Q&A: Infinite Regress
Infinite Regress
Question
Have a good week,
I wanted to ask you whether the reason an infinite regress seems implausible
is that if infinitely many causes have to come before every event, then no event would ever occur. For example, imagine that you are standing in line to enter a certain door. And in front of you in line there is a finite number of people, and every so often someone goes through the door, so after some time your turn will come. But if there are infinitely many people in front of you in line, then your turn will never come. And not only your turn; the turn of the person in front of you will also never come, and so on. It follows that no person could ever pass through the door. And in the analogy—no event could ever occur. But in practice, events do occur, and that shows that there is a first cause from which everything begins.
Answer
This formulation appears in Duties of the Heart, in the Gate of Divine Unity. But in mathematics today this is considered an “illegitimate” formulation, because you cannot speak about the far edge of an infinite chain. Still, what you are saying could itself be the reason why it is illegitimate. I would formulate it differently: there is nowhere to begin from, because infinity is not a specific point but a limit in a potential sense. Even on the number line, you cannot be located at minus infinity and start moving rightward. That is not mathematically defined. After all, an explanatory regress is a movement backward from the later to the earlier, from the effect to the cause/explanation. But when you try to examine whether you have in fact obtained an explanation, you have to move through the causal chain from the beginning and go forward to the effect. That is an undefined process.
Discussion on Answer
First, I’m not sure I agree with the formulation you proposed for the problem of regress. The problem is not that each turtle in itself is unstable, but that there is no initial turtle. True, in the background there is an assumption that each turtle in itself is unstable, for if one of them were stable in and of itself there would be no need for turtles beneath it, and in particular not for the first turtle, but that is a side assumption.
Second, I don’t see any difference at all between the two examples. In the train-car example too, no car gives an explanation without the others, because its own speed is not explained from itself. Therefore it too requires its predecessors. Exactly the same applies to every turtle: if its standing did not itself require an explanation, then it would contain a sufficient explanation, but that does not exist (its standing requires the others in order to explain it).
In other words: in both cases, if there were a stable turtle or a car whose speed was self-explanatory and did not require explanation, we could stop there. But in both cases there is no such turtle/car, and therefore in both cases there is an infinite regress. There is no difference at all.
And if you go back to the formulation I suggested at the beginning for the problem of regress—that there is no first link—you will see clearly that the train-car example offers no explanation either, and in it too one cannot accept an infinite regress.
Doesn’t the same argument also apply to the eternity of God? After all, if He had existed for an infinite amount of time before He decided to create the world, then that would “never happen,” as you said.
Regarding God, one can use a potential formulation: there was never a time when He did not exist. You do not have to use the concrete formulation that He has existed for an infinite amount of time. That is unlike an explanatory chain, which is composed of links. There you have to appeal to an actual infinity.
1. Thanks! I saw this example in Moshe Ratt.
2.
I wanted to ask more about the turtle parable you presented in the booklet, and I’ll use another parable as an opposite example, one in which infinite regress does not lead to failure at all.
As I understand it, the main claim in your turtle parable is that each turtle is not stable in the air on its own. For example, Turtle 1—if it were standing in the air by itself, it would fall. And likewise, if we add Turtle 2 standing beneath it, that gives no advantage to Turtle 1, because Turtle 2 by itself is also unstable. What would give Turtle 2 stability is standing on something that touches the floor, but as stated, that did not happen.
That is, even if we extend the chain to infinity, infinity has no power to do the impossible—namely, when each entity on its own has an inherent defect: it does not touch the floor.
But I think one can give another parable in which that problem does not apply (and this parable could serve as an analogy for the physico-theological proof). I’ll call it “the train parable.”
The train parable imagines a long train made up of connected cars, and we ask: how is the final car moving at a speed of 50 km/h?
There, an answer in the form of Car 2 moving Car 1 is a completely sufficient answer. Because each car, by itself, gives a full explanation for the speed of the next car. And in such a case, even if there are still things that require explanation (Car 2), in the end each car gives a *full explanation* for the next car all by itself.
In such a parable, where each component by itself gives a full explanation for the speed of the next car, it seems that this really does create a full explanation for the movement of the cars.
By contrast, the turtle parable is a bit different, because Turtle 2 does not explain Turtle 1 unless Turtle 2 is standing on a turtle that touches the floor. And so I think that the example of the physico-theological proof is more similar to the train-car example than to the turtle example.
And in the parable of the train cars, it is not at all clear that an answer which *indirectly* creates an infinite regress is problematic. Because each car does indeed provide a full explanation for the car before it.
So true, in the end there is an infinite regress there, but it is a byproduct created indirectly. The explanation is complete throughout all its parts. In such a case, one can accept an infinite regress.
By contrast, it seems that the cosmological proof, according to some of its presentations (such as why there is something rather than nothing), is actually more connected to the turtle parable than to the train.
So I’d be glad to know what the Rabbi thinks about this clear distinction?