1. Introduction

Recall that one of the noticeable features of the Ontological Argument is that it is a deductive argument that claims to be a priori--i.e., it claims that its premises can be known independent of experience, with only logic and language alone.  In contrast, the Cosmological Argument is an a posteriori argument. This means that it relies on our experience of the world--beyond the tools of logic and language alone--to determine the truth of its premises. More specifically, cosmological arguments begin with facts known a posteriori such as: the universe exists, that things are in constant flux or change, that some things are caused to come into existence by other things, and that the universe and almost everything in it is contingent.

In addition, the Cosmological Argument is also deductive (like the Ontological Argument), which means that it aims to be the sort of argument whereby if the premises are true, the conclusion must be true as well. Thus, if we find that the argument is valid, and the premises are true, then the conclusion--that God (i.e., the first uncaused cause, the first unmoved mover, a necessary being, etc.) exists--must necessarily follow.

2. Aquinas' Five Ways

    The First Way: The Argument From Change (or Motion)

Aquinas claims that if we look around the world, we will see that things are always changing (or moving). For example, plants begin from seed, change to saplings, grow to maturity, and then eventually die. Leaves change with the seasons, birds change their plumage, etc. Even rocks change as sentiment is slowly worn away by wind or weather. Aquinas gives the example of wood, which changes in temperature and composition when brought into contact with fire. For all of these various changes in the world, claims Aquinas, something had to bring about the change. Plants, to change from seed to sapling, have to have something outside of them which causes this change. Wood, which changes from cool to hot, needs something outside of it--e.g., fire--that brings about this change, Aquinas believes that "a thing in the process of change cannot itself cause that same change; it cannot change itself." But he also thinks that there must be a first cause of change that is not caused to change itself, or a first mover that is not moved--i.e., a first unmoved mover.

    The Second Way: The Argument From Causation

Aquinas claims that if we look around the world, we will see that things are caused to come into existence by other things. Children are caused to come into existence by their parents, who are in turn caused to some into existence by their parents, etc. We never observe anything causing itself, for this, Aquinas argues, would be absurd. However, the series of causes cannot go back infinitely. If you do not have a first cause, then there cannot be any intermediate causes, nor a last. So there must be an uncaused first cause--and this we call God.


    The Third Way:: The Argument From Contingency

Contingent vs. Necessary: Before we dive into Aquinas' Third Way, it will help to get a grasp on the difference between contingent things and necessary things. A contingent thing is one that either in fact exists, but might not have, or one that does not in fact exist, but might have. For example, Alumni Hall exists, but it might not have (we can imagine that they just never built it); so Alumni Hall is a contingent thing. Unicorns, on the other hand, do not in fact exist, but it seems possible that they might have; so unicorns are contingent things. There are lots of contingent things: you, me, your parents, my parents, etc. In contrast, a necessary thing is one that in fact exists, but is also something that could not have failed to exist. In other words, it is logically impossible that a necessary being could have not existed. Many people think that numbers are necessary things--i.e., that the world could never have been such that numbers did not exist. Of course, relevant to our present discussion, many think that God is similar to numbers in this way--that is, that God could not have failed to exist, and hence, is a necessary being.

Possible Worlds: Using the possible worlds analysis that we discussed in class, we can put the distinction between contingent and necessary things this way: a contingent thing is one that exists in at least one possible world, but not all. A necessary thing is one that exists in all possible worlds--i.e., there is no possible world in which this thing does not exist.]

In the Third Way, Aquinas claims that if we look at the world, we will find that there are contingent beings all around us. We realize that not everything is something that must be, for we observe things before they come into existence, and then see them go out of existence. Aquinas supposes that not everything can be contingent in this way, for he thinks that if everything need not have been, then at one time there was nothing. But, he continues, if at one time there was nothing, then there wouldn't be anything now; for things cannot come into  existence by themselves, but must have been brought into existence by something that is already in existence. Thus, it must not be the case that there are only contingent beings. It must be that there is a necessary being, on which the existence of all other contingent beings depend. For Aquinas, this necessary being is God.

    The Fourth Way: The Argument From Excellence

Aquinas claims that if we look around the world, we will observe that some things are better than others. some more good, some more beautiful, etc. He believes that such comparative terms admit of a "best", a "most" good, etc. Aquinas thinks that there is a limit to which all things that admit of a degree try to reach. So there must be something that is most perfect, he argues--something that all things strive to reach. This perfect being, he claims, is God.

