Revisiting the Argument from Motion

[Bakmoon]

To expand on that last bit (alas, I was too slow with my edit):

Basically, the (all of these) argument says that there must be something which needs no explanation, because it just is. One of the common counter arguments is “ok fine, but why can’t that be ‘the universe’.” In this case, we could say “why can’t that be an infinite chain?” If infinite chains can happen without being caused or without any external explanation, then they are such things. But things (well thing) of that sort must have certain properties logically deduced from the self contained nature, (uniqueness, simplicity, etc.) and infinite chains of events fail to have them.

(Emphasis added)

The argument from motion never asserts anything about explanation. If you try to convert the argument from motion into an argument from explanation you will find that there are big problems. If you do convert it and then put it into the form of a series of syllogisms you will see the major snag.

 

[Linusthe2nd]

If you actually look at Aristotle’s arguments against an infinite regress of motion in section one of book seven of the Physics he really only makes one argument. First he points out that in the sequence of A being moved by B being moved by C etc… the time it takes for A to move is finite, but the motion of the entire series is infinite, and you can’t have an infinite motion in a finite amount of time.

The problem with this kind of argument is that it only works if the motions are simultaneous. If B occurs before A and C occurs before B etc… then although you do have an infinite, because each part of it occurs at a different time it is only a potential infinite rather than an actual infinite.

Even in terms of the power of the cause being passed down there is no actual infinity with an infinite causal chain. Allow me to demonstrate this first by means of a finite causal sequence. Suppose A is moved by B which is moved by C. The causal power of C moves B and is expended, and the causal power of B in turn moves A. Or alternatively one could say that the causal power of C is converted into the causal power of B which then moves A. The essential point here is that A doesn’t receive an inherited effect of everything in the causal chain but is only moved by the causal power of B.

In the case of an infinite sequence that is not simultaneous we have A being moved by B being moved by C etc… Because the causal power of each term in the sequence is expended (or converted if you prefer) A will not be moved by an actually infinite inherited causal power of B+C+D+… but is instead only moved by the causal power of B, even in the case of an infinite sequence, and so Aristotle’s argument fails.

In the case of Aristotle’s argument in Book 8 section 5 Aristotle gives another argument that goes :

But this isn’t really an independent argument because he doesn’t give new justification for assuming that a causal series needs a new term. Presumably Aristotle is simply using that passage to refer back to his argument in book 7 section 1 as if it is an independent argument against an infinite causal regress then it is simply begging the question, and I doubt Aristotle would intend that.

Looking over Aquinas’ commentaries on the Physics, I haven’t seen any actual original arguments on the issue, just paraphrases of Aristotle’s arguments on the issue.

Interesting comments, I will get with you as soon as I can but I will need more time. Glad to see you actually looked at the sources.

Linus2nd’

 

[Linusthe2nd]

Just thought I’d summarize some standard objections. We’ve discussed them before and I know you don’t accept them, but they remain formidable:

1. The argument divides the world into things which depend on other things. If instead we take a holistic view that all things are interdependent, then things are just a way of conveniently cataloging the world and a thing can’t have an independent existence. As a result the claim that a thing cannot move (change) itself is incoherent.
2. By dividing the world into things, there is an unwarranted assumption that processes must have a beginning, middle and end. But if all things are interdependent then “whatever is in motion must be put in motion by another” and “this cannot go on to infinity” are incoherent.
3. The assumption that motion needs a cause is unwarranted. It is simpler to assert that motion is the default, and we’re pretty sure this is the case in the observable universe (Newton’s first law).
4. The argument is a posteriori (“evident to our senses”) and yet the concepts of potentiality and actuality are introduced without any evidence that they exist objectively, or are anything more than a somewhat contrived attempt at a qualitative reductionism.
5. The argument is presented as a proof, yet no a posteriori argument can be.

Don’t have time to answer you now, maybe in a few days.

Linus2nd

 

[Bakmoon]

Interesting comments, I will get with you as soon as I can but I will need more time. Glad to see you actually looked at the sources.

