How can this premise in the Cosmological Argument be true?

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Hi!

I’m reading Peter Kreeft’s A Short Summa, which is a short book of excerpts of St. Thomas Aquinas’ Summa Theologica. I have read the article in which St. Thomas describes five ways to prove the existence of God.

I’m having trouble understanding one of the premises in the argument, however. In particular, the premise “this cannot go on to infinity” is puzzling to me. I do not see how that premise can be true. Why cannot an infinite chain of causes exist? It seems that he is begging the question: “if no first cause exists, then no second causes exist, and we know second causes exist. Then a first cause must exist.” How can we know that the causes we see are second causes, and not simply N+1th causes?

Thanks!
Ben
 
Hi!

I’m reading Peter Kreeft’s A Short Summa, which is a short book of excerpts of St. Thomas Aquinas’ Summa Theologica. I have read the article in which St. Thomas describes five ways to prove the existence of God.

I’m having trouble understanding one of the premises in the argument, however. In particular, the premise “this cannot go on to infinity” is puzzling to me. I do not see how that premise can be true. Why cannot an infinite chain of causes exist? It seems that he is begging the question: “if no first cause exists, then no second causes exist, and we know second causes exist. Then a first cause must exist.” How can we know that the causes we see are second causes, and not simply N+1th causes?

Thanks!
Ben
Earlier this month Trent Horn did a show called "Arguments For (and Against) God’s Existence. catholic.com/radio/shows/arguments-for-and-against-gods-existence-13906

He did that show to defend the arguments for God’s existence against common objections, and to answer arguments against God’s existence using philosophical principles. I haven’t listened to the whole show yet, but in the first hour he does at one point discuss the cosmological argument, and he uses an analogy that I think is helpful:

If you saw a bunch of train cars going along on a track, it wouldn’t be reasonable to suggest that each train car was simply pulled along by the next one unto infinity. And this isn’t just intuition.

Yes, intuition tells us that there has to be an engine at the front (the first cause), but at a deeper level we can know that the boxcars can’t be pulling each other along because no boxcar has the ability to move itself, let along another boxcar.

I think that’s why we can know that the chain of causes can’t go to infinity: no material cause is sufficient to move itself, create itself, provide a sufficient reason for its own existence, etc.

Listen to the show for more detail, but I hope that helps.
 
Hi!

I’m reading Peter Kreeft’s A Short Summa, which is a short book of excerpts of St. Thomas Aquinas’ Summa Theologica. I have read the article in which St. Thomas describes five ways to prove the existence of God.

I’m having trouble understanding one of the premises in the argument, however. In particular, the premise “this cannot go on to infinity” is puzzling to me. I do not see how that premise can be true. Why cannot an infinite chain of causes exist? It seems that he is begging the question: “if no first cause exists, then no second causes exist, and we know second causes exist. Then a first cause must exist.” How can we know that the causes we see are second causes, and not simply N+1th causes?
He doesn’t claim that an infinite chain of causes can’t exist. It can. He says that the infinity must be bounded on one side – like when we count numbers, we start with 1. We could go on forever, but not without starting with 1.

If the race didn’t start, then the race isn’t going on. 🤷
 
Hi!

I’m reading Peter Kreeft’s A Short Summa, which is a short book of excerpts of St. Thomas Aquinas’ Summa Theologica. I have read the article in which St. Thomas describes five ways to prove the existence of God.

I’m having trouble understanding one of the premises in the argument, however. In particular, the premise “this cannot go on to infinity” is puzzling to me. I do not see how that premise can be true. Why cannot an infinite chain of causes exist? It seems that he is begging the question: “if no first cause exists, then no second causes exist, and we know second causes exist. Then a first cause must exist.” How can we know that the causes we see are second causes, and not simply N+1th causes?

Thanks!
Ben
Thomas is talking about a vertical infinite series as opposed to a horizontal infinite series. An example of the later would be an infinite series of fathers and sons which is logically possible. However, each member of that series must have a cause of its existence here and now. You exist but neither you nor your father accounts for your current existence. You exist here and now, so there must be a cause for the fact that you do not cease to exist here and now. There cannot be an infinite series of such causes, eventually we must arrive at a self caused cause which causes your existence.

