So, in Chapter 12 Philipse examines Cosmological Arguments in an attempt to show that they aren’t going to work. He differentiates between two main types of cosmological arguments: deductive ones like the classic “First Cause” arguments, or inductive ones to the best explanation. As it turns out, Swinburne also prefers the latter sorts of arguments, so Philipse is going to start by attempting to show that deductive arguments aren’t as promising as inductive ones so that he can spend the bulk of the chapter focusing on inductive arguments and thus also on Swinburne’s arguments and explanations. This will work as long as you end up agreeing with him that deductive arguments aren’t promising avenues to take. If you don’t accept that, then the complicated arguments Swinburne advances will seem like nothing more than a waste of time when simpler and as if not more promising arguments are available.

The problem is that the meat of Philipse’s arguments against deductive arguments are nothing more than taking the two most popular deductive arguments and attempting to show that they don’t work. Sure, he brings in Swinburne’s argument that deductive cosmological arguments aren’t sound, but he — rightly — points out that it’s not easy to argue that without examining the specific arguments themselves. But Philipse then goes on to insist that the literature has done that for pretty much *all of those specific cases* and decides to demonstrate that by picking *two* examples and showing that they are not sound and so can be dismissed. Of course, this would in no way demonstrate that *all possible* deductive arguments are not sound, so it doesn’t even defend against the specific counter *that Philipse himself raised*. He *could* have made a decent argument if he had tried to show that having a universal premise would risk them not being sound or would at least lead us to think that establishing universal premises was too difficult a task to be considered reasonable, but he doesn’t even do *that*. So even if we accept that he’s right about the two arguments he addresses, we have no reason to think that deductive cosmological arguments are just a dead end.

And when it comes to the two arguments that Philipse *tries* to address, I find that I have to express my deepest gratitude to him, because his attempts to refute them have led me to come to the realization of why they, in fact, *actually seem to work*. Whether or not I can get to God from those two arguments, when it comes to establishing some kind of First Cause or First Element the arguments seem conclusive. Thus, instead of making me doubt their validity, he’s only made me even more certain that the arguments are right. That’s … probably not what he was going for.

Let me start with the first argument, which is essentially the argument from contingent causes, and I’ll quote his presentation of it here:

1. A contingent entity exists (that is, and entity of which we can suppose without contradiction that it does not exist), or a contingent event occurs.

2. Each contingent entity or event has a sufficient cause.

3. Contingent entities or events alone cannot constitute, ultimately, a sufficient cause for the existence of a contingent entity or the occurrence of a contingent event.

4. Therefore, at least one necessary entity or event exists (that is, an entity or event of which we cannot suppose without contradiction that it does not exist or occur). And because it exists necessarily, it does not stand in need of an explanation.[pg 223]

While I wouldn’t normally quote the counter argument when quoting from a book — as it’s usually not worth the effort to do so when a summary will do just as well and usually be clearer — here I have to quote what he’s saying so that everyone can check to see if my interpretation of it is correct:

What one should repudiate is premise (3), since causal explanations cannot but refer to causes that exist or occur contingently. If one explains causally an event

Ewith reference to a causeC, what one means is that,ceteris paribus, ifChad not occurred,Ewould not have occurred either, assuming there is no causal redundancy. Hence, it is essential to the very meaning of the word ’cause’ that we can always suppose without contradiction that a causeCdid not occur.[ibid]

You would think that someone who was in fact a philosopher would do two things here. First, one would assume that in examining this they would take the concept of a necessary object, put it in the place of *C*, and see if the statement “If C had not occurred, E would not have occurred” still makes sense or itself produces a contradiction. Philipse doesn’t seem to have done that, because it seems pretty obvious that, yes, saying that still makes sense. What it really means to be a necessary entity or event is that it is not possible for it to not have occurred. So what we would say is that C occurred and C *had* to occur. And because C occurred, E occurred. Now, if C *hadn’t* occurred, then E *wouldn’t* have occurred. But, of course, C *did* occur, because it *had* to occur. Why is that case that much different from the case where we observe that a contingent C happened in the past that produced an event E? Isn’t it *just* as contradictory to assert that if C hadn’t happened then E wouldn’t have happened? After all, C *did* happen, and we can’t change that now. Once C happens or exists, then E will happen. *Why* C happens or exists doesn’t impact that. It seems to me that Philipse has fallen into a “If humans evolved from apes, then why are there still apes?” argument. His entire argument relies on interpreting the first part of the if as being an actual statement about C, which then implies that to make the conditional work we’d have to *actually assert* that C might not have occurred. But we don’t need to and don’t do that. The conditional, then, does not in any way imply that it is actually physically or conceptually possible for C to not exist or have occurred, which would be the contradiction. The statement is talking about the dependency of E on C, and not making any actual conceptual statement about C itself. So this argument fails.

