The following is the first of Thomas Aquinas’ five ways of
establishing the existence of God. For our immediate purpose, we are merely trying to establish a beginning of causes. That the first cause is known as God, or how or to what
extent we have defined God, is secondary to our immediate discussion. For now,
we are merely interested in establishing a beginning.
Aquinas’ first way, from the Summa Theologica, is as follows:
It is certain, and evident to our senses, that in the world
some things are in motion. Now whatever is in motion is put in motion by
another, for nothing can be in motion except it is in potentiality to that
towards which it is in motion; whereas a thing moves inasmuch as it is in act.
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. Therefore, whatever is in motion must be put in motion
by another. 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; as the staff moves only
because it is put in motion by the hand. Therefore it is necessary to arrive at
a first mover, put in motion by no other; and this everyone understands to be
God. (ST, 1.2.3)
Now many introductory philosophy texts have ridiculed the
sentence which says “ But this cannot go on to infinity, because then there would
be no first mover.” The accusation is that Aquinas assumes a first mover
without proving there to be one. But this criticism misunderstands Thomas’
meaning of movement, for his context is that of ongoing causation of movement. Thomas gives us an explanation when he states “as the staff moves only because it is put in motion by the hand.”
Assume you are in your car, and pull up to a railroad crossing, and you see a series of boxcars rolling past. It would be absurd to say “The boxcars need no engine,
for there could be an infinite series of boxcars.” This is absurd, for boxcars
can only be moved, cannot generate movement, and cannot move themselves. If there is movement in the boxcars, there has to be something pulling the boxcars that is much different from a boxcar, something that can cause movement while itself is not being
moved by another. So a series of things being moved cannot go on to
infinity, for there would be nothing causing the movement in the whole chain. Perhaps
to the modern ear Thomas’ statement should read ‘But this cannot go on to
infinity, because there would be nothing causing the movement.’
Thomas is speaking of motion as continuous and present, as
in the example of the hand moving the staff. To Thomas, if there is motion, it
is immediate and continuous through the entire chain. Increasing the length of
the chain of objects being moved does nothing to eliminate the conclusion that
something is moving the chain of objects. Increasing the length of the chain of
objects to infinity merely increases the need for a cause of the entire set of
objects. If there is movement, something must be currently causing the
movement, while itself is not being moved by another. Posing the boxcars as being in a large circle still does not solve the problem, for boxcars can still not generate movement.
Further, theoretical infinites are no help to us in determining causality in the real world. We readily admit that a theoretical infinite can be placed into a theoretical situation, or plugged into a math formula. But math formulas that calculate things do not prove that the things actually exist in the world. So we find no answers in theoretical infinites that are not attached to actual things.
The question then arises about sequential infinites, or finite things that happen in succession. Suppose we come across a long line of dominoes in the road before us, going to the left and right as far as we can see. We suddenly see the dominoes falling over, each one knocking over the next one in line. Our question is then: “Could there have been an infinitely long string of dominoes that were always knocking the next one over?”
First, we are faced with the fact that something would have had to manufacture and set up this infinite string of dominoes, which defies explanation. We have not an infinite amount of materials to make dominoes with, or an infinite road to place them. Second, proposing the existence of an infinite string of falling objects leaves unexplained how the falling was created in the first place. In everything we observe, such a sequence would have had to be initiated. Supposing an infinite string of dominoes leaves us without an explanation of how the falling action came to exist. Of course, a lack of an explanation here does not prove that the falling did not exist everlastingly, but it does present us with a type of “atheist of the gaps” theory: we have no explanation for an observed sequence, so by golly, it must have always existed with no cause. This is an unacceptable answer.
Third, as we observe this string of dominoes falling over, if it were infinite, we must ask ourselves “how did the falling get to me?” If the line of dominoes were infinitely long, it seems the falling would always be an infinite distance away from me. The atheist might reply, “Well, the ones currently falling over have to be somewhere. It just so happens that it is next to you.” But this misunderstands infinites. If the line were truly infinite, then the falling would always, at all instances, be an infinite distance away from any one point on the line. Pick any domino, and the falling would have been an infinite distance away. Since the falling is happening in sequence, it is impossible to select a domino where the falling is not an infinite distance away. The dominoes are always falling, but never arriving anywhere, which is an absurdity.