Linus2nd’

I love going back to the sources. I’ll try to get around to the relevant portions of Aquinas’ commentary on metaphysics, but I’ll have to re-read the Metaphysics by itself first because somehow I always get lost trying to find what I’m looking for.

After that I’ll present my thoughts on the relevant arguments in the Metaphysics and Aquinas’ commentary on it, and then I’ll probably re-read the sections of the Summa Contra Gentiles just for good measure.

 

[Bakmoon]

I finally found the relevant section in the Metaphysics. In Book Kappa section 12 Aristotle discusses change and mentions:

Further, the process [of causation] will go on to infinity, if there is to be change of change and coming to be of coming to be. What is true of the later, then, must be true of the earlier; e.g. if the simple coming to be was once coming to be, that which comes to be something was also once coming to be; therefore that which simply comes to be something was not yet in existence, but something which was coming to be coming to be something was already in existence. And this was once coming to be, so that at that time it was not yet coming to be something else. Now since of an infinite number of terms there is not a first, the first in this series will not exist, and therefore no following term exist.

In brief, Aristotle’s argument goes something like:

1. If an infinite causal series does not have a first term, it cannot begin
2. A causal series that extends infinitely backwards does not have a first term
3. Therefore a causal series extending infinitely backwards cannot begin

However Aristotle doesn’t give any argument to support the claim that an infinite series needs a first. This isn’t surprising, especially considering that the Metaphysics doesn’t seem to be a work that Aristotle put together as a coherent work, but is likely a compilation of parts of his notes done after his death, so it is understandable that parts are incomplete. With Book Kappa in particular there has been speculation that Aristotle might not have written it as it just goes over subjects already discussed in the Physics.

Aquinas in his commentary on this passage doesn’t add any support for this point either but assumes it just as Aristotle. He just gives a paraphrase of the argument saying:

And if this generation also came to be at some time, since it is not possible to have either an infinite regress or any first term among infinite things, it is impossible ever to come to any first process of generation. But if the preceding member in a series does not exist, there will be no succeeding member, as has been pointed out above, and the consequence will be that “there will not be a subsequent one,” i.e., one which follows it. It follows, then, that nothing can come to be or be moved or be changed. But this is impossible. Hence change of change is impossible.

Next I’ll be looking at Aquinas’ argument in the Summa Contra Gentiles.

 

[Bakmoon]

In the Summa Contra Gentiles Aquinas addresses the issue of an infinite chain of movers in Chapter 13 where he simply paraphrases Aristotle’s arguments which I have already mentioned, reviewing Aristotle’s argument that an infinite chain of movers form a single body which produce an infinite amount of motion in a finite time and two variations on the argument I already addressed from the Metaphysics. All of the other variations of the argument from motion in the Summa Contra Gentiles just go over the subtleties of the other parts of the argument but not the infinite chain.

 

[Linusthe2nd]

If you actually look at Aristotle’s arguments against an infinite regress of motion in section one of book seven of the Physics he really only makes one argument. First he points out that in the sequence of A being moved by B being moved by C etc… the time it takes for A to move is finite, but the motion of the entire series is infinite, and you can’t have an infinite motion in a finite amount of time.

The problem with this kind of argument is that it only works if the motions are simultaneous. If B occurs before A and C occurs before B etc… then although you do have an infinite, because each part of it occurs at a different time it is only a potential infinite rather than an actual infinite.

Here is the way Thomas answers in the Summa Contra Gentiles, Book 1, Ch 13:

[11] The second proposition, namely, that there is no procession to infinity among movers and things moved, Aristotle proves in three ways.

[12] The first is as follows [VII, 1]. If among movers and things moved we proceed to infinity, all these infinite beings must be bodies. For whatever is moved is divisible and a body, as is proved in the Physics [VI, 4]. But every body that moves some thing moved is itself moved while moving it. Therefore, all these infinites are moved together while one of them is moved. But one of them, being finite, is moved in a finite time. Therefore, all those infinites are moved in a finite time. This, however, is impossible. It is, therefore, impossible that among movers and things moved one can proceed to infinity.

