Aquinas, the Five Ways, Infinite Regress, and Aristotle

[Bakmoon]

The other day I was skimming through the Summa Theologica, and when going over Aquinas’ five ways of demonstrating the existance of God, I noticed that the various cosmological arguments refer only very briefly to the impossibility of an infinite regress.

Is the issue of infinite regress discussed elsewhere in the works of Aquinas, or was he alluding to some sort of argument already laid down by Aristotle or something?

 

[empther]

Is the issue of infinite regress discussed elsewhere in the works of Aquinas…?

What is there to discuss?

The concept is extremely simple, immediately understood and obvious.

 

[Bakmoon]

What is there to discuss?

The concept is extremely simple, immediately understood and obvious.

I mean, did either Aquinas or Aristotle discuss at some length justification that an infinite regress is impossible?

 

[Linusthe2nd]

The other day I was skimming through the Summa Theologica, and when going over Aquinas’ five ways of demonstrating the existance of God, I noticed that the various cosmological arguments refer only very briefly to the impossibility of an infinite regress.

Is the issue of infinite regress discussed elsewhere in the works of Aquinas, or was he alluding to some sort of argument already laid down by Aristotle or something?

He talks about it in the Summa Contra Gentiles and probably in other places as well. And yes, he is considering Aristotle’s arguments for the existence for God as well. And I’m sure the Arab and Jewish philosophers referred to it as well.

The point is that you cannot have an actual infinite regress in instrmental causality, therefore we must arrive at a First Unmoved and Unmovable Cause, and this we call God.

 

[Linusthe2nd]

I mean, did either Aquinas or Aristotle discuss at some length justification that an infinite regress is impossible?

You have to think about it some. Each moved effect is moved from potentiality to actuality by an actuality which was moved from potentiality to actuality by an actuality which was moved from potentiality to …etc. here and now. So at this instant, in which all causes and effects have a relationship of potential actuality to actuality here and now, we must quickly arrive at a First Unmoved and Unmoveable Cause, one that is Pure ACT, or God who is Pure Act.

It is important to realize that we are thinking Vertically, the here and now. An infinite regress into the linear past ( horizontically) is impossible and is not considered for the reason that such linear causes have no bearing on the hear and now. For example, your Father’s existence and that of all your ancestors have no bearing on your existence and activity here and now. Such ancestors may be deceased but you still live and act.

 

[Bakmoon]

You have to think about it some. Each moved effect is moved from potentiality to actuality by an actuality which was moved from potentiality to actuality by an actuality which was moved from potentiality to …etc. here and now. So at this instant, in which all causes and effects have a relationship of potential actuality to actuality here and now, we must quickly arrive at a First Unmoved and Unmoveable Cause, one that is Pure ACT, or God who is Pure Act.

It is important to realize that we are thinking Vertically, the here and now. An infinite regress into the linear past ( horizontically) is impossible and is not considered for the reason that such linear causes have no bearing on the hear and now. For example, your Father’s existence and that of all your ancestors have no bearing on your existence and activity here and now. Such ancestors may be deceased but you still live and act.

I understand the arguments that Aquinas presents, its just that when reading most of the Summa you find that he addresses each aspect of the points of argument in some detail, even the fairly minor points (for example, in the first way, he very carefully defines using examples what he means by the idea that something cannot have actuality and potentiality in the same sense, something that ordinarily wouldn’t need much discussion) and I was wondering if the reason why he doesn’t discuss the issue of infinite regress in detail is that he already did it somewhere else or if some other philosophical text had already examined the issue in detail, so Aquinas wouldn’t feel the need to explain in detail what had already been discussed.

 

[sw85]

A quick Wikipedia search reveals he has a book touching on the topic, Posterior Analytics: en.wikipedia.org/wiki/Infinite_regress

Note that what Aristotle says isn’t strictly that an infinite regress of dependent events cannot exist, but that it cannot be traversed. That it cannot be traversed surely therefore means it cannot exist.

Note that Aristotle also sees this as essentially axiomatic, i.e., as requiring no proof. It’s just obviously true. You can start at 0 and count towards infinity, but you can’t start at 0 and count backwards to negative infinity.

 

[MilesVitae]

A quick Wikipedia search reveals he has a book touching on the topic, Posterior Analytics: en.wikipedia.org/wiki/Infinite_regress

Note that what Aristotle says isn’t strictly that an infinite regress of dependent events cannot exist, but that it cannot be traversed. That it cannot be traversed surely therefore means it cannot exist.