So we conclude that both simultaneous causation and sequential causation cannot be infinite. If we observe motion, or causality, in the real world, it cannot have gone on for an infinite sequence in the past. If we observe a cause, logic forces us to conclude that there is a first cause, one that is not being caused by another. This we call God.
Thomistic Bent 
Great. What we know about god from this argument is that god is something capable of knocking over a domino, an argument for monism by the way.
Excellent.
Am I correct that there can be no infinite in reality (only in mathematics?).
I assume that means that time had a beginning, which for our meager minds begs the question of what time could mean before this beginning (if “before can have meaning in this instance – if not, how do we think of the term “before” as applied to the beginning of time?).
Secondly, if infinites cannot exist, does that mean the universe has some sort of actual end, limit, or edge (ie: space is not infinite)?
If so, what lies beyond the edge, or how are we to think about that?
Hope you can reply and apologize for so many questions.
–Wm Brown
Forest, Virginia
What the argument holds is that everything in the following list must have a first cause, and a string of prior causes cannot go back to infinity:
–Things with beginnings
–Things made of physical matter (which are always finite)
–Things composed of parts
The things in this list must have a beginning. Once this is established, we can then conclude that the beginning, which is the first cause, is itself uncaused, without a beginning, not made of matter, and not composed of parts. If any of these were the case for the first cause, it would be subject to the argument in the post………it would require a prior cause and would not be the first cause, which the argument concludes must exist.
The post does not demonstrate that no infinites can exist. Christians, including me, have often been guilty of saying “actual infinites cannot exist” which is an imprecise sloppy statement. Instead, the agrument in this post concludes that a first cause must exist, and we go on to conclude that this first cause is infinite. The atheists accuse us of special pleading, but this is incorrect, since the first cause is not subject to the things the argument speaks about……the things in my list above. What the argument does is conclude there must be a first cause, and we then conclude this first cause is not limited.
As to time, we get confused when we think of time as a state of being…..something that we are “in” or “out” of. Instead, time is merely a measure of change between two things. “15 minutes” is only relevant when we measure a certain distance of earth rotation compared to the sun. So time is merely a measure of change. God does not change, therefore He is not subject to time. We change and the universe changes so we experience time. There can only be a “before the beginning” in reference to logically prior to the creation of the universe. Peter, in one of his epistles, speaks of God “before time began.”
As to the universe, it is not infinite since it had a beginning. Any series of successive events after that is a finite series that continues to grow. Therefore at any moment it is a finite size. Whether it continues to grow is another question for another day.
“but it does present us with a type of “atheist of the gaps” theory: we have no explanation for an observed sequence, so by golly, it must have always existed with no cause. This is an unacceptable answer.”
I agree that this is an unacceptable answer. It is not an argument that I have made, or that I would expect to see other atheists make. We are responding to the idea that the infinite is impossible. I merely aim to show that infinity is logically consistent and one possibility. A finite universe/multiverse is certainly a possibility as well. The opposite of “infinity is impossible” is not “it must be infinite”, but rather it is “infinity is a possibility”
“But this misunderstands infinites. If the line were truly infinite, then the falling would always, at all instances, be an infinite distance away from any one point on the line”
I think you are still imagining a start to this process. If there truly is an infinite line of dominoes, there is no start, that’s the whole point. And any two points on the timeline are a finite distance from one another, but since it is an infinite line, no matter how big a number we pick we can find two dominoes that far apart from one another. If these dominoes are falling, then they have always been falling. There was no finger at the beginning of the line that flicked them that got the whole process going, because there is no beginning. That’s the whole point, there is no first domino. We might colloquially say something like “the dominoes started falling an infinite amount of time ago”, but what we really would mean is that there was no start, it just has always been falling.
Let’s go back to what you said “the falling would always, at all instances, be an infinite distance away from any one point on the line”. In this case, where is the falling happening? I would say there is no domino an infinite distance away, because infinity is not a number. In the situation that you described there is no falling, because there are no dominos falling. Infinity is not a number, there is no domino in the infinity-ith position. And yet, infinity is a concept that makes sense here, there are an infinite number of dominos. If we have an infinite string of dominoes, and somewhere along the way they are tumbling, then they have been tumbling forever, without a beginning.