The second thing a philosopher ought to do here is actually attack the logic itself, and not simply look to provide a counter-argument, which is what Philipse’s argument actually does here while in the guise of refuting premise (3). The reason to do this is that we don’t want to end up in an Antinomy, where we have two sound logical arguments that lead to the opposite conclusions. Again, Philipse claims to be attacking premise (3), but what he’s really doing — by his own words — is making an argument that the concept of cause makes necessary events — at least ones that have any causal power — incoherent. But that doesn’t attack the original logic that says that you can’t stop at a contingent event, and that by definition every contingent event must have a sufficient cause explaining it. And this argument would go as follows: for an event to be contingent, it means that its existence depends on some event or cause that causes it to happen as opposed to the alternatives. This means that for any contingent event we can ask for an explanation of it, meaning that we can ask what made it so that it happened as opposed to something else (which might be nothing). Let’s call that C. Now, C can either be contingent or non-contingent. If it is contingent, then we would say that *its* existence depends on another event, C’. Which we could then go and examine to see if C’ is contingent or non-contingent. And so on and so forth. Thus, for any contingent event C we could never stop there, because there would always be something left that we would need to explain, which is why C itself happened, which we can only explain by appealing to another event C’. If, however, that C is *non*-contingent, then it needs no further explanation for its existence and so we can stop there.

You can argue that my argument depends a lot on us needing an explanation or still having something to explain, which might not be necessary (this might be an epistemological as opposed to a conceptual argument). Fair enough, but remember that Philipse wants us to do theology like science, and science can *never* say that if there is still something there to be explained that we can simply stop there and claim that we’ve explained enough. Science can argue that we *can’t* find out that explanation, but that’s *definitely* an epistemological as opposed to a conceptual argument, and so can’t refute the idea that what we have is a necessary entity or event C out there that stopped our chain of explanation. So Philipse would still need a conceptual argument to refute the idea that there’d still be something out there that can’t be contingent to be the explanation for the contingent entity or event we are considering.

Let me quote the second argument:

1. This event in the universe is fully or partially caused by earlier events. The same holds for other events. They are caused by causal chains going backwards in time.

2. Infinite causal regresses are impossible.

3. Therefore, there must have been a first cause of each causal chain.[ibid]

Philipse uses the standard reply of appealing to Cantorian Set Theory to demonstrate that we can, indeed, have an infinite causal regress. The problem is that the classic examples use there are things like the set of all integers, the set of all positive integers, and so on and so forth. The problem is that these causal sets are not like those, but are more like the Fibonacci sequence, where the existence of any element in the set is determined by earlier elements in the set, except for the initial terms, which have to be stipulated by definition. So, to weaken Philipse’s logic, what he’d have to show is that dependent sets can be infinite in the same way as, say, the set of all integers. If they can’t, then you can’t use Cantorian Set Theory against the argument.

So, having weakened the argument, let me again provide a positive argument for why that isn’t the case. In generating the set of all integers, I can generate a number at random and see if it belongs to the set and add it if it ought to be in the set (and isn’t already there). So I could generate the set, then, by randomly generating 100, 350, 2, 19 and so on and doing so until I have the entire set. Sure, it’s not *physically* possible for me to do that, but it’s *conceptually* possible for me to do that. Thus, I can generate any element of the set at any time and be able to determine if that element should be in the set and, in fact, even add it to the set.

Can I do that for a simple dependent set, where, say n_{m} is determined by n_{m-1} + 1, where n is a positive integer? So I generate 56. Is 56 in the set? Well, in order to determine that, I’d have to know what its m would be if it *was* in the set, so that I can determine if n_{m-1}+1 = 56. So that means that there needs to be at least one other element in the set before I can determine if *this* element is in the set. And since that applies to every element in the set, I can’t add any element to the set until I know that *another* element is in the set. *Except* for n_{0}, the initial term. If I stipulate that n_{0} is 55, then 56 is clearly in the set. But if I stipulate that n_{0} is 233, then it clearly *isn’t* in the set. Thus, no element can be added to the set until I add an element that is not dependent on any other elements in the set to the set.

And it turns out that for any dependent sets that we come across, we *always* specify by definition some elements that exist in the set but that aren’t dependent on any other elements in the set. And as soon as we do that, we can then generate the rest of the elements that exist in that set, by proceeding from those initial elements to the next elements down the line. So we cannot proceed infinitely past that starting point and maintain a sensible set that actually contains elements.

Since causal regressions, by (1) are dependent sets, the same thing applies to them. No element can be said to be in that causal regression unless we can specify an initial term that kicks this all off. Sure, if we *see* a dependent causal regression we can identify it as such and trace it backwards in time, but mathematically we’d have to expect there to be an initial term that is not dependent on any other elements in the set. Thus, mathematically it really does look like the argument holds.

There might be places where I go wrong with these arguments, but the important point is that Philipse has certainly not established that even *these* two deductive arguments are not fruitful, let alone that *no* deductive arguments are not fruitful. And since he hasn’t established that, I see no reason to follow him and Swinburne down the complicated rabbit hole of inductive arguments to the best explanation. Which makes the rest of the chapter irrelevant, and so I’m not going to bother addressing it.

Next up: Design arguments.