Is this St. Thom’s position as well? Unless I’ve misunderstood his reasoning in the first three of the Five Ways, this is not why he rules out the possibility of an infinite regress of instrumental causes (and, from what I understand, he isn’t strictly concerned, even there, with ruling out the possibility of any infinite instrumental causal series - even if we hypothetically grant the possibility of such a series, the series would be insufficient to explain itself and his argument would still stand).

I would think that Thomas would reject the reason you’ve given for believing that there cannot be an infinite series of events, since he believed philosophy could not prove the world had a beginning.

Edit: Actually, I decided to just look for it in the Summa (newadvent.org/summa/1046.htm). In reply to objection 6 of article 2 there,

Objection 6. Further, if the world always was, the consequence is that infinite days preceded this present day. But it is impossible to pass through an infinite medium. Therefore we should never have arrived at this present day; which is manifestly false.

Thomas says,

Reply to Objection 6. Passage is always understood as being from term to term. Whatever bygone day we choose, from it to the present day there is a finite number of days which can be passed through. The objection is founded on the idea that, given two extremes, there is an infinite number of mean terms.

 

[sw85]

I’m not sure what St. Thomas’ position was. But no doubt that He did not think therefore that the world could be the product of an infinite regress of causes. He thought the universe itself (i.e., space) could be (not necessarily was) causeless and eternal, but that nothing in it happened until God acted therein.

 

[MilesVitae]

I’m not sure what St. Thomas’ position was.

See the edit to my above post - he seems to have rejected Aristotle’s position.

He thought the universe itself (i.e., space) could be (not necessarily was) causeless and eternal, but that nothing in it happened until God acted therein.

I think this is what Aristotle believes, but not what Thomas thinks. See reply to object 1 of article 2 here, newadvent.org/summa/1046.htm. What Thomas believed was that it could not be philosophically demonstrated that the world had a beginning, but it could be demonstrated philosophically that the world was created by the one God.
After all, in On Being and Essence and elsewhere in the Summa, Thomas argues that there can be only one being whose essence and existence are identical, and that all other things must be caused.

 

[Linusthe2nd]

I understand the arguments that Aquinas presents, its just that when reading most of the Summa you find that he addresses each aspect of the points of argument in some detail, even the fairly minor points (for example, in the first way, he very carefully defines using examples what he means by the idea that something cannot have actuality and potentiality in the same sense, something that ordinarily wouldn’t need much discussion) and I was wondering if the reason why he doesn’t discuss the issue of infinite regress in detail is that he already did it somewhere else or if some other philosophical text had already examined the issue in detail, so Aquinas wouldn’t feel the need to explain in detail what had already been discussed.

He doesn’t need to discuss it any more or explain it anymore. His students understood very clearly what he was saying in the argument without any more elaboration. What more would you like to discuss about it? It is obvious you cannot have an infinite regress of causes and effects, vertically, here and now. You have to have something that is first, a first Actuality which Itself had no potentiality but which simply Was, a Pure Actuality. What don’t you understand?

So, now I think I see what you are trying to say. Yes, the idea I think may have been brought up by Aristotle. However, St. Albert the Great, St. Thomas’ own teacher was sure to have used the idea. And again, the Arab and Jewish philosophers did as well but they were borrowing from Aristotle. I don’t know if Plato used the idea or not.

I don’t know when ST. Thomas first used the idea. I know he used it in the S.C.G. in his proofs there and that was much before he composed the S.T. Where else he may have used it I don’t know but it is one that he often used throughout his works. Does that help?

 

[Bakmoon]

A quick Wikipedia search reveals he has a book touching on the topic, Posterior Analytics: en.wikipedia.org/wiki/Infinite_regress

Note that what Aristotle says isn’t strictly that an infinite regress of dependent events cannot exist, but that it cannot be traversed. That it cannot be traversed surely therefore means it cannot exist.

Note that Aristotle also sees this as essentially axiomatic, i.e., as requiring no proof. It’s just obviously true. You can start at 0 and count towards infinity, but you can’t start at 0 and count backwards to negative infinity.

Would you happen to know where in the works of Aristotle he discusses it? Is it somewhere in Metaphysics?