[13] Furthermore, that it is impossible for the abovementioned infinites to be moved in a finite time Aristotle proves as follows. The mover and the thing moved must exist simultaneously. This Aristotle proves by induction in the various species of motion. But bodies cannot be simultaneous except through continuity or contiguity. Now, since, as has been proved, all the aforementioned movers and. things moved are bodies, they must constitute by continuity or contiguity a sort of single mobile. In this way, one infinite is moved in a finite time. This is impossible, as is proved in the Physics [VII, 1].

[14] The second argument proving the same conclusion is the following. In an ordered series of movers and things moved (this is a series in which one is moved by another according to an order), it is necessarily the fact that, when the first mover is removed or ceases to move, no other mover will move or be moved. For the first mover is the cause of motion for all the others. But, if there are movers and things moved following an order to infinity, there will be no first mover, but all would be as intermediate movers. Therefore, none of the others will be able to be moved, and thus nothing in the world will be moved.

[15] The third proof comes to the same conclusion, except that, by beginning with the superior, it has a reversed order. It is as follows. That which moves as an instrumental cause cannot move unless there be a principal moving cause. But, if we proceed to infinity among movers and things moved, all movers will be as instrumental causes, because they will be moved movers and there will be nothing as a principal mover. Therefore, nothing will be moved. "

I like 14 and 15 better because they are easier to understand. So it is clear that there can be no infinite regress and there has to be an Unmoved Mover that is Pure Act ( as Aristotle himself implies, since an Unmoved and Unmovible Intelligence, must be Pure Act). If there is no Unmoved Mover, then there is nothing else either, which is clearly false.

Even in terms of the power of the cause being passed down there is no actual infinity with an infinite causal chain.

Aristotle and Thomas just proved that an infinite regress is impossible. How is your statement here any different? I don’t see the difference.

Allow me to demonstrate this first by means of a finite causal sequence. Suppose A is moved by B which is moved by C. The causal power of C moves B and is expended, and the causal power of B in turn moves A. Or alternatively one could say that the causal power of C is converted into the causal power of B which then moves A. The essential point here is that A doesn’t receive an inherited effect of everything in the causal chain but is only moved by the causal power of B.

Yes, but C intends to exsert only that particular power to achieve the desired, particular effect. This is not to deny that the intervening instruments may have other powers which have not been exsrted. I see no problem here…

In the case of an infinite sequence that is not simultaneous we have A being moved by B being moved by C etc… Because the causal power of each term in the sequence is expended (or converted if you prefer) A will not be moved by an actually infinite inherited causal power of B+C+D+… but is instead only moved by the causal power of B, even in the case of an infinite sequence, and so Aristotle’s argument fails.

I don’t see how you can have such an infinite sequence. I think Aristotle proved that any such infinites series would consist of movers and moved moving simultaneorsly as one motion.

I think I am running out of space. Will continue on another post.

Linus2nd

 

[Linusthe2nd]

In the case of Aristotle’s argument in Book 8 section 5 Aristotle gives another argument that goes : " If then everything that is in motion must be moved by something, and by something either moved by something else or not, and in the former case there must be some first mover that is not itself moved by anything else, while in the case of the first mover being of this kind there is no need of another (for it is impossible that there should be an infinite series of movers, each of which is itself moved by something else, since in an infinite series there is no first term)

But this isn’t really an independent argument because he doesn’t give new justification for assuming that a causal series needs a new term. Presumably Aristotle is simply using that passage to refer back to his argument in book 7 section 1 as if it is an independent argument against an infinite causal regress then it is simply begging the question, and I doubt Aristotle would intend that.

I could not locate your reference. Are you sure it was in Thomas’ commentary on Physics Book 8, ch 5?

At any rate, it is not a new argument. he is simply showing that there cannot be an infinite number of first movers, that there can only be one. That is the way I read it. Aristotle often repeats thems or ideas he has proved or demonstrated before as a prelude to or as proof to something new. I don’t see how this could be " begging the question."

