If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again. But this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover;

I am not entirely sure why this is true. I think my problem is that it seems we can extrapolate from this to say that nothing is infinite. But that isn't true.

St. Thomas has no problem with infinity in general--for example, he argues that the beginning of the world in time is knowable only through revelation. The key is the difference between an accidentally ordered infinite series vs. an intrinsically ordered series. Try this: http://edwardfeser.blogspot.com/2010/08 ... eries.html

The analogy I often use to illustrate why there must be a first is a light bulb and a very long extension cord

See we can truthfully say the lightbulb is powered by the extension cord. And that extension cord can get that power from another, and so on. But no matter how long the cord, ultimately there must be a battery or a generator...something which puts the juice into the wire. Hence the wire cannot go on infinitely, it must need a power source somewhere

Secondary causes are by definition like that wire. By definition they can only give because they have received, otherwise they would be the first and therefore there would be no more links in the chain. But if all of the links in the chain of causes are like this, that they all receive from another, then we simply can never get the ball rolling, because no addition of links in the chain substitute for the motion they pass alone by receiving, just as no number of cords substitute for that battery at the end.

You might find it helpful if going through the 5 ways to look at the 5 ways in the Summa contra gentiles. While not a simple text, St. Thomas gives multiple arguments for each of the premises that, in the Summa Theologiae, are just asserted.

This can be found here

http://dhspriory.org/thomas/ContraGentiles1.htm#13

I only present the 3rd argument against an infinite regress. There are two others (one based on things moved having to be bodies, the 2nd is based on the "ordered series" part and begins at the opposite end as it were)

will do.




very helpful image. Thank you.




I own it. I will look over the additional arguments again.

Obi's reply is the important one. If I may expand on it, Thomas isn't talking about an infinite series of temporal events, as in A happens and then B and then C and then D, etc. He is talking about an infinite series of simultaneous events, such as A is causing B such that B is causing C such that C is causing D, etc. In the former, you can take away A and B, C, and D will still happen. Imagine, for instance, a series of dominoes. You knock over the first, which knocks over the second, which knocks over the third, etc. Now, suppose that while the dominoes are still falling, you remove the first dominoe from the table. Does that stop the chain from continuing? Of course not. On the other hand, imagine a train, in which the engine is pulling a car, which in turn is pulling another car, which in turn is pulling another car, etc. Now, suppose that you took away the engine. Would the cars continue to be pulled? No. After the inertia wears off, they will stop--and they will stop precisely because they are no longer being pulled.

Thomas, in fact, thinks that you can't use his argument to prove that the universe had a temporal origin. Thomists, for that reason, typically aren't fans of the Kalam Cosmological Argument (as popularized by Craig, statued thus: That which comes into existence must have a cause; the universe came into existence; therefore, the universe must have a cause -- where the minor premise is usually defended by arguing that an infinite number of past events is logically absurd).

So, to your post in particular, then, Thomas wouldn't have a problem saying that some things are infinite. He just would say that chains of simultaneous causes--what Obi rightly called an intrinsically ordered series--can't be infinite. Beyond the post he recommended, I'd also point you to Richard Howe's discussion of this issue in his "Two Notions of the Infinite in Thomas Aquinas' Summa Theologica I, Questions 2 and 46."

I am not sure how taking away the engine equates to an infinite series.



I am confused by the general phrasing of "intrinsically ordered series" and things like it. But it seems I have plenty of reading to do in order to become familiar with those phrases. Thanks for the link.

Think of it this way: You can have an infinite amount of freight cars in the freight yard doing nothing. St. Thomas is fine with that. They can even be coupled together into an infinitely long train, and St. Thomas is fine with that.

But if the train starts moving ... let's start with the car at the end of the train. What's making it move? The car in front of it. What's making that car in front of it move? The car in front of that car? What's making that one move? The next car, and so on. This can't go on forever because then there would be nothing actually supplying the motive power. Something has to be making everything else move.

There is always something else that would be moving the thing in front of it though...

I guess I don't see why the chain of causes can't keep going.

Unless, we talk about it temporally. But it seems I have been instructed not to do that.
In other words, if the cause of one domino falling is infinitely far away, then it never would have started...

Is that right?

Suppose for a moment that the cars are on a circular track and there is no first car and no last car...just a series of box cars all connected in a circle. But they are moving. There still has to be a "first" mover to get the motion started.

I am beginning to understand that infinite means no first. I guess that is the key isn't it?

How about this. I have one of those interlocking plastic monkies. He is almost at the bottom of an infinitely high wall (which itself is not possible, but that is an aside). He is hanging on another monkey and so on and so on, as far as you can see. Still, you can reason, what is holding them up? I have to realize that they must be attached to the wall somewhere. But then that nail or that monkey which is glued or whatever the case may be is the first. No other monkey after him explains that property of hanging on the wall. They only explain how the subsequent monkeys share in that hanging. Without a first and there an end point, and therefore not an infinite series, they would not be hanging from the wall

I have been doing some reading up on this lately.

An infinity is without completion (as completion means something which has begun and ended = finitude).