 

[Linusthe2nd]

A quick Wikipedia search reveals he has a book touching on the topic, Posterior Analytics: en.wikipedia.org/wiki/Infinite_regress

Note that what Aristotle says isn’t strictly that an infinite regress of dependent events cannot exist, but that it cannot be traversed. That it cannot be traversed surely therefore means it cannot exist.

Note that Aristotle also sees this as essentially axiomatic, i.e., as requiring no proof. It’s just obviously true. You can start at 0 and count towards infinity, but you can’t start at 0 and count backwards to negative infinity.

In his cosmological arguments Thomas assumes, for the sake of argument, that the universe is eternal. His use of " infinite regress " in these arguments has nothing to do with that but to show that each effect, here and now, cannot have an infinite number of causes. All the causes of an effect have to be operating simultaneously, here and now. So we arrive at a First Uncaused Cause quickly, right now so to speak.

 

[Bakmoon]

He doesn’t need to discuss it any more or explain it anymore. His students understood very clearly what he was saying in the argument without any more elaboration. What more would you like to discuss about it? It is obvious you cannot have an infinite regress of causes and effects, vertically, here and now. You have to have something that is first, a first Actuality which Itself had no potentiality but which simply Was, a Pure Actuality. What don’t you understand?

Well, he didn’t need to discus or explain what he meant by something not being able to have potentiality and actuality in the same sense, and yet he gives several examples to clarify it in his argument from motion. I think it’s part of his writing style to clarify exactly what he means and how it is to be understood even when discussing , so when I see that Aquinas didn’t discuss or define much on the issue of infinite regress, I am tempted to think that he did it intentionally, possibly as a way to prompt the reader to go to the works of Aristotle for a fuller discussion of the topic.

And just as a sidenote, I don’t think that you can just say that an infinite regress is obviously impossible. I don’t think even Aquinas thought it was something not worth giving some justification for, because he gives justification for it in the discussion on efficient cause, and if he thought the matter were obvious, he would have just said a regress is impossible and leave it as an assumption, but he felt the need to give proof for it.

 

[Bakmoon]

So, now I think I see what you are trying to say. Yes, the idea I think may have been brought up by Aristotle. However, St. Albert the Great, St. Thomas’ own teacher was sure to have used the idea. And again, the Arab and Jewish philosophers did as well but they were borrowing from Aristotle. I don’t know if Plato used the idea or not.

I don’t know when ST. Thomas first used the idea. I know he used it in the S.C.G. in his proofs there and that was much before he composed the S.T. Where else he may have used it I don’t know but it is one that he often used throughout his works. Does that help?

Yes, what I am trying to understand was whether Aquinas was sort of giving an homage to Aristotle on purpose, but I don’t know where in the works of Aristotle to look. I know Aristotle mentions that an infinite regress is impossible in little alpha in Metaphysics
but I can’t find anything more specific.

 

[Linusthe2nd]

Yes, what I am trying to understand was whether Aquinas was sort of giving an homage to Aristotle on purpose, but I don’t know where in the works of Aristotle to look. I know Aristotle mentions that an infinite regress is impossible in little alpha in Metaphysics
but I can’t find anything more specific.

I think the works of Aristotle are online somewhere. You can look for yourself. Someone above mentioned Posterior Analytics.

 

[Linusthe2nd]

Well, he didn’t need to discus or explain what he meant by something not being able to have potentiality and actuality in the same sense, and yet he gives several examples to clarify it in his argument from motion. I think it’s part of his writing style to clarify exactly what he means and how it is to be understood even when discussing , so when I see that Aquinas didn’t discuss or define much on the issue of infinite regress, I am tempted to think that he did it intentionally, possibly as a way to prompt the reader to go to the works of Aristotle for a fuller discussion of the topic.

And just as a sidenote, I don’t think that you can just say that an infinite regress is obviously impossible. I don’t think even Aquinas thought it was something not worth giving some justification for, because he gives justification for it in the discussion on efficient cause, and if he thought the matter were obvious, he would have just said a regress is impossible and leave it as an assumption, but he felt the need to give proof for it.

Well, the young men Thomas was teaching were much more serious than the ones we have today and they usually came from the most educated and most well to do classes. So I am sure they had already had " lessons " on the " infinite regress. " So it was unnecessary for the Professor of his day to elaborate.

But it should be obvious to you that you cannot have an infinite regress of instrumental causes. It is impossible because there has to be a first cause of movement/change. If there is no first cause there is no instrumental or intermediate causes and therefore no last or immediate cause and therefore no movement or change. But movement and change is evident, so there must be a First Uncaused Cause. I don’t see the difficulty.