Looking over Aquinas’ commentaries on the Physics, I haven’t seen any actual original arguments on the issue, just paraphrases of Aristotle’s arguments on the issue.

He does disagree with A’s reasoning in a few places. Yes, his object is not to introduce anything new but to present A’s thought for his students and to elucidate it where needed.

Aristotle can be daunting, that is why he was attempting to make it easier to understand.

Linus2nd

 

[Linusthe2nd]

ATT: Bakmoon

I finally found the relevant section in the Metaphysics. In Book Kappa section 12 Aristotle discusses change and mentions:

Quote:
Further, the process [of causation] will go on to infinity, if there is to be change of change and coming to be of coming to be. What is true of the later, then, must be true of the earlier; e.g. if the simple coming to be was once coming to be, that which comes to be something was also once coming to be; therefore that which simply comes to be something was not yet in existence, but something which was coming to be coming to be something was already in existence. And this was once coming to be, so that at that time it was not yet coming to be something else. Now since of an infinite number of terms there is not a first, the first in this series will not exist, and therefore no following term exist.

In brief, Aristotle’s argument goes something like:

Quote:

1. If an infinite causal series does not have a first term, it cannot begin
2. A causal series that extends infinitely backwards does not have a first term
3. Therefore a causal series extending infinitely backwards cannot begin

However Aristotle doesn’t give any argument to support the claim that an infinite series needs a first. This isn’t surprising, especially considering that the Metaphysics doesn’t seem to be a work that Aristotle put together as a coherent work, but is likely a compilation of parts of his notes done after his death, so it is understandable that parts are incomplete. With Book Kappa in particular there has been speculation that Aristotle might not have written it as it just goes over subjects already discussed in the Physics.

He has proven these things either earlier on Metaphysics or Physics. If Thomas comments on anything, he will sometimes give a reference to an earlier book or a different work ( e.g. De Anima, etc. ).

Aquinas in his commentary on this passage doesn’t add any support for this point either but assumes it just as Aristotle. He just gives a paraphrase of the argument saying:

Yes, that is his usual procedure.

And if this generation also came to be at some time, since it is not possible to have either an infinite regress or any first term among infinite things, it is impossible ever to come to any first process of generation. But if the preceding member in a series does not exist, there will be no succeeding member, as has been pointed out above, and the consequence will be that “there will not be a subsequent one,” i.e., one which follows it. It follows, then, that nothing can come to be or be moved or be changed. But this is impossible. Hence change of change is impossible.

Linus2nd

 

[Linusthe2nd]

In the Summa Contra Gentiles Aquinas addresses the issue of an infinite chain of movers in Chapter 13 where he simply paraphrases Aristotle’s arguments which I have already mentioned, reviewing Aristotle’s argument that an infinite chain of movers form a single body which produce an infinite amount of motion in a finite time and two variations on the argument I already addressed from the Metaphysics. All of the other variations of the argument from motion in the Summa Contra Gentiles just go over the subtleties of the other parts of the argument but not the infinite chain.

I can’t keep up with you, I don’t have any servents here. I do all my own shores, plus I have other interests and obligations. But keep it up, we will make a philosopher out of you yet. Read some of Thomas’ other stuff - just as a change of pace.

Linus2nd

 

[Bakmoon]

Aristotle and Thomas just proved that an infinite regress is impossible. How is your statement here any different? I don’t see the difference.

Look at the relevant portion of Aristotle’s primary argument in the Phyisics. He Says:

Let A then be moved by B, B by C, C by D, and so on, each
member of the series being moved by that which comes next to it. Then since
ex hypothesi the mover while causing motion is also itself in motion, the motion of the moved and the motion of the mover must proceed simultaneously (for the mover is causing motion and the moved is being moved simultaneously); so it is evident that the motions of A, B, C, and each of the other moved movers are simultaneous. Let us take the motion of each separately and let E be the motion of A, F of B, and G and H respectively the motions of C and D;
…
Now let us further take the time in which A has completed its motion, and let it be represented by K. Then since the motion of A is finite the time will also be finite. But since the movers and the things moved are infinite, the motion EFGH, i.e. the motion that is composed of all the individual motions, must be infinite. For the motions of A, B, and the others may be equal, or the motions of the others may be greater; but assuming
what is possible, we find that whether they are equal or some are greater, in both
cases the whole motion is infinite. And since the motion of A and that of each of
the others are simultaneous, the whole motion must occupy the same time as the
motion of A; but the time occupied by the motion of A is finite: consequently the
motion will be infinite in a finite time, which is impossible.