In class I explained how this argument is a kind of ontological argument. Can you see why?

    The Fifth Way: The Argument From Harmony

Begin with the observation that there is order and harmony in nature. This harmony, Aquinas argues, admits of a being with awareness and understanding, For only a being with awareness and understanding  could direct all of nature to its goal (whatever that is) and keep everything in order. Thus, this being with understanding must exist, and is God.

In class I explained how this argument is a kind of Teleological argument. Can you see why?

3. Aquinas' Second and Third Way Formalized

    Second Way Formalized--The Argument from Causation

    (1) There are things that are caused.
    (2) Nothing can be the cause of itself.
    (3) There cannot be an infinite regress of causes.
    (4) Thus, there had to be a uncaused first cause.
    (5) The uncaused first cause is God
    (6) Therefore, God exists.

    Third Way Formalized--The Argument from Contingency

    (1) Every being is either necessary or contingent.
    (2) Not every being can be a contingent being.
    (3) So there exists a necessary being upon which all of the contingent beings depend.
    (4) This necessary being is God.
    (5) Therefore, God exists.


4. Elaboration on Premise (3) of Aquinas' Second Way

In class, I read Aquinas' reasons for premise (3) of the second way. Here, again, is what he has to say:

"Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate cause, whether the intermediate cause be several, or only one. Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes there will be no ultimate, nor any intermediate cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false." Aquinas, Summa Theologica, First Part, Question 2, Article 3.

I summarized the above line of reasoning roughly as follows: Imagine that we have a chain of events, A, B, and C, where A causes B, and B causes C. Let us grant for the sake of argument that A is the first cause, B is the intermediate cause, and C is the ultimate cause such that if the first cause, A, wouldn't have happened, then the intermediate cause, B, wouldn't have happened, and hence C wouldn't have happened. Now if, contrary to our assumption, the chain of causes A-B-C went 'on to infinity'--if something caused A, and something caused the cause of A, and so on without end--then there would be no FIRST cause. But, Aquinas argues, if there is no first cause, then there can be no intermediate causes, and hence no ultimate cause. If there were no A, there would be no B, and hence no C. But the 'ultimate cause' that Aquinas is referring to is the universe as a whole, here and now, which we all know exists. So: if there were no first cause, there would be no ultimate cause--nothing here and now. Since there clearly is something here and now, it must be that there was a first cause. Hence, there cannot be an infinite regress of causes--i.e., Premise (3).

I claimed in class that the above line of reasoning was spurious. Can you figure out why?

Answer: the problem primarily lies with a conflation between taking away a cause and there being no first cause. It is true that in an infinite series of causes--a series of causes that goes back forever, where each thing is caused by a prior cause, and so on without end--that in such a series there is no first cause. But all that this means is that there is no thing or event that we can point to that is the FIRST cause (for, by hypothesis, the causes go back forever). Yet it does NOT mean that any of the causes are erased or taken away or removed from the series.

To illustrate the point, consider the number line of negative integers, terminating at 0:


5. Alternative Arguments for Premise (3)

So are there any other considerations that might lend support to premise (3) of Aquinas' Second Way? Below is one suggestion:

    Infinity is Weird!

One reason you might think that a series of causes couldn't go back infinitely is that the mere idea of an infinite series of causes is just too weird to make any sense. The problem lies not with a series of causes, per se, but rather with the fact that the series is purportedly infinite. In other words, infinity is just too weird of a concept to make any sense, so this is why there cannot be an infinite series of causes.

Below are some examples of infinity's weirdness.

(i) A subset of an infinite series is just as big as the original series!

Here's one illustration to show why you might think that infinity is weird: Imagine that you have an infinite number of cockroaches in your apartment. You have three exterminators who come to your apartment to give you an estimate. The first says that he can eliminate 30% of the cockroaches, the second says he can get rid of 50% of the cockroaches, while the third guarantees that he can eliminate up to 95% of the suckers! Intuitively, it seems you should go with the third exterminator, since he can guarantee he'll get rid of a higher percentage of the bugs than the other guys. However, taking 30% of an infinite number of bugs will leave you with just as many bugs as if you had taken 50%, or even 95%: you will still be left with an infinite number of bugs no matter which exterminator you hire! So given your options, it seems you should just save your money and not hire any of the three exterminators!

To see this, imagine all of the positive integers:.