However there is a wonderful little book by Edward Feser called " Aquinas " and you can order it online for about $20. You can check it out at some libraries. He can explain what I am trying to say much better.

 

[Linusthe2nd]

Yes, what I am trying to understand was whether Aquinas was sort of giving an homage to Aristotle on purpose, but I don’t know where in the works of Aristotle to look. I know Aristotle mentions that an infinite regress is impossible in little alpha in Metaphysics
but I can’t find anything more specific.

Thomas did think a lot of Aristotle but I don’t think he was " doing homage." That was not Thomas’s style.

 

[Bakmoon]

… It is impossible because there has to be a first cause of movement/change. If there is no first cause there is no instrumental or intermediate causes and therefore no last or immediate cause and therefore no movement or change. But movement and change is evident, so there must be a First Uncaused Cause. I don’t see the difficulty…

I think that argument fails on the basis of false analogy. In essence,the argument against infinite regress goes like this:

1. All finite causal sequences of events have the property that if the first event were not to occur, the entire sequence does not occur.
2. An infinite regress of causal events is analogous to a finite sequence of causal events.
3. By 1 and 2, an infinite regress of causal events has the property that if the first event were not to occur, the entire sequence does not occur as well.
4. This universe has events.
5. By 3 and 4, the events of this universe are not part of an infinite regress.

The problem in the argument is in premise 2, as things involving infinities are often quite dis-analogous to their finite brethren. Not even looking at something as philosophically complex as causation, this is quite apparent, for example in the case of basic mathematical operations like calculating sums.

To illustrate, consider basic addition. One of the most basic rules of addition is that it is associative, meaning that it doesn’t matter how you group the terms. In other words, (1+2)+3 is the same as 1+(2+3). This is a fundamental aspect in math of how addition works. However, this isn’t true of infinite sums. To prove this we can consider the famous Grandi series. It goes like this: 1+1-1+1-1+1… and so on. If you group the terms (1+1)-(1+1)-(1+1)… you get zero, but if you group them 1+(1-1)+(1-1)+(1-1)… it ads up to 1. Therefore, the associative property of addition doesn’t apply to infinite series.

So for even the most basic and most obvious things we know about (such as basic arithmetic) we can’t assume that they are applicable to things involving infinities.

 

[Linusthe2nd]

I think that argument fails on the basis of false analogy. In essence,the argument against infinite regress goes like this:

1. All finite causal sequences of events have the property that if the first event were not to occur, the entire sequence does not occur.
2. An infinite regress of causal events is analogous to a finite sequence of causal events.
3. By 1 and 2, an infinite regress of causal events has the property that if the first event were not to occur, the entire sequence does not occur as well.
4. This universe has events.
5. By 3 and 4, the events of this universe are not part of an infinite regress.

The problem in the argument is in premise 2, as things involving infinities are often quite dis-analogous to their finite brethren. Not even looking at something as philosophically complex as causation, this is quite apparent, for example in the case of basic mathematical operations like calculating sums.

To illustrate, consider basic addition. One of the most basic rules of addition is that it is associative, meaning that it doesn’t matter how you group the terms. In other words, (1+2)+3 is the same as 1+(2+3). This is a fundamental aspect in math of how addition works. However, this isn’t true of infinite sums. To prove this we can consider the famous Grandi series. It goes like this: 1+1-1+1-1+1… and so on. If you group the terms (1+1)-(1+1)-(1+1)… you get zero, but if you group them 1+(1-1)+(1-1)+(1-1)… it ads up to 1. Therefore, the associative property of addition doesn’t apply to infinite series.

So for even the most basic and most obvious things we know about (such as basic arithmetic) we can’t assume that they are applicable to things involving infinities.

Well, I’m not going to get into an endless debate on the subject. You either see it or you don’t. Do get the book I suggested, it is a good read and is written by someone who understands the subject much better than anyone here.

I would point out however that # 4 does not happen unless there is a first uncaused cause. That " events " do occur is proof that there is a first uncaused cause which sets all instrumental cause in motion/change/existence right now. You understand of course that this has absolutely nothing to do with either the finitne or the eternal existence of the universe ? The fact is that even if the universe were eternal ( which I deny ) there would still have to be a first uncaused cause for each and every change/movement and there would have to be a cause for the existence of the universe. Good luck.