And the same is true for everything that exists in the world at this instant. So we can say that the whole world, here and now, must have a cause for its existence. Eventually this has to be a self caused cause which causes the world to exist and this we call God.

Linus2nd .
 
**Thomas Aquinas turns the cosmological argument into a argument for the subsisting power of God over creation. I personally don’t see the connection. He renounces the kalam cosmological argument in the Summa in the article on whether it is an article of Faith that creation was not from eternity. For some strange reason he doesn’t think you can believe something from faith and from reason at the same time. The Kalam argument looks at eternity backwards, so its hard to grasp. It also “shows” that a point with an infinite line going one way is inherently illogical. Aquinas admits that we cross infinite points in finite time in his article on whether angels pass through intermediate space, but that is because motion is one step ahead of matter. He contradicts himself when he says that all the points can’t be gone thru individually and yet he says there can be an infinity of accidental causes in his article on whether the universe of creatures always existed.(supertask, see online standford philosophy encyclopedia); this also contradicts the intuition of dmar198. Vatican I said we can **know **from reason that God exists, but I don’t think it can be proven like a mathematical proposition. intuitive knowing from the world aroundus
 
**He renounces the kalam cosmological argument in the Summa in the article on whether it is an article of Faith that creation was not from eternity. **For some strange reason he doesn’t think you can believe something from faith and from reason at the same time. ****

It’s not a strange reason if what we are told from faith contradicts what we gather from reason. Aquinas, if I correctly understand your above remark, is following Aristotle’s principle of identity … that a thing cannot be true and false at the same time. That was the heresy promoted by Siger of Brabant and Aquinas refuted it.
 
Aquinas doesn’t belief God is a matter of supernatural faith, but natural faith. He doesn’t think you can know something by reason and also believe it because of revelation
 
He doesn’t claim that an infinite chain of causes can’t exist. It can. He says that the infinity must be bounded on one side – like when we count numbers, we start with 1. We could go on forever, but not without starting with 1.

If the race didn’t start, then the race isn’t going on. 🤷
But then how do you explain the integers? They have no smallest element.

I suppose you could put them in a sequence like 0, 1, -1, 2, -2… but then how would you deal with uncountable sets like the real numbers?
 
But then how do you explain the integers? They have no smallest element.

I suppose you could put them in a sequence like 0, 1, -1, 2, -2… but then how would you deal with uncountable sets like the real numbers?
You are talking about the numbers themselves. I am talking about a listing of the numbers. The numbers themselves are infinite in all directions, but any listing of the numbers must have a first object in the listing. (A listing of numbers is a series of events.)

I understand that this is controversial. But I think it is sensible enough, and I think it’s what Aquinas meant.
 
You are talking about the numbers themselves. I am talking about a listing of the numbers. The numbers themselves are infinite in all directions, but any listing of the numbers must have a first object in the listing. (A listing of numbers is a series of events.)

I understand that this is controversial. But I think it is sensible enough, and I think it’s what Aquinas meant.
Okay, but I think we disagree as to what time is meant to achieve. A time coordinate/parameter is usually regarded as a real number that is meant to order events, not list them. An infinite regression still preserves order. Indeed, if it didn’t, we couldn’t call it a regression.

You may be able to argue that there is a beginning of the universe because of the Big Bang Theory, but this isn’t a priori knowledge. Consistent models of the universe can be conceived without specifying a beginning. For instance, Newton’s Laws are reversible–you can run them backward forever with no difficulties.
 
Okay, but I think we disagree as to what time is meant to achieve.
You’re going to have to explain that sentence to me. “Is meant” is very confusing. Meant by whom? And in what sense does time “achieve” anything?
 
At first glance, the possibility of an infinite regress of past events and causes doesn’t seem particularly controversial. However, upon closer inspection, you soon realize that it is simply incoherent with the way we know the universe to behave. What is infinity minus infinity? In math, there is no solution to that problem. The infinite is an idea conjured up by our intellect. It doesn’t apply to the contingent universe we are familiar with.

“The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought. The role that remains for the infinite to play is solely that of an idea.”

-David Hilbert

In my opinion, it seems rational to believe that there was a first cause that lead to the existence of all contingent reality.

-Phil
 
I personally think this is one of the problem of many modern authors when it comes to philosophy.

there are a few things some modern authors, even Kreft :(, seem to miss. It could be that they are talking to a modern argument so they are mixing it in with their arguments.