Obviously, there's an infinite number of them. So assign one positive integer to each one of your infinitely many bugs. Now take 30% of them away--e.g., take every third number (or cockroach) away:


How many are you left with? An infinite! If you don't believe me, tell me where you think the series of numbers or cockroaches ends, and I'll always be able to show you the next one in the series. And the next. And the next...

Now take 50% of those away--e.g., take every other number (or cockroach) away:


How many are you left with? An infinite still! Again, if you don't believe me, tell me where you think the series of numbers or cockroaches ends, and I'll always be able to show you the next one in the series. And the next. And the next...

Now take 95% percent of those away--e.g., take away 95 out of every 100 numbers (or cockroaches):


How many are you left with? Still an infinite number!! Again, if you don't believe me, I'll prove it to you easily. 

So, infinity is awfully weird since you can divide it by 1/3 or 1/2 or 9/10 (or 1/3 and then 1/2 of that and then 9.5/10 of that, which I did above) and still wind up with just as many as you started with! Anything that has this sort of consequence (or so this argument might run) can't possibly correspond to any sort of coherent concept, and so an infinite series of causes--a series that has gone on forever and has no beginning--must be just as incoherent. Thus, there cannot be an infinite series of causes, making premise (3) of Aquinas' Second Way come out true.

(ii) Hilbert's Hotel

Another example is Hilbert's Hotel. Wie will discuss this example in class.

In class, however, I will try to show that while Hilbert's Hotel is indeed odd and surprising, and perhaps a bit funky or weird, it does not follow from this that an actual infinite series is impossible. One way we showed this is by carefully laying out the example as I did in class. At no point did we run into a contradiction, which would have been an indication of something that was impossible, nor were we, at any point in the puzzle, unable to figure out which person was assigned to which room. This indicates that infinity, while complicated and unusual, is not an incoherent concept. In fact, once we were familiar with certain rules, we could predict what we could do in order to make room for more and more guests, even knowing that all of the rooms were occupied. So while the idea of an infinite series may be unusual, its unusual-ness need not be grounds for thinking that it's impossible.

(iii) The Infinite Series of Walls

Imagine that we are building a series of walls, where each wall is made out of indestructable material. No matter how thin the walls get, nothing can penetrate them. We build one wall one foot thick. Then halfway between this wall and an arbitrary point some distance away, we place another wall half as thick as the first wall. Then half way between this second wall and the arbitrary point, we place another wall half as thick as the second wall. Then we place another wall halfway between this third wall and the arbitrary point, making sure that this fourth wall is half as thick as the third wall. And so on. Imagine also that we get faster and faster at constructing these walls so that eventually we have infinitely many walls placed between our first wall and the arbitrary point. To illustrate, imagine that the first wall is labeled "1", the second wall is labeled "2", etc., that the arbitrary point is marked " ° ", and that they are placed like so:

    Infinity is Weird? B.F.D!!

In response to the above examples, and the claim that in light of these, infinity is too weird to make any sense, one might argue as follows: "Infinity is weird? B.F.D! In fact, that's exactly what is so characteristic about infinity. Sure, it's weird. And, sure, one of the weird things about infinity is that a subset of an infinite series can be put into a one-to-one correspondence with the original set, such that (on one way of describing things) we are left with just as many as we started out with. But just because infinity is weird doesn't mean that it's incoherent. Plenty of mathematicians and set theorists, for example, can make perfect sense of infinity. Moreover, they can make sense of some infinite series being larger than others. They coherently work with infinity, and find it theoretically useful to do so. So it is not enough to support premise (3) of Aquinas' Second Way by simply pointing to the mere weirdness of infinity. For it's weirdness does not entail that it is incoherent."

What do you think of this response? Is there another way you might defend premise (3)? Discussion in class.


    Infinity is Weird? Then what is God?

Another objection to consider is this: suppose you would like to defend premise (3) of Aquinas' Second Way, and you do so by appeal to the "Infintity is Weird" line of reasoning. If infinity is weird, then perhaps it is incoherent, and thus an infinite series of causes will be just as incoherent as an infinite anything, and so there cannot be an infinite series of causes on pain of absurdity. But if this is the line of reasoning you want to endorse, then you will have to be very cautious about the sort of attributes that you will ultimate claim that God has. For many theists believe that God is infinite in some way--either he is infinitely powerful, or infinitely good, or knows infinitely many things (e.g., he knows that 1 + 1 = 2, and he knows that 1 + 2 = 3, and he knows that 1 + 3 =4, etc.), or that he is eternal (which might be a kind of infinite existence), etc. But if you want to claim that inifnite is weird or incoherent, then God cannot have any infinite attributes or be infinite in anyway, or else he will be weird or incoherent as well. And you will not want to claim that the idea of infinite is OK for some things, like God, but not OK for others, like series of causes, on pain of being ad hoc. So one must be careful about the "Infinity is Weird" defense of permise 3 of Aquinas' Second Way, and make sure that this line of reasoning is consistent with the rest of the theistic picture.



