Why infinite regress is impossible?

[STT]

I already searched the forum and google it.

 

[IWantGod]

Because there is no such thing as an actually infinite number of something. There is not an amount, quantity, or number of things, that can add up to an infinite because an infinite is quantitatively indefinable. There is no exact amount that can define a point were you actually have an infinite number of something and so the idea is meaningless.Thus if there were an infinite regress, this would be a contradiction because you would have an actually infinite number in the past; and so it’s impossible. There is only ever the potentially infinite number.

 

[Gorgias]

From this article, which I just found by Googling “why is an infinite regress impossible?”…

If all such causes are merely intermediate, then some causal activity is passing through the entire chain, but no member of the chain can explain it. Whether the intermediate causes are limited or unlimited in number, they cannot alone explain the causal process that runs through the entire chain. Solely a first cause that initiates the entire chain can do that – a first cause uncaused.

Now, to reconsider that chain of intermediate reasons described above, we see that the same problem arises. The problem is that each prior reason is not really sufficient unto itself. If it were, it would be a first reason, not an intermediate one. It is called intermediate precisely because it is passing along a reason that it itself does not fully explain. Otherwise, the chain would stop right there. If one looks for the sufficient reason of A, it is not fully in B, since B depends on C to fulfill its own reason. If one regresses to infinity in looking at intermediate reasons, the fully sufficient reason will never be found, since none of the intermediate links provides the complete reason for the final effect. Each one leaves some of the needed reason lacking. If one regresses the chain to infinity, the total sufficient reason is never found – and thus, the final effect lacks a sufficient reason. But that is impossible. Thus, there must be a first sufficient reason, which is its own reason – otherwise the principle of sufficient reason itself would be violated.

 

[Maximilian75]

This podcast may help you

Pints With Aquinas: 33: What's the contingency argument for God's existence?

 

[AlNg]

Zeno’s paradox shows you can have an infinite number of steps (each one becoming smaller than the previous) in a finite interval.

 

[STT]

Because there is no such thing as an actually infinite number of something.

There are things as actual number of things. Think of universe. It is infinite otherwise it is bounded with by a boundary and that boundary is bounded by… etc. which this leads to infinite regress.

There is not an amount, quantity, or number of things, that can add up to an infinite because an infinite is quantitatively indefinable. There is no exact amount that can define a point were you actually have an infinite number of something and so the idea is meaningless.Thus if there were an infinite regress, this would be a contradiction because you would have an actually infinite number in the past; and so it’s impossible. There is only ever the potentially infinite number.

You are just proving that infinity cannot be reached which this is different from that infinity does not exist.

 

[IWantGod]

You are just proving that infinity cannot be reached

I think an actually infinite number is meaningless because there is no actual quantity that can be said to be infinite. It’s indefinable.There is always a finite amount no matter how large the quantity or how many numbers you add. Only a potentially infinite number exists…

But if you agree that i have proven that an infinity cannot be reached, then you must agree that we couldn’t possibly have reached an infinite number of events in actual reality, so what sense does it make to say there is an actually infinite past? If an infinite number cannot be achieved i fail to see how an infinite regress could actually be achieved.

 

[STT]

From this article, which I just found by Googling “why is an infinite regress impossible?”…

If all such causes are merely intermediate, then some causal activity is passing through the entire chain, but no member of the chain can explain it. Whether the intermediate causes are limited or unlimited in number, they cannot alone explain the causal process that runs through the entire chain. Solely a first cause that initiates the entire chain can do that – a first cause uncaused.

I don’t agree with the bold part.

Now, to reconsider that chain of intermediate reasons described above, we see that the same problem arises. The problem is that each prior reason is not really sufficient unto itself. If it were, it would be a first reason, not an intermediate one. It is called intermediate precisely because it is passing along a reason that it itself does not fully explain. Otherwise, the chain would stop right there. If one looks for the sufficient reason of A, it is not fully in B, since B depends on C to fulfill its own reason. If one regresses to infinity in looking at intermediate reasons, the fully sufficient reason will never be found, since none of the intermediate links provides the complete reason for the final effect. Each one leaves some of the needed reason lacking. If one regresses the chain to infinity, the total sufficient reason is never found – and thus, the final effect lacks a sufficient reason. But that is impossible. Thus, there must be a first sufficient reason, which is its own reason – otherwise the principle of sufficient reason itself would be violated.

I don’t agree with this part either. There is no sufficient reason in an infinite chain of causality and there is no need for it so it is meaningless to argue based on it.

 

[STT]

I think an actually infinite number is meaningless because there is no actual quantity that can be said to be infinite. It’s indefinable.There is always a finite amount no matter how large the quantity or how many numbers you add. Only a potentially infinite number exists…

But if you agree that i have proven that an infinity cannot be reached, then you must agree that we couldn’t possibly have reached an infinite number of events in actual reality, so what sense does it make to say there is an actually infinite past? If an infinite number cannot be achieved i fail to see how an infinite regress could actually be achieved.

Sorry, I have to correct myself. An infinity cannot be reached by finite number of entities. A+A+A+A…<infinity if the number of A is finite otherwise you can catch infinity.