You have gotten close to one of the reasons why an infinite succession is an absurdity.
I am not assuming a beginning. Once again: in the supposed infinite line of dominoes, we can select any domino….any one at all in the line with no beginning…..and there was a point prior to that domino when the falling action was an infinite distance in the past. Being an infinite distance in the past, the falling has an infinite number of dominoes to knock down, which is impossible by succession.
Now you correctly pointed out that there is a finite distance between any two dominoes. But we are not talking about finite distances….we have an infinite line with no beginning, with the falling happening way back there. So at one time, the falling was always an infinite distance away from any one domino we may pick. Infinites cannot be crossed. Therefore, a beginning is necessary.
“Now you correctly pointed out that there is a finite distance between any two dominoes.”
“there was a point prior to that domino when the falling action was an infinite distance in the past.”
Those two comments contradict one another. How can the falling action be an infinite distance in the past if there is no domino that is at a position an infinite distance away? Any time there is falling action, it has to be some particular domino that is falling. There is no domino an infinite distance away, and therefore there cannot be a falling action an infinite distance away.
If we cannot speak of an infinite distance away, then we cannot make any conclusions about the possibility of an infinite series crossing this distance to reach me, and we therefore have no ability to conclude infinite series are a possibility. So such a position is either self refuting or invalid. The post stands.
Infinity exists as a concept, and therefore applying it to numbers does not make sense. That is the point.
Infinite dominoes still does not make sense. It is easy to just say “If they are falling, they have always been falling.” without considering the logical inconsistencies. First off, if the dominoes are truly falling in a line, then they are indeed working within a cause and effect scenario. Each individual domino has its own cause and its own effect.
Think of it like time. Let’s say that you have a 1 billion sided die (somehow), and you roll it once every 1 billion years. So given infinite time and infinite rolls, how many times you would have to roll it before you landed on the number 1 billion? Well, infinity stretches in both directions, that is the point. You would have an infinite number of rolls into the future as well as the past. So not only will you roll 1 billion an infinite number of times in the future, you will also have already rolled it an infinite number of times in the past. You can’t point to a specific point in time where this would not be the case. Go back a googolplex number of years, still an infinite number of 1 billion rolls in the past and future, go forward a googolplex, still an infinite number of 1 billion rolls in the past and future.
If the infinite dominoes are falling, there should be no particular area where they are falling. Theoretically, if you pick a domino at random, then the dominoes that are ‘currently falling’ would be an infinite distance away because you are dealing with an infinite number of dominoes. You could start following the line of dominoes into one direction for eternity and you would never arrive at the dominoes that are ‘currently falling’, because since there is an infinite number of dominoes the falling ones would ALWAYS be an infinite number of dominoes away.
Something that is infinite can not be a chain of causes and effects like these dominoes, but must be consistent throughout eternity, with either all dominoes always being standing or all dominoes always being fallen, otherwise it wouldn’t make sense. But then you have a problem, because the dominoes are no longer engaging in cause and effect, which is contrary to the original question.
An infinite string of dominoes could not have ‘always been falling’ because that is an impossible scenario. You would have an infinite number of dominoes that would have already fallen, and an infinite amount that are still standing, and the event (ie: the dominoes currently falling) would always be an infinite distance away from all dominoes. You cannot pinpoint a single number (or domino) within an infinite amount of numbers, or dominoes, because the odds of choosing any particular number (or domino) is infinity to 1. It is easy to say “Well, SOMETHING has to be chosen!” but this still ignores the logical inconsistencies. It assumes that something was indeed chosen and that this scenario of infinite cause and effects is somehow not only possible but something that necessarily already happened. It is simply not a conceivable event that could occur in reality.
I just want to highlight one little piece from you last paragraph
“You would have an infinite number of dominoes that would have already fallen, and an infinite amount that are still standing, and the event (ie: the dominoes currently falling) would always be an infinite distance away from all dominoes.”