Aquinas says
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
First Aquinas is not talking using our modern understanding of language. Motion in the 21st century is thought in a strictly scientific way. A bowling ball has motion as it moves down the lane. Motion to put it simply is movement from point a to point b. People don’t know of anything in motion that is anything more than that. Look back earlier in his explanation. (I think many people miss this and fail to realize what is going on)
For motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be reduced from potentiality to actuality, except by something in a state of actuality. Thus that which is actually hot, as fire, makes wood, which is potentially hot, to be actually hot, and thereby moves and changes it. Now it is not possible that the same thing should be at once in actuality and potentiality in the same respect, but only in different respects. For what is actually hot cannot simultaneously be potentially hot; but it is simultaneously potentially cold. It is therefore impossible that in the same respect and in the same way a thing should be both mover and moved, i.e. that it should move itself.
For aquinas this is what motion is. I have a coffee cup sitting next to me it is potentially cold. But my coffee cup could not move one cm and it still become actually cold. This is motion for aquinas. A movement from potentiality to actuality, nothing more nothing less. That is also the modern notion of motion. The bowling ball is potentially moving from lane to pins. Only when the person bowls the ball does that become actual. Even in that action it is still constantly going from potentiality to actuality.

The thing is Aquinas says that an infinite regress IS possible, but it is shown by divine revelation that God created us and there is a beginning. I don’t remember where this is found but it is out there.

When Aquinas in this talks about this can’t go on to infinity he means that an infinite regress can’t exist in itself. Something that is always active must be responsible for things that are in motion.

Atheist always tend to use the who created God argument. Many Christians can’t respond to it, because they have a Kantian view of the world. A causes B is the only cause that exists. Many don’t have an understanding of primary causality, formal causality final causality etc.
 
But then how do you explain the integers? They have no smallest element.

I suppose you could put them in a sequence like 0, 1, -1, 2, -2… but then how would you deal with uncountable sets like the real numbers?
the difference is that numbers do not depend on one another for their existence; the claim is not that there cannot be actual infinities, but that an actually infinite series or set or whatever, is itself in need of an explanation or cause of its existence.

in other words, if one member of a series depends for its existence on something else, then simply increasing that series in number so that it consists of an infinite number of things all of which rely for their existence on something else, does not suddenly explain or account for the existence of any of them.
 
Hi switalabe,

You seem to confuse an infinite number of effects with an infinite number of causes. But infinity of effects, by definition, is never reached ; every effect adds to the *number *of effects, so you will always have a definite number of effects. And a definite number of effect posits a definite number of causes. You finally reach a cause that is not an effect, a cause that exists necessarily. We call it God.
 
The thing is Aquinas says that an infinite regress IS possible, but it is shown by divine revelation that God created us and there is a beginning. I don’t remember where this is found but it is out there.

When Aquinas in this talks about this can’t go on to infinity he means that an infinite regress can’t exist in itself. Something that is always active must be responsible for things that are in motion.

Atheist always tend to use the who created God argument. Many Christians can’t respond to it, because they have a Kantian view of the world. A causes B is the only cause that exists. Many don’t have an understanding of primary causality, formal causality final causality etc.
To be fair, I think Aquinas would allow that an infinite regress could be possible, but that it couldn’t sufficiently explain its own existence or even how an Uncaused Cause (aka God) could affect the present from a time in the infinite past. Hilbert’s writings confirm this.

In other words, for anyone looking, a la the principle of sufficient reason, for a sufficient explanation for a causal chain within the chain itself, an infinite regression would be ruled out in principle. You could not, by definition have a sufficient reason for an infinite chain of events within that very chain of events.

That does not rule out the possibility of infinite causal chains existing if the sufficient reason for the existence of the chain itself is “outside” the chain.

This is where Aquinas gets into the difference between causes per se and per accidens

Take the train example.

It is true that the motion of the cars currently in front of us (the present) would never have been passed to these cars if the initial movement began an infinitely long time ago since, for one, infinity would rule out “initial” by definition.

What Aquinas is saying is that a chain of accidental “motion” or change could not depend upon an initiator of that motion from the infinite past.

However, that does not, by itself, rule out the possibility of an infinite chain of “motion” if the initiator is not in the chain itself, but outside of it.