Aristotle’s argument boils down to this:

1. If X moves Y then X and Y are simultaneous
2. In an infinite causal series ending in A, A is moved by B which is moved by C etc…
3. Therefore by induction, all the terms of such an infinite causal series occur simultaneously
4. The total amount motion for causal series is equal to the sum of the motion of its terms
5. An infinite sum of non-zero positive (like motion) amounts is infinite
6. Therefore an infinite causal series has an infinite amount of motion
7. An infinite amount of something occurring in the present is an actual infinity
8. An infinite causal series has an infinite amount of something (i.e. motion) as its terms occur simultaneously
9. An infinite causal series is an actual infinity
10. An actual infinity cannot exist
11. An infinite causal series is an actual infinity
12. Therefore an infinite causal series cannot exist

Can we agree to work off of this as an accurate formalization of Aristotle’s argument? If it isn’t, then how would you correct it to be an accurate depiction of his argument? Once the argument has been properly established I will give my full analysis.

 

[Bakmoon]

I could not locate your reference. Are you sure it was in Thomas’ commentary on Physics Book 8, ch 5?

My mistake. It turns out it was actually from Book 6 chapter 5, not Book 8. I’m actually only reading through Aquinas’ commentaries from the site. I read through the parts of Aristotle’s main text in PDF form but it seems PDF of the Physics has its bookmarks a little off so I thought it was book 8.

At any rate, it is not a new argument. he is simply showing that there cannot be an infinite number of first movers, that there can only be one. That is the way I read it. Aristotle often repeats thems or ideas he has proved or demonstrated before as a prelude to or as proof to something new. I don’t see how this could be " begging the question."

The only reason why I cite the passage from book 6 is because it has that bit at the end about an infinite series of movers requiring a first term and it would be improper for me to not mention it even though it is not a complete argument. Of course, Aristotle gives his completion of his point in Book 7.

He does disagree with A’s reasoning in a few places. Yes, his object is not to introduce anything new but to present A’s thought for his students and to elucidate it where needed.

Aristotle can be daunting, that is why he was attempting to make it easier to understand.

Linus2nd

My intent in saying that Aquinas didn’t advance new arguments in his commentaries but merely paraphrased them is not to criticize him but mainly to show that I’m not leaving out any major points raised by Aquinas on the issue. Paraphrases have an essential role to play in Aristotle especially. For example, In addition to writing comprehensive commentaries on Aristotle, Ibn Rushd also wrote a complete set of epitomes and a complete set of paraphrases on Aristotle that were very valuable.

 

[Linusthe2nd]

Just thought I’d summarize some standard objections. We’ve discussed them before and I know you don’t accept them, but they remain formidable:

Not formidable. No argument can be convincing to someone who either cannot understand or who comes to the table with an ideological conviction that makes agreement impossible ( e.g. the East and the West ).

1. The argument divides the world into things which depend on other things. If instead we take a holistic view that all things are interdependent, then things are just a way of conveniently cataloging the world and a thing can’t have an independent existence. As a result the claim that a thing cannot move (change) itself is incoherent.

Oddly enough the interdependence of things does not make the existence of individual beings contrary to reason. It certainly didn’t cause A. and T. any problems. And it doesn’t cause me any problems. I’m surpirsed you have the view you just expressed. I don’t see the two as mutually exclusive.

