

Or, to put it another way, we know that we exist, but knowing that we exist doesn’t explain why. If we ask why we exist, and we say because the universe immediately prior to us was in such a state that we would come to exist soon, that’s fine as far as it goes. But then we’d have ask why that was so, or we haven’t answered the question yet.

And if you say that that is so because the universe prior to that state was in a state that would make it so that the universe must enter into the state that must then produce us, that’s also fine, so far as it goes. But the question still isn’t answered because I don’t know why the universe was in that state. You can repeat this as often as you like, but it won’t ever actually answer the question, even if each causal link is valid, and even if each posited state of the universe actually occurred. It’s not that you’re saying anything wrong, just that the question hasn’t been answered, and asking it an infinite number of times doesn’t make it any more answered. And the question won’t be answered until you get to something that simply must be true.

If you never stop asking why, or if you never step outside of the infinite regress and say “and this infinite series of events happened because ____”, then all you’ve done is given a sequence of implications that doesn’t explain anything because it is fundamentally unexplained. We’re in the 0=1 because 1=2 case again - the implications are fine, and we know that if any one of the things we propose were true then 0 would in fact equal 1, but since we haven’t show that we haven’t shown that 0=1.

The answer to “why do we exist?” would be “we were produced by an infinite regression.” You may ask “why does the infinite regression exist?” but that is a separate question. We might ask that question if we were trying to decide whether a finite regression was more likely than an infinite one, but we are not.

We are not setting out to prove that 0=1, that would be equivalent to trying to prove that we exist. We have started by taking a statement to be true, and are reasoning based on that.

 

[TheTrueCentrist]

Infinite regress cannot be a valid way of proving things because if it were, it would prove things that are false. The 0=1 because 1=2 because 2=3 case is the easiest example.

We are not trying to prove our current existence based on infinite regression. We have taken our current existence as fact.

 

[TheTrueCentrist]

The universe is a closed system in the sense that there is nothing outside to supply energy to it or take energy from it,
but the universe is not a closed system in being trapped inside itself, or being trapped within a fixed space, or in being limited in any way like that.
The universe is always expanding, everything is escaping its previous location, and everything is spreading out more and more diffused ( thinly distributed ) forever with nothing to ever bring it all back together.

Why the universe (or any system) doesn’t exchange energy with its surroundings is irrelevant. It is traditionally considered a closed system because it doesn’t seem to exchange energy with its surroundings. I am fairly certain that this concept would be covered in the first week of Thermo 101 at any university.

As I’ve already indicated, everything will fly ever apart more thinly dispersed forever. There is no briinging it all back together.

No one is saying that it would be brought back together. If the universe is described by chaotic growth, then it would essentially be a complex multiverse, with regions of space becoming their own universes, and growing infinitely.
en.wikipedia.org/wiki/Chaotic_inflation

There is nothing outside the universe. There isn’t even an "outside of " the universe because space is where matter is, as I’ve already quoted scientists as saying. I’m not interested in ridiculous A-team theories.

As I’ve said, the speculative nature of these theories is why I didn’t want to bring them up. There are theories which support both sides. Unless there is some conclusive scientific evidence to more convincingly prove these theories, then we should leave them out of the debate. A high-school level description of entropy hardly constitutes such a theory.

 

[TheTrueCentrist]

Everything else I said is supposed to be explanation about why it fails, since a counter example doesn’t explain much by itself, but the counter example is enough to show that infinite regress does not, in fact, work.

See the cigar mystery of the Grand Hotel:
en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel#The_Grand_Hotel_Cigar_Mystery

This is essentially what you are trying to point out. You wish to say that it is impossible for us to get a cigar (i.e. be caused) by simply going to the previous time infinitely. However, since we actually got cigars (i.e. actually were caused) we have a basis to begin our regression.

 

[Iron_Donkey]

See the cigar mystery of the Grand Hotel:
en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel#The_Grand_Hotel_Cigar_Mystery

This is essentially what you are trying to point out. You wish to say that it is impossible for us to get a cigar (i.e. be caused) by simply going to the previous time infinitely. However, since we actually got cigars (i.e. actually were caused) we have a basis to begin our regression.

Except induction and regression are backwards. Induction is A(1) => A(2) => A(3) =>…, so if A(1) is true then A is true for every n.

Regression is A(1) <= A(2) <= A(3) <=… . So if A is true for any N, then A is true for all n < N. There is no possible starting point to prove the whole thing true, and certainly A(1) (we exist) doesn’t do the job, because it doesn’t imply (or cause or whatever) any of the others.