Take the infinitely long train. It could not be powered by a locomotive at one end, partly because there is no end to begin with, but also because “motion” could not be transmitted from the infinite past to the present - it would never get here.

However, if what it is that “powers” the chain of train cars is not a locomotive at the end but, if this were, say, a child’s play set consisting of an infinitely long train on an infinitely long track, the child’s hand at a specific location in time and space could by pushing it from somewhere in the middle, transfer motion in both directions (front and back) at the same time. Similarly some conception of the “hand of God” (Unmoved Mover, motion per se, etc.) could effect the motion of the train from the present in both directions - from the past and into the future - moving the train forward. In other words, if the “motion” or “cause, per se, of motion” were imparted in the present there would be no need to overcome the problem of an actual infinite and Aquinas would be quite correct to admit the conceptual possibility of an infinite universe provided the present was key to explaining the “motion” of the universe in both temporal directions, i.e., the infinitely long train is moved “from the middle,” from the present by a cause of motion “outside” of the train itself.

The problem with this analogy is that the child’s hand only explains one aspect of the train (its motion in the commonly held sense,) whereas the principle of sufficient reason requires that everything about the train (size, shape, colour, location, existence, etc.) be explained, but a “past dependent” explanation can never suffice for the same reason a past dependent explanation for motion doesn’t.

When Aquinas insists, for example, that God “sustains” all of creation in existence, he is maintaining that the subsistent cause of reality is from the eternal “Now,” not from “the past” pushing forward. This means that causal chains could conceivably be of infinite length in either direction since time, itself, could be generated atemporally.

That doesn’t mean that infinite causal chains necessarily exist, but merely that they are not ruled out a priori. Current Big Bang cosmology is demonstrating that the universe itself is not an infinite causal chain.

Either way, whether the universe is infinite or not, Aquinas’ argument is not affected because he demonstrates that any cause, to sufficiently explain what is required of it, cannot merely operate within either an infinite or finite chain since an Uncaused Cause (Unmoved Mover) must logically account for its own existence (why anything exists at all) prior to (and independent of) explaining anything else.

I think you misunderstand Kreeft, by the way.
 
You’re going to have to explain that sentence to me. “Is meant” is very confusing. Meant by whom? And in what sense does time “achieve” anything?
Time is a concept that is meant to clarify our understanding of the universe, like “mass” and “space”. I was pointing out that it achieves this splendidly without providing a list, as it need only order events to be useful.
the difference is that numbers do not depend on one another for their existence
I hate to be “that guy” but I have to disagree here. If you develop, say, the theory of integers axiomatically, the negative numbers arise as a consequence of the axioms of order and the axiom of additive inverses (opposites). So from this perspective, -1 exists because 1 does, -2 exists because 2 does, and so forth. Furthermore, 2 exists because 1+1 has to be well-defined, so both -1 and -2 exist because 1 exists.

Now we don’t actually talk about contingencies in math, but only logical implication. So I think our main disagreement is the assumption that modality and contingencies have to come into play at all. Spacetime is conceived as a 4-dimensional abstract space. Saying that the past has to exist for the future’s sake is like saying that a region in another space, say a 2D plane, has to exist for the sake of the rest of the plane. It really isn’t immediately obvious what you mean, let alone that the assertion is true.
 
Time is a concept that is meant to clarify our understanding of the universe, like “mass” and “space”. I was pointing out that it achieves this splendidly without providing a list, as it need only order events to be useful.
Is there something to which “time” refers? Besides the “concept”, I mean? Something human-independent?
 
Is there something to which “time” refers? Besides the “concept”, I mean? Something human-independent?
I remember reading a book by Sean Carroll which suggests that we owe our perception of time to entropy. The interesting thing about entropy is that (insert the usual disclaimer about only applying to closed systems here) it can only increase. Thus I can tell when a building’s been deserted for a while because it has fallen into disrepair, which is a state of higher entropy.

Imagine if we lived in a universe with only conservative forces such that every event is perfectly reversible. The universe may be like billiard balls colliding on a frictionless table where the collisions are perfectly elastic, for example. I could record some footage of such a situation, play the video in reverse, and no one could tell the difference. Entropy, friction, and nonconservative forces are how you distinguish past from future.

So basically all we need to have a conception of time is to find an observable quantity that only increases or decreases.
 
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