6. Even if Premise 3 of Aquinas' Second Way is True, So What?

If you haven't got a headache yet because of all this talk of infinity, you might be thinking to yourself: "Look. Who cares whether premise three is true or not? I need not come down on whether there can or cannot be an infinite series of causes. Because even if premise three is true, and the argument does go through, what does this ultimately show anyway? All it proves is that there was an uncaused first cause. It doesn't show that this uncaused cause is still around, nor does it show that there was only one. It also doesn't show that this uncaused cause is all-powerful, all-knowing, all-good, personal, etc. It doesn't show anything, really, except that there was at least one uncaused first cause that got everything started. This first uncaused cause could have been as small and insignificant and morally indifferent as an inanimate atom. Whoop-dee-effin-do."

Response: it's true that, even if sound, this argument alone doesn't prove what the uncaused first cause was like. It doesn't even show that the uncaused first cause is unique. But keep in mind that Aquinas thinks he has given 5 different arguments for the existence of God. Each one aims to prove something different: the first way aims to show that God is immutable, the second that God is the uncaused first cause (the creator), the third that God is necessary, the fourth that God is all-good (or the moral standard), and the fifth that God is intelligent and all-knowing. So it is important whether this argument goes through since, together with the the other arguments, and assuming that they too go through, we have a  piece-meal argument for the existence of the traditional Judeo-Christian God. And this surely is a big deal. 

What we must keep in mind, however, is that while Aquinas meant to have all of these 5 argument stand together, if upon individual scrutiny these arguments show to be unsound, then it won't matter how many arguments Aquinas has up his sleeve. 5 leaky buckets stacked together will still leak water; similarly, 5 unsound arguments will be as good as no arguments at all.



7. Other Objections to Aquinas' Second Way?

    The Principle of Sufficient Reason (or PSR)

One might be tempted to argue that the main intuition behind premise (3) of Aquinas' Second Way is the thought that the universe and everything in it had to get going at some point; something, somewhere had to get the whole thing started. There seem to be at least two ideas behind this thought: (1) the intuition that infinity is weird, and that because of this, the concept of an infinite series of causes is just cognitively hard to grasp, but also (2) the idea that every fact in the world has to have a reason or explanation behind it. This second idea is commonly called the Principle of Sufficient Reason (or PSR). Since the weirdness of infinity is dealt with above, I'll use this section to talk about PSR.

Leibniz (1646-1716) in his Monadology §32 stated a version of PSR as follows: "no fact can be real or existing and no statement true without a sufficient reason for its being so and not otherwise."

To see why PSR might be an intuitive principle, imagine a giant glowing orb hovering in our classroom. Imagine that we had a team of scientists, mathematicians, a police force, and entire investigative team to figure out why the orb was there, how it got there, and what was going on. Suppose that after much testing and investigating, it was concluded that there was absolutely no reason why the orb was there. There was no explanation for how this thing came into existence, nor how it was made or who put it there, etc. It was concluded that the orb just was, and that that was the end of it. Would this be satisfactory? If you think not, it might be because you expect and assume that there is an explanation for everything. The idea that there is an explanation for everything is essentially what the PSR is trying to capture.

Here's how all this is supposed to relate to premise (3) of Aquinas' Second Way: you might think that the (3) has to be true because even if there could be an infinite series of causes--that is, even if you grant that there could be such a thing as a series of causes that goes back forever and never had a *first* cause--you might think that such a series would violate the Principle of Sufficient Reason. Why? Well, because even an infinite series needs a reason or explanation for why the whole series is there. In other words, if there were an infinite series of causes, then why is the series there at all, rather than not there? The idea is supposed to be that positing an infinite series of causes doesn't get at the heart of the matter--namely, what is the explanation for there being anything here in the universe at all?