Let me use the cigar example. You are in a hotel with infinite rooms into which no cigars are supposed to enter. Yet you have a cigar. We know this. But I ask why you have a cigar, or how you managed to get it into this hotel. (This explanation of how/why is in fact a proof that you have a cigar, where we don’t consider the fact that it’s in your hand as sufficient basis, but anyway.)

You say you went and got the cigar from room 2. Ok, that’s fine. But there aren’t supposed to be any cigars in the hotel, so how did it get into room 2? Well, the guy in room 2 got it from room 3, and the guy in room 3 got it from room 4, etc. That’s all well in good, and maybe even possible, but that doesn’t answer the question: where did the cigar come from?

That is the question. The infinite regress doesn’t ever answer that question, and the fact that the cigar is in the hotel just tells us what the final statement of our explanation should be (that I am enjoying a cigar in room 1). It does not give us the chain of events that leads to it being there, and it certainly doesn’t mean that any chain of events that would lead to it being there actually happened, or even that any chain of events that leads to it could be possible.

I think I may have been confusing with my word choice earlier. The fact is though, that any answer to the question “why are we here” that actually answers the question must actually prove (or cause/lead to if you prefer that terminology) that we are here without taking it as a given. So we are in fact looking for a proof that we are here, because any explanation of why we are here would prove that we are, even if we (somehow) were unaware of the fact.

Otherwise, if you do not require our explanation to prove that what they explain occurred without assuming that they did, I could say “We are here because I like cheese”. For obviously the facts “we are here” and “I like cheese” together prove (lead to) the fact that we are here. But that is, I think you’ll agree, a rather meaningless notion of explanation - essentially saying that everything is self explaining and also saying that there are perfectly valid explanations for things that are not in fact true, which makes no sense (not to mention everything being explained by its negation eg “I am here because I am not here”).

 

[Poseidon]

I am new to this thread and didn’t read all 12 pages of comments before posting this, so if I’m repeating something I apologize. I think that this question is not a philosophical one, but a matter of physics. The question of whether infinite regression is possible isn’t really answerable with out present knowledge of physics. The universe has a finite age: 13.7 billion years. It started with the big bang, and before the big bang the universe did not exist. At present, we have no idea what happened “before” the universe (before is in quotes because time is a dimension of the universe, so there really was no before the universe. Time started with the big bang).

There are a lot of theories on what caused the universe to exist. God is obviously one guess. Some people say that there is a multiverse, or a kind of “soap bubble” conglomeration of universes (think the bubbles in a bubble bath, and each bubble represents a universe) that is constantly budding off new universes. Some people think that each time a black hole forms it pinches off a part of that universe, causing a new one to form. Some people say that the universe simply appeared out of nothing. All of these explanations (except for the “appeared out of nothing” one) still don’t explain where the universe, multiverse, or whatever originally came from. Therefore people conclude that there must have been something to cause everything that exists to appear. That something, according to the proof of Aquinas, is God.

 

[CGDouglas]

Except induction and regression are backwards. Induction is A(1) => A(2) => A(3) =>…, so if A(1) is true then A is true for every n.

Regression is A(1) <= A(2) <= A(3) <=… . So if A is true for any N, then A is true for all n < N. There is no possible starting point to prove the whole thing true, and certainly A(1) (we exist) doesn’t do the job, because it doesn’t imply (or cause or whatever) any of the others.

Exactly this,

Tracing existence back through regression must logically be reversable, Thus in order to regress, progress must be possible, else regression cannot be. Both regression and progression in this form starts at the basis of 1 an existence.

God Bless,

Christopher.

 

[JDaniel]

I now argue that the “God” answer to creation is in fact a specific case of an infinite regression.

1. God has keeps his own time, which is completely separate from ours

TTC:

We are saying that God is outside of time. Allow me to repeat the key word: “outside.” What part of “outside” means “his own time?”

Usually, when “infinity” is predicated of God, it means 'unlimited," or “un-restricted” power(s). But, it also means, in my opinion, as a determinant, that He is of Infinite magnitude. He is the Infinite magnitude Spiritual Being. In other words, there does not exist anything beyond Him, outside of Him, inside of Him, next to Him, over Him, under Him, or around Him. There can be no thing that displaces Him. His Being permeates everything. Think of an atom. Its nucleus is 50,000 times smaller than its electron shell, and consists of dimensionless point particles. The electron shell consists of Infinite Nothingness (God) and one or more dimensionless point particles.

a. Without a “before and after” he could not cause anything.

While “before” and “after” may be predicable in the situation of Creation or, causal activities, one cannot attribute them in any essential way to an Infinite Being. Besides, ‘time’ is still an exigency that holds a tenuous relationship with reality in most of Physics. In order for your proposition to be true, there would have to exist a thing of similar order, that co-exists with God, but is not itself infinite and is, therefore, able to traverse infinity.