I agree with the first 2 things here, there would have always been an infinite number that have already fallen, and there would always be an infinite number that are still standing, but the last statement is false. The domino that is currently falling is 1 away from the last one that has fallen, and one away from the next one that is about to fall. In fact, if you focus on any specific domino anywhere along the chain, it is a finite distance away from the current falling domino.
So even though there is an infinite number of dominos in the past, and in the future, the current falling domino is a finite distance away from any specific domino
The problem lies, once again, in trying to single out any one domino. Since there are infinite dominoes, any domino you pick at random would be infinitely far away from the falling dominoes.
Think of it like this. Suppose we have an infinite number of numbers. Now, let’s only look at numbers 1 through 2. There are still an infinite number of numbers between these two points: 1.1, 1.2, 1.9, etc.. If you single out 1.99999999999999 and say it is the closest number to 2, you would be wrong because you can always add another number onto the end of the decimal. Say that starting at one, we will begin heading towards two. Each trip we make will get us half way the remaining distance to 2. When will we arrive at 2? The answer is never. 1.5, 1.25, 1.125, etc. etc.. on and on for infinity. There is an infinite number of numbers between any two numbers on a number line that stretches to infinity in both directions. Same thing goes for dominoes, it is just hard to imagine because you are trying to see it from a physical point of view, when in reality infinity can’t exist within our own physical world. We can’t really have infinite dominoes, or infinite space, or infinite anything made of matter. The key is not the ‘distance’ between two dominoes, it is the number of dominoes between them. Once again, it doesn’t make sense to apply physical attributes to something that defies physical possibility.
But this strays from the original topic of this article. You cannot have an infinite chain of falling dominoes. You cannot justify the falling of the dominoes with itself when the falling is a cause and effect event and is not consistent (ie: it would be consistent if all dominoes were standing and would never fall, or if all dominoes were fallen but were never standing). It is difficult to explain because we are trying to use physical objects to explain a non-physical phenomenon. Turtles all the way down is a paradox for a reason.
You are switching between different conceptions of infinity. If we are thinking of an infinite line of dominoes, we should be considering each domino as being assigned to an integer. So each domino is distance 1 from the next. We wouldn’t think of having a domino as lying on each rational number (or each real number if you want to get really crazy) as the thickness of the dominoes would then cause a problem.
“You cannot have an infinite chain of falling dominoes.”
I still don’t think this statement has been justified.
“It is difficult to explain because we are trying to use physical objects to explain a non-physical phenomenon.”
That’s true, analogies are always dangerous to use as they can be useful for highlighting an idea, but all analogies have their limits and can sometimes wind up being mixed up or confused along the way. Still useful but care must always be taken.
It won’t met me reply to your most recent message, so I will reply to this one instead:
The problem is that while we agree that applying infinity to physical objects doesn’t make sense, that is exactly what scientists try to do when they say that the physical universe has existed for eternity, claiming that it ‘created itself’. Even if you somehow had an infinite number of dominoes, there would need to be an event that caused them to start falling. If you simply say they have always been falling then that contradicts cause and effect, which is what this universe runs off of. You cannot start an infinite string of cause and effects starting with an effect and not a cause.
Everything that operates under cause and effect MUST have had a beginning. Furthermore, anything that has always existed will never cease to exist.
“Even if you somehow had an infinite number of dominoes, there would need to be an event that caused them to start falling.”
But if there were an infinite number, what does starting even mean? Saying that they had to “start falling” implies that there is a first one, but there is no first one. If you insist that there is a first one you are also forcing there to only be a finite number of them in the past, which I think is why it feels like a contradiction from your perspective. Essentially, assume there is an infinite past, but make another assumption that smuggles in finiteness and there is an apparent contradiction. (Note: I’m not entirely sure this is the way you are thinking about this, but it is a mistake I have seen others make in the past and I’m making a guess).
“If you simply say they have always been falling then that contradicts cause and effect”
I don’t follow this logic, even if there is an infinite string, each domino falling is caused by the domino falling before it. I don’t understand how cause an effect are contradicted here.
BTW, I’m going on vacation for a few weeks in a couple days and might not get back to this right away, but I really find this conversation interesting so I’ll be back later if you keep responding. I really love this topic.