1. By dividing the world into things, there is an unwarranted assumption that processes must have a beginning, middle and end. But if all things are interdependent then “whatever is in motion must be put in motion by another” and “this cannot go on to infinity” are incoherent

I don’t see the two conditions as mutually exclusive. In your view, you either have to agree that nothing exists except motion or that only static being exists, in which case the universe is incoherent, or you must hold that the universe is incomprehensible. And for those who believe in the Scriptures none of these positions can logically be held.

1. The assumption that motion needs a cause is unwarranted. It is simpler to assert that motion is the default, and we’re pretty sure this is the case in the observable universe (Newton’s first law)

Again motion and being are not mutually exclusive. These were the ancient ideas that Aristotle proved false. Newton’s first law proves no such thing.

1. The argument is a posteriori (“evident to our senses”) and yet the concepts of potentiality and actuality are introduced without any evidence that they exist objectively, or are anything more than a somewhat contrived attempt at a qualitative reductionism.

Aristotle and Thomas and thousands of philosophers say differently, even many of the " modern " philosophers.

1. The argument is presented as a proof, yet no a posteriori argument can be.

Again, false, for the same reasons just stated. Why not read the sources as Bakmoon is doing?

God Bless
Linus2nd

 

[Linusthe2nd]

My mistake. It turns out it was actually from Book 6 chapter 5, not Book 8. I’m actually only reading through Aquinas’ commentaries from the site. I read through the parts of Aristotle’s main text in PDF form but it seems PDF of the Physics has its bookmarks a little off so I thought it was book 8.

The only reason why I cite the passage from book 6 is because it has that bit at the end about an infinite series of movers requiring a first term and it would be improper for me to not mention it even though it is not a complete argument. Of course, Aristotle gives his completion of his point in Book 7.

My intent in saying that Aquinas didn’t advance new arguments in his commentaries but merely paraphrased them is not to criticize him but mainly to show that I’m not leaving out any major points raised by Aquinas on the issue. Paraphrases have an essential role to play in Aristotle especially. For example, In addition to writing comprehensive commentaries on Aristotle, Ibn Rushd also wrote a complete set of epitomes and a complete set of paraphrases on Aristotle that were very valuable.

Good, I understand. Averroes ( Ibn Rushd ) was one of those through whom we came to know Aristotle. A great philosopher with whom Aristotle and Thomas disagree on some key points.

Linus2nd

 

[inocente]

Not formidable. No argument can be convincing to someone who either cannot understand or who comes to the table with an ideological conviction that makes agreement impossible ( e.g. the East and the West ).

Oddly enough the interdependence of things does not make the existence of individual beings contrary to reason. It certainly didn’t cause A. and T. any problems. And it doesn’t cause me any problems. I’m surpirsed you have the view you just expressed. I don’t see the two as mutually exclusive.

I don’t see the two conditions as mutually exclusive. In your view, you either have to agree that nothing exists except motion or that only static being exists, in which case the universe is incoherent, or you must hold that the universe is incomprehensible. And for those who believe in the Scriptures none of these positions can logically be held.

Again motion and being are not mutually exclusive. These were the ancient ideas that Aristotle proved false. Newton’s first law proves no such thing.

Aristotle and Thomas and thousands of philosophers say differently, even many of the " modern " philosophers.

Again, false, for the same reasons just stated. Why not read the sources as Bakmoon is doing?

To be clear these are not my objections, they are a summary of standard objections to the argument from motion made by large numbers of people over the years and published by a number of sources.

They are for the most part objections to the speculative reductionism of A & AT, which is not self-evident but just assumed without any reasoning. For instance, by simply dismissing A & AT’s way of dividing up the world, infinite regression is not an issue. A more minor objection is that the argument relies of physics which is known to be false.

I didn’t intend to debate the objections as it’s all been done before. The issue is simply that the argument from motion is a very poor vehicle for proselytization since the only rebuttal possible to the standard objections is the one you make - that fans alone understand and the rest of the world is too ignorant or too obstinate to comprehend.

Which is the kind of rebuttal used by flat earthers and alien abductionists and no end of mystics. In other words, not just highly unconvincing but likely to send folk running in the opposite direction.