 

[STT]

This podcast may help you

Sorry, but that really didn’t help.

 

[IWantGod]

Sorry, I have to correct myself. An infinity cannot be reached by finite number of entities. A+A+A+A…<infinity if the number of A is finite otherwise you can catch infinity.

But there is no otherwise. To speak of an an actually infinite quantity or number is to speak of something that is made of finite parts or irreducible points that add up to an actual infinite. To argue for an infinite regress of events, you are by definition arguing for an an actually infinite number of a finite amount. and since finite amounts cannot possibly add up to a point that can be defined as actually infinite it is meaningless to speak of an infinite regress because the addition of numbers only ever allows a potential infinite; never an actual infinite.

An infinite regress is impossible.

 

[gregoryphealy]

From a Thomist perspective, an infinite regress of secondary causes is possible. As others in this thread have mentioned with Zeno’s Paradox, we don’t have to look far to find an infinite series of causes. There’s an infinite number of infinitely small discrete steps within a finite period of time, thus implying infinite series of secondary causes within that same finite amount of time. Beyond that, the causal chain could loop back on itself or do all kinds of wonky stuff, too. But it still stands that the infinite causal chain must have a first cause.

Imagine a simple situation in which there exists a first cause and one intermediate cause. If we remove the first cause, of course, the situation is invalid. Now we add more intermediate causes and after each one if we try to remove the first cause the series becomes invalid. Continue adding intermediate causes, and there is still an invalid causal series if the first cause is removed after each intermediate is added to the chain ad infinitum.

 

[STT]

From a Thomist perspective, an infinite regress of secondary causes is possible. As others in this thread have mentioned with Zeno’s Paradox, we don’t have to look far to find an infinite series of causes. There’s an infinite number of infinitely small discrete steps within a finite period of time, thus implying infinite series of secondary causes within that same finite amount of time. Beyond that, the causal chain could loop back on itself or do all kinds of wonky stuff, too. But it still stands that the infinite causal chain must have a first cause.

Imagine a simple situation in which there exists a first cause and one intermediate cause. If we remove the first cause, of course, the situation is invalid. Now we add more intermediate causes and after each one if we try to remove the first cause the series becomes invalid. Continue adding intermediate causes, and there is still an invalid causal series if the first cause is removed after each intermediate is added to the chain ad infinitum.

We could have infinite intermediate causes, so there is no need for first cause.

 

[STT]

But there is no otherwise. To speak of an an actually infinite quantity or number is to speak of something that is made of finite parts or irreducible points that add up to an actual infinite. To argue for an infinite regress of events, you are by definition arguing for an an actually infinite number of a finite amount. and since finite amounts cannot possibly add up to a point that can be defined as actually infinite it is meaningless to speak of an infinite regress because the addition of numbers only ever allows a potential infinite; never an actual infinite.

An infinite regress is impossible.

Why infinite sum of things is impossible? Think of Zeno’s paradox.

 

[IWantGod]

Think of Zeno’s paradox.

The idea that you can have a potentially infinite series of halves is not the same thing as arguing for an actually infinite regress of events.

 

[STT]

The idea that you can have a potentially infinite series of halves is not the same thing as arguing for an actually infinite regress of events.

You can have actual infinity. Think of 1/x where we gradually go toward x=0.

 

[IWantGod]

To halve something a potentially infinite amount of times is not the same thing as saying that you have an actually infinite amount of something.

 

[STT]

To halve something a potentially infinite amount of times is not the same thing as saying that you have an actually infinite amount of something.

Is it possible to reach from 1 to zero? If yes then 1/x is an actual infinity.

 

[IWantGod]

Is it possible to reach from 1 to zero?

To move from 1 to 0 is not the same thing as moving an infinite number of times…

The qeustion of Zeno paradox is not operating in the same context as an infinite regress

 

[Wesrock]

It depends upon the type of infinite regress. I could conceive a line of infinite dominoes, with an infinite number of fallen ones behind and an infinite number of fallen ones in front. I see no issue with an infinite regress of that type of series. Neither did Thomas Aquinas. In those series, prior actors did their job and were done. Once a domino falls, it doesn’t matter if I remove it from the sequence. It won’t stop the domino effect from continuing with the ones actively falling and yet to fall.

The issue is in series where all the actors in the series need to be continuously active in order to preserve the series. If I suspend a lamp from a ceiling using a chain of links, one end needs to actually be attached to the ceiling. If an end isn’t attached to a ceiling it doesn’t matter how many links I add to the chain. I can add an infinite number of links. It doesn’t get the lamp off the ground. Therefore, if I know I have a lamp suspended by a series of chain links, I know that one end must be grounded to something else in order to actually hang the lamp. Likewise, in this type of series, if I remove any of the chain links from the middle (like we did with the fallen domino), the lamp still comes crashing to the ground. In the domino series a fallen domino had did its job and was done. It didn’t affect future dominos. In the chain series each link in the chain is constantly active and is constantly dependent on the chain being grounded, because the ability of one link to hold up another link is not something passed on once for all, but is something that it derives each and every moment.