That’s the point. It does not make sense to apply infinity to such a scenario. Something truly infinite doesn’t have a beginning. Yet cause and effect (ie; the falling dominoes) implies a beginning; a point where no dominoes were falling.
To say they were always falling also makes no sense. Given infinite time, then an infinite number of dominoes would already have fallen. There would be no reason to assume that any particular domino would still be standing, as it has had an infinite amount of time for the ‘falling’ to reach it. Like I said, it just doesn’t make sense. An order of events must have a beginning, something had to knock over the first domino that wasn’t simply another domino. An eternally standing domino would be no problem theororetically. If something is capable of changing, then it could not have been existing for eternity. It would have had to have changed as an effect of a cause, which can’t be itself. Thus only something constant which never changes can be the eternally existing ‘first mover’. God is that mover. He is the existential constant of all things.
If the universe began, did its beginning not induce a change in God, at least in his identity? If not it seems that we must either say that he universe always existed within God, just in a state wihich was somehow not essentially different from the current one, yet atemporal, or we must say that something else incomprehensible occurred. Either way, this argument looks like it amounts to a convoluted shrug.
When God created, His being and essence did not change. The universe changed in that it went from a state of potentially existing to a state of actually existing. God, however, being the cause, did not change. When an effect is caused the effect is changed not the cause. We may refer to God as creator, but since He acts from eternity, He was always a creating being, although we did not see the effect except in time. Further, creator is merely a title that we assign, not a change in being. For example, God is always wrathfully toward those who rebel and is always loving toward those who repent. When we decide to stop rebelling and repent, we move from Gods wrath to His love. We changed but God did not.
But this does not affect the fact that the universe could not go back infinitely into the past, which is the subject of the post.
The universe always existed in God as an actual potentially exists in its cause. It did not always exist as actual in God.
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“It is certain, and evident to our senses, that in the world
some things are in motion. Now whatever is in motion is put in motion by
another, … 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.”
False. Aquinas fails in his most basic premise, and thus his entire argument is worthless from the very beginning.
It is “evident to our senses” that many things that are observed to be in motion are not moved by anything. else.
You move yourself. Aquinas moved himself. This most obvious example should have been plain to Aquinas, yet he and millions of his followers fail to recognize this glaring counter example to his (false) premise.
A worm moves itself, as does a clock, a submarine, a rocket ship, an amoeba and countless other things.,
“But this cannot go on to infinity, because then there would be no first mover,”
Blatant begging the question fallacy. His conclusion is of a first mover, but here he asserts a first mover to conclude a first mover. This is also a false dichotomy, assuming the only choices are either a unmoved first mover or infinity, there being a third choice, mutually moving movers that together form a finite first mover each part of which move the other.
“and, consequently, no other mover; seeing that subsequent movers move only
inasmuch as they are put in motion by the first mover; as the staff moves only
because it is put in motion by the hand.”
This is shallow reasoning because the hand is moved by the rest of the person and the person as a whole does in fact move itself. All Aquinas had to do was think this back a couple more steps, but he failed, and this argument fails so badly I can scarcely believe anybody does anything but laugh at how absurd the First Way is.
Aquinas was quite familiar with your point. He speaks extensively in his writing of agency, which is the ability of a person to create a thought or make a decision or an action based on their own power. The example he gives in the explanation is a person holding a stick and pushing a stone. The stone is moved by the stick, which is moved by the hand, which is moved by the arm. As he extensively speaks of agency, he would obviously know about the person moving himself. So what is the answer? Did he miss an obvious point, as you suggest?
The answer is in what Aquinas calls “act and potency” which merely means actual and potential. Humans are a mixture of actual and potential, and the part of us that is actual can move the potential to actuality. No potential can move itself to actuality; only something already actual can cause a potential to move to actual. The worm can move itself because there is an actual worm that has the ability to move forward. Humans have enough actuality to get a stick an move a stone.
But how did we get the actual? The actual part of us cannot have created itself. Something else caused me and you and gave us the actual ability to potentially move ourselves and move stones. But what caused that cause? We are then back to whether there can be an infinite series of prior causes, which is the point of this post. There cannot. This was the point of his first way, which Aquinas explains above.