One response to this line of reasoning is as follows: what explains each individual member of the purported infinite series is the member that came before it. Since each individual member is then explained, this is all that's needed to explain the whole series. In other words, once we have explained why each individual member is in the series, there is no further question as to why the whole series is there--for it is explained piecemeal, by the explanation of each of the parts of the series.

Discussion to be continued...

    PSR vs. Brute Facts, and God

To contrast PSR, I suggested that you could have the Brute Fact view of the universe. This basically says that there can be such things as brute facts--things or events in the universe that simply do not have a reason or explanation . So, essentially, this view claims that PSR is false, and that some things in the universe simply have no explanation as to why they are here, or how they came about. Some things, in other words, just are. 

One reason to think that the Brute Fact view of the universe is correct is because you might think that explanations have to end somewhere. For example, you might think that sometimes a perfectly legitimate explanation for why something has happened is just because of coincidence or chance. Imagine, for instance, that you go to Woody's on Franklin St. for lunch. When you walk in, you see that one of your other friends is there already. "What a lucky coincidence!", you tell her, and the two of you sit down to eat. Now, if someone were to ask why the two of you were at the same place at the same time for lunch, it seems that a perfectly legitimate response would be: just chance or coincidence. You went in to lunch because you were walking by and realized you were hungry, and your friend had just happened to do the same thing moments before. Now maybe 'chance' counts as an explanation here. If so, it seems we can still ask the question: well, why was it chance that brought you two at the same place at the same time? Yet this question doesn't seem to have a ready answer. So, what's appealing about the Brute Fact View of the universe is that it does seem that at some point in giving explanations--even if we grant that sometimes 'chance' can count as a legitimate explanation--the explanations have to stop somewhere. That you and your friend met by chance at Woody's, in other words, is something that just seems to be a brute fact; there is no further explanation to be had.

If this is right, and the Brute Fact view of the universe is plausible, then what does this mean for the Cosmological Argument? What does it mean for Aquinas' premise (3) of his Second Way?

One might contest that saying that God is the reason for why there is a universe as opposed to not--e.g., saying why there is something rather than nothing--is no better than saying that the universe being here is just a brute fact. Do you think this is right? Why or why not?


    No God, God, and Magic

In class we discussed three possible theories that might explain how and why the universe is here--or, as I put it in class, why there is something rather than nothing: (i) the No God view, (ii) the God view, and (iii) the Magic view. The No God view seemingly embraces the Brute Fact view of the universe. At a certain point, science will be unable to answer the big, philosophical questions such as why there is something rather than nothing. Or, rather, they will just have to resort to an answer such as: "no reason, it just happened that way." The God view, on the other hand, will say that there is a reason why there is something rather than nothing, and that reason is God. God explains why things are the way they are and aren't some other way. The Magic view is similar to the God explanation, in that Magic is the thing that supposedly explains why things are the way they are.

However, it is interesting to pin down why we are inclined to think that one of these explanations is objectively better than the others. For example, we may think that a commitment to PSR would lean us toward the God view or the Magic view, since these explanations yield an explanation for everything. Built into both theories is an entity or power that provides its own expiation. When we ask why God is here or why God did what he did, we can claim that God provides his own explanation. God was always here, or was uncaused, or provides his own reason for being here. Magic, similarly, can be explained as being something special--something different from--ordinary stuff in that it doesn't require the same sorts of reasons or causes for its existence. It's Magic, after all! But why isn't the positing of such entities or forces just another way of saying: "no reason why these things have the characteristics they do. They just do! That's how they're made! It's in their nature!" How is this ultimately much different than saying that the universe just is the way it is?

In other words, looked at solely in terms of an explanation--not what makes us feel better, and more warm and fuzzy about the universe--why is one explanation better than the other? And what do these explanations ultimately reveal about the distinction between PSR and the Brute Fact view of the universe. Are they really all that different? Or are they different in principle, but we have just failed to give any theory that genuinely adheres to PSR? Discussion in class...



    Argument from Contingency

Because of time constraints, we probably won't get to discuss in detail Aquinas' Third Way, the Argument from Contingency. But one thing to consider are ways in which this argument might be better or worse than Aquinas' Second Way, the Argument from Causation.

Discussion in class.



    Further Questions to Think About

Can you think of any other objections to Aquinas' Second Way, apart from the aforementioned ways of attacking premise (3)? Are there other worries we might have about premise (3)? What about the other premises? Why or why not? Discussion in class.

---