So, you can imagine infinite numbers on a number line only because the numbers have a starting point, namely 0, and then progress towards infinity, but the number line is never completed as inifinity cannot be reached. Even if you start writing the numbers down (making the imaginary line into a real line), there is always a future that cannot be reached and which remains imaginary.

Therefore, an infinite number line of real numbers will always have some part of it which must continue to be an imaginary line (imaginary being the key word here).

What about infinite regression (no beginning)?

Any series of real events (writing numbers, universes causing other universes) which is in the past and has come forward through time (time being asymmetrical) to the present, is a completed (already accomplished) series of real events.

But an infinity of real events can never be completed (accomplished).

Therefore, an infinite regression of real events, by definition, cannot be accomplished, and nothing exists.

But something does exist.

Therefore, an infinite regression of real events is impossible.

(I hope I got that right.)

Nope. As far as reason goes, the universe could have always existed. At least St. Thomas thought so (who would deny an actually infinity, even in the imagination, and in mathematics in general too as a side point)

As was made in earlier posts, as far as the 5 ways go, temporal succession has nothing to do with it.

Nothing prevents such a temporal sequence of having existed. There is no logical contradiction in saying, there never was a beginning. We have good reason, as far as natural light goes, for saying that in fact we had a beginning. But that is irrelevant here.


Let the earth be as old as you will. We are looking at an instant. A chain of causation, hic et nunc, here and now.

Well, don't just say "Nope". How am I ever gonna learn from that? Please show me where my reasoning breaks down. I am basing the prohibition of infinites in reality on a paper delivered by David Hilbert: On the infinite

Maybe Doom will pipe in on this. I have been told he has a rudimentary understanding of this stuff.

First of all, good to see you back, pax!

Second, you might want to check out the link I gave will. There are two sorts of philosophical infinities, one possible and one not. You're conflating the two.

Good to talk with you again, as well, Father.

I am not approaching this from a Thomistic point of view, but am rather trying to get a good understanding of the arguments put forward by Father Robert Spitzer. He referenced the paper by Hilbert, which I managed to find online, and have read it over a few times. Hilbert just flat out prohibits infinities -- Cantorian sets, which he loves -- for real things. His argument, which I understand is generally accepted by mathematicians (whatever they are) is that allowing infinites for real things undermines finite mathematics and makes it contradictory and meaningless. I don't have a lot of training in these sorts of things, but I can grasp the basic concepts, and it sure does seem to me that Father Spitzer is actually making a purely scientific argument for Thomas's uncaused cause argument -- what Father Spitzer calls "an unconditioned Reality".

Anyways, I never knew that Saint Thomas's argument was ontological and not mechanical.

See? I always learn from you, Father!**

(Mostly I have learned not to click on links you provide until I check them in the quote box for Rick Rolls first.)

pax, there is no reason why I should accept that the world could not be infinitely old, as far as an argument about an infinite existing goes. The burden is on the one trying to make that argument. As the past does not exist in act, we do not have an actual infinity existing in this case. It is an accidental series where the terms do not exist in act at once. Why should that even be a problem, a priori? There can be argument based on empirical evidence that, in fact, the universe is not of an infinite age (but even that is not certain, as based purely on empirical evidence there are several possibilities besides a finite age)

In anycase, since your response was to the OP, it is sufficient to point out that you are not talking about the same thing

The are many points I could take issue with in your post, but I didn't see any reason to start a debate, bring up Dedekind, what mathematics is, how that relates, etc. And we would have to get on the same page in terminology. There is certainly not actual infinity that is imaginary in the sense of actually being in the imagination. The imagination cannot project something that is infinite, not actually at least.

So the existence of the universe could be infinite, but the we cannot have infinite movers?

As far as natural reason can show, yes, as far as what the 5 ways show at least. St. Thomas did not think you could prove a finite age for the world.

I just want to throw this in the mix. I am not convinced that St. Thomas Aquinas was all that convinced that an actual infinite was possible or even rationally conceivable. Rather, I think that he was skeptical about attempts that had been made to disprove it. Those are two different things. And there are plenty of mathematicians on record who say that the infinite is an idea and not something that has any application to real things. It is something that allows for the conception of new ideas and provides for a workspace that can always accommodate new expansion, but itself is never actually infinite. It is only as big as we need it to be, and we never need it to be actually infinite.

As I read through St. Thomas' work on the infinite, I find a mixed bag of sentiment toward the infinite. It seems that what has been interpreted as his being against any sort of possible argument against an actual infinite, is really only his being against any attempt that HAD BEEN MADE as being sufficient or incontrovertible. I also find that that the idea of an actual infinite is not something that he necessarily finds rational, but just that his acceptance of it not being so in time can only be due to faith because all such arguments against an actual infinity have, in his view failed, so his adherence to a finite past are on faith.

I realize there are better read people on the board here than me, but, as I take a look at everything Aquinas says on the subject, I am finding that what I learned ABOUT WHAT HE SAID, doesn't exactly match up with what I actually read. It's a little more complicated. I also think that a modern Thomist must take into to account what we have gathered through the natural sciences as well... just as we have with biology and other controversial statements made by the Angelic Doctor.

FJ