 

[Linusthe2nd]

To be clear these are not my objections, they are a summary of standard objections to the argument from motion made by large numbers of people over the years and published by a number of sources.

They are for the most part objections to the speculative reductionism of A & AT, which is not self-evident but just assumed without any reasoning. For instance, by simply dismissing A & AT’s way of dividing up the world, infinite regression is not an issue. A more minor objection is that the argument relies of physics which is known to be false.

I didn’t intend to debate the objections as it’s all been done before. The issue is simply that the argument from motion is a very poor vehicle for proselytization since the only rebuttal possible to the standard objections is the one you make - that fans alone understand and the rest of the world is too ignorant or too obstinate to comprehend.

Which is the kind of rebuttal used by flat earthers and alien abductionists and no end of mystics. In other words, not just highly unconvincing but likely to send folk running in the opposite direction.

You remind me of Lucy in the comic strip Peanuts. Poor Charlie could never do anything to please Lucy. There was a constant dark cloud following her around.

It doesn’t surprise me at all that many people reject A. and T, most of the world doesn’t accept Christ either. So should we stop talking about Christ because he is so unpopular? Oh, BTW, I don’t think the philosophy of A. and T. are used primarly as evangalization. Most Catholics who engage in philosophy do so because they either find in so interesting or because they are Theologians who find it useful, or perhaps both. It is certainly not used by the vast number of Catholics. You will notice the the philosophy forum usually gets about half the views as the religious and theological forums.

God Bless
Linus2nd

 

[Linusthe2nd]

Look at the relevant portion of Aristotle’s primary argument in the Phyisics. He Says:

Aristotle’s argument boils down to this:

1. If X moves Y then X and Y are simultaneous
2. In an infinite causal series ending in A, A is moved by B which is moved by C etc…
3. Therefore by induction, all the terms of such an infinite causal series occur simultaneously
4. The total amount motion for causal series is equal to the sum of the motion of its terms
5. An infinite sum of non-zero positive (like motion) amounts is infinite
6. Therefore an infinite causal series has an infinite amount of motion
7. An infinite amount of something occurring in the present is an actual infinity
8. An infinite causal series has an infinite amount of something (i.e. motion) as its terms occur simultaneously
9. An infinite causal series is an actual infinity
10. An actual infinity cannot exist
11. An infinite causal series is an actual infinity
12. Therefore an infinite causal series cannot exist

Can we agree to work off of this as an accurate formalization of Aristotle’s argument? If it isn’t, then how would you correct it to be an accurate depiction of his argument? Once the argument has been properly established I will give my full analysis.

You know I have a hard time visualizing an infinite series, one member of which moves in finite time. Go back to my post #27 where I mentioned that arguments given in comments 14 and 15 were my arguments of choice. But go ahead with your argument, but all those A B and C’s make my head swim.

Linus2nd

 

[inocente]

You remind me of Lucy in the comic strip Peanuts. Poor Charlie could never do anything to please Lucy. There was a constant dark cloud following her around.

It doesn’t surprise me at all that many people reject A. and T, most of the world doesn’t accept Christ either. So should we stop talking about Christ because he is so unpopular? Oh, BTW, I don’t think the philosophy of A. and T. are used primarly as evangalization. Most Catholics who engage in philosophy do so because they either find in so interesting or because they are Theologians who find it useful, or perhaps both. It is certainly not used by the vast number of Catholics. You will notice the the philosophy forum usually gets about half the views as the religious and theological forums.

Not sure about your comparison of A & TA with Christ. Besides the little matter of Aristotle not being God, a reason why we don’t see temples dedicated to him is he’s wrong on a lot of stuff, plus Christ is inspiring and relevant to everyday life, which Aristotle is not.

As for the philosophy forum getting fewer viewers, it might have something to do with more readers being switched off than switched on by dry abstractions. Just a theory.

btw Lucy is good for Charlie. She constantly challenges his naive philosophy.

 

[Linusthe2nd]

Not sure about your comparison of A & TA with Christ. Besides the little matter of Aristotle not being God, a reason why we don’t see temples dedicated to him is he’s wrong on a lot of stuff, plus Christ is inspiring and relevant to everyday life, which Aristotle is not.