August 12, 2017 at 1:03 pm |

I’m not familiar with what you call “[using] the standard reply of appealing to Cantorian Set Theory to demonstrate that we can, indeed, have an infinite causal regress”. And my Google-fu seems to fail me today. Would you be so kind as to either explain how infinite causal regress occurs in Cantorian Set Theory, or direct me to some other webpage that explains it? I’m familiar with the mathematical basis, but not how it relates to logic or the cosmological argument.

Thanks!

August 12, 2017 at 1:30 pm |

The argument, as best as I can explain it, is that we only thought that you couldn’t have an infinite causal regress because you couldn’t have one for finite sets. If infinite sets behave like finite sets, then that would be a good argument for the infinite causal sets that we’re talking about. Thus, you can’t have an infinite regress because sets don’t work that way. Cantor showed — or, at least, presumed — that infinite sets can have some very odd properties, including that you can have a set that is infinite on both ends (think the set of all integers). And if we can have a set that is infinite on both ends, then we could have a causal chain stretching off into infinite while still extending infinitely into the past, despite what our intuitions say. And Cantor’s theories turn out to be quite counter-intuitive, leading to the idea that infinite sets are just incredibly counter-intuitive for us, weakening the intuitive support we have for that cosmological argument.

As I pointed out, when you compare that causal chain to infinite DEPENDENT sets, the math doesn’t work out as well.

August 15, 2017 at 3:06 am |

I’ve been thinking about infinite sets and infinite causal regresses, and I don’t really see the mathematical point you try to make. You claim that the set of all integers Z is different from the set, let’s call it Y, where n(0)=233 and n(m)=n(m-1)+1. The difference, you say, is that it’s conceptually possible to determine if a number x belongs to Z without reference to any privileged, “first” member of Z.

Well, how would you do that? By looking at the numerical representation and seeing that it doesn’t have a decimal point? That’s just an artefact of notation. Mathematically, we check if x belong to Z by seeing if we can find two positive integers i and j such that x=i-j. So in order to check if x belong to Z, we need access to the set of all positive integers, named N.

And how do we define N? Well, exactly in the same way as we defined Y above, except that n(0)=1.

(Point of nitpicking: we actually start with saying that 1 belongs to N, then say that every element of N has a successor, and then define “add one” as moving from an element n(m-1) to its successor n(m). Same thing.)

So, mathemathically, the set of all integers has a privileged first member. The number 1. (It is also possible to define the integers starting from n(0)=0, but at any rate you need a first member.)

Your move 🙂

August 15, 2017 at 5:09 am |

My claim is this: there is a definition that makes something an integer that you can use to determine if something is an integer without appealing to something else that’s already in the set. So, using the definition from wikipedia:

So, conceptually, you can take a number and see if it can be written without a whole component, and know if it should be in Z without having any other number in the set first. You can’t do that for a dependent set.

But even if you’re right, it doesn’t impact the argument, as all you’d do is show that even for those sets there must exist an element in the set whose existence is not determined by any other element in the set, which would then justify the cosmological arguments.

August 15, 2017 at 12:54 pm |

Like I said, integers being written with no fractional part is a notational artefact. More specifically, it’s an artefact of using an integer base (most commonly ten, two or sixteen). There is nothing to stop me from using two-and-a-half as a base. Now, 101 in base ten means a-hundred-and-one, in base two it means five, and in base sixteen it means two-hundred-and-fifty-seven. All of which are integers. However, in base two-and-a-half, 101 means seven-and-three-quarters, which is not an integer, despite being written without a fractional part in this base.

You are correct that I didn’t disprove your argument in favor of the cosmological argument. I mostly argue that there isn’t any mathematical difference between the set of all integers and the infinite sets you call “dependent”. The cosmological consequences is something I’d have to think more about, before I say anything. I’ve studied mathematics, but I’m pretty new to philosophy.

Thanks for a nice discussion!

August 17, 2017 at 6:07 pm |

For me, it’s the other way around [grin].

Philosophically, you need to make them mathematically identical in a way that doesn’t require a first element.

But I’m still not convinced that they aren’t different in a way that matters. You talked about starting at 1, for example, but since you are generating the set of all integers — including the negative ones — you’d need two functions: one that adds onto 1 to get all the positive ones, and one that subtracts from 1 to get all the negative ones. This means that the set really does run infinitely in both directions from your starting point. In theory, you could pick any integer and generate infinitely in both directions. You CAN’T do that for my dependent set.

This leads to another question: the reason we can start at 1 is that we can determine that 1 is an integer without having to generate anything in the set first. If we choose 1, that’s not an arbitrary choice, but is in fact us choosing something that is an integer. That’s why we could in theory pick ANY integer as the starting point, but can’t do that for my example.

Note that the first argument DOESN’T apply to the set of positive or negative integers, but then those sets DO have a set starting point. The second argument — which just supports my initial argument — DOES apply to them.

The big mathematical question, though, is this: if I pick a number at random — say 53 — how would you determine if that is or isn’t a integer? I doubt you’d generate or even reference the set specifically itself. But in my example, if you wanted to see if it was a, say, Stoicistic number, you’d have to reference the set, generate it, and stipulate the first number in the set.