1. God’s timeline is infinite.

An utter contradiction. Infinity can’t have a “timeline,” except as postulated by a very imaginative person, who is having a tough time grasping the idea.

a. If God’s timeline were finite, God would have a beginning, but God is the “uncaused cause.”

1. Therefore, prior to this universe being caused, there has passed an infinite amount of time.

How can one possibly attribute a successionary, aggregative, finite structure to that which is Infinite?

a. We cannot conclude how many things God has caused.

Correct, if by “conclude” you mean “sum up.”

b. It is possible for God to have caused an infinite number of things

It may be possible.

1. Therefore, the existence of God can be considered an infinite regression.

Except that you are still bound to Time, which is best defined (if Real) as “an aggregating succession of non-contemporaneous distension.” Time is a finite, but potentially infinite, successionary (avoiding contradictory states) aggregating distension. You are trying to apply a finite whole (perhaps a transfinite of some sort) to the infinite. Even if you surround it with brackets, i.e., [1,2,3,…,n] you have nothing more than a mathematical representation of a conceptualization, i.e., a being of reason.

God bless,
jd

 

[empther]

TrueCentrist’s latest :hey_bud:'ering:

Why the universe (or any system) doesn’t exchange energy with its surroundings is irrelevant. It is traditionally considered a closed system because it doesn’t seem to exchange energy with its surroundings. I am fairly certain that this concept would be covered in the first week of Thermo 101 at any university.

Ignores what I said, that the universe is expanding forever, therefore, it’s entropy is increasing and there’s no chance, not even one in 10^10000000000000000000000000000000000000000000000000000,
or one in 10^infinity,
that it can ever be reversed.

You should take Thermo 101. It’s clear from your many ridiculous comments about the universe’s entropy being reversible that you don’t begin to understand the first thing about the subject.

 

[levinas12]

If the universe itself contains these infinite regressions, why should there not be an infinite regression of causes?

The question is whether there is such a thing as a vicious infinite regress. You could say that an infinite regress is vicious if you can’t even “make” the “first move” in the game.

For example, if, to “understand” a proposition, you must first know all of its “entailments”, then this might involve a vicious infinite regress. Because each “entailment” involves an infinite number of other “entailments”. Therefore, you couldn’t even get started in “understanding” the original proposition.

The Platonic dialogue, Parmenides, has (possibly) an example of a vicious infinite regress, the Third Man argument (as Aristotle called it). If you invoke a Form to explain why two particular things resemble each other, then you are forced to invoke a second Form to explain wny the particulars and the first Form resemble each other. For example, you have two particular circles and you invoke the Form of Circle (which itself is circular) to explain the resemblance. But then you have invoke a second Form of Circle to explain the resemblance between the particular circles and the First Form. The Third Man argument involves (maybe) a vicious infinite regress.

For Thomas, the question of a vicious infinite regress comes up with respect to the concentric cosmic spheres which are embedded in one another. These spheres turn in various ways and are the efficient causes of all motions in the Universe. The motion of the spheres is simultaneous (like interconnected gears). Would the motions in the Universe (e.g., the movement of the sun, stars, planets) be possible if there were an infinite number of spheres simulatenously revolving on their respective axes? Could there be an infinite number of simultaneously turning gears? Is this a case of a vicious infinite regress where no motion could even get started?

 

[levinas12]

I should add that Aristotle and Thomas Aquinas did not have a problem with an infinite time series. For them, the notion of a world without a beginning did not involve a vicious infinite regress.

Of course, Thomas, for biblical reasons, subscribed to a world that began a finite time ago.

For an interesting take on all of this, see Kant’s first antinomy in the Critique of Pure Reason where he proves both that the world had a beginning in time and did not have a beginning in time.

 

[TheTrueCentrist]

I should add that Aristotle and Thomas Aquinas did not have a problem with an infinite time series. For them, the notion of a world without a beginning did not involve a vicious infinite regress.

Of course, Thomas, for biblical reasons, subscribed to a world that began a finite time ago.

For an interesting take on all of this, see Kant’s first antinomy in the Critique of Pure Reason where he proves both that the world had a beginning in time and did not have a beginning in time.

I believe Al-Ghazali also admitted the possibility of an infinite regression.

 

[Poseidon]

There is a fundamental problem with most people’s conceptualizations of regress here. Time is a dimension of the universe. Did you get that? Of this universe. Outside of the universe there is no time. Time does not exist outside the universe, therefore “regress” as we know it involving going back farther and farther in time does not work because time has a beginning. “Before” the big bang time, and therefore temporal regress, did not exist.