As for the philosophy forum getting fewer viewers, it might have something to do with more readers being switched off than switched on by dry abstractions. Just a theory.

btw Lucy is good for Charlie. She constantly challenges his naive philosophy.

Good Grief Lucy! I never compared A. and T. A. with Christ - you are kidding, right?

Charlie

 

[Bakmoon]

You know I have a hard time visualizing an infinite series, one member of which moves in finite time. Go back to my post #27 where I mentioned that arguments given in comments 14 and 15 were my arguments of choice. But go ahead with your argument, but all those A B and C’s make my head swim.

Linus2nd

Infinite series do that to everyone I think I’ll get to Aquinas’ reformulations of Aristotle’s argument in terms of requiring a first term later as I would rather get the really complex argument out of the way first.

Aristotle’s argument which goes like this:

1. If X moves Y then X and Y are simultaneous
2. In an infinite causal series ending in A, A is moved by B which is moved by C etc…
3. Therefore by induction, all the terms of such an infinite causal series occur simultaneously

1. The total amount motion for causal series is equal to the sum of the motion of its terms
2. An infinite sum of non-zero positive (like motion) amounts is infinite
3. Therefore an infinite causal series has an infinite amount of motion

1. An infinite amount of something occurring in the present is an actual infinity
2. An infinite causal series has an infinite amount of something (i.e. motion) as its terms occur simultaneously
3. An infinite causal series is an actual infinity

1. An actual infinity cannot exist
2. An infinite causal series is an actual infinity
3. Therefore an infinite causal series cannot exist

This argument has two flaws by my analysis. The reasoning itself is sound, premise 1 and 5 have problems, and I think that premise 10 requires clarification in regards to motion.

I’ve already given an important critique of premise in post 15 on page one. To elaborate:

Because causes often (indeed almost always) precede their effects rather than occurring simultaneously with them it is absurd to say that a mover and moved (which in Aristotelian terms is the same as saying an efficient cause and its effect) themselves always occur simultaneously. For example, If I set up a line of three dominoes and push the first one down, the first serves as the efficient cause of the fall of the second, which serves as the efficient cause of the fall of the third. And yet, the motion of the first, second, and third dominoes are not simultaneous.

One way to resolve this contradiction is to say that there is an intermediate causal agency of some kind. We would probably refer to this as simply a force in the case of physical motion. However, even so, it is clear from observation that there is no simultaneity in this case. If forces were also simultaneous then that would mean that domino three is simultaneously acted upon by the force from domino 2, domino 1, and the force imparted from my finger to domino 1 in the first place. This is clearly not the case as if it were so then the longer you make the domino chain the greater total force acting on the last domino would be as all of the previous forces would accumulate. As this clearly does not happen one must reject premise 1.

The other problem is premise 5. It is demonstrably not the case that an infinite series of positive values yields an infinite result. In mathematics an infinite series that adds up to a finite total is referred to as a convergent series. For example the infinite series 1+1/2+1/4+1/8… where each term is half the magnitude of the previous term the total result of this infinite series is two. Incidentally this is the basis of how Zeno’s dichotomy paradox is resolved in modern times. For most modern philosophers, Zeno actually got it right that motion involves passing over an actual infinity of locations. However, the total of time elapsed is not infinite as it is a convergent series rather than a divergent one.

This actually ties in with my issue with premise ten that an actual infinity cannot exist. I think that Zeno’s paradoxes are correct except in the case of concluding that infinite time required to complete an infinite series. Aristotle tries to escape the actual infinity of motion by saying that if you actually try to count out and divide the individual points you only have a potential infinity, but that’s missing the crux of the argument that the number of actual points themselves are infinite regardless of whether or not you discern them, and so it is an actual infinity.

I think a reasonable person of today would have to modify Aristotle’s assumption that actual infinities are impossible and instead say that only divergent actual infinities are impossible and that convergent actual infinities are not impossible.