LCA – Points 2 to 4

In our previous post on Leibniz’ Cosmological Argument, we examined the first premise, the PSR. I would summarize the PSR with the claim “reality is fundamentally intelligible”, though we go into more technical detail in that previous post. To remind you, here is the full argument:

  1. Every contingent fact has an explanation.
  2. There is a contingent fact that includes all other contingent facts.
  3. Therefore, there is an explanation of this fact.
  4. This explanation must involve a necessary object.
  5. This necessary object is God.

Here we will examine points 2 to 4. These are reasonably simple, and although they are sometimes disputed there shouldn’t be anything too controversial here. Most skeptics who deny this argument will take issue with premises 1 or 5.

(2)               There is a contingent fact that includes all other contingent facts.

It is at this point that we must define what a “contingent” fact is. Briefly, a contingent fact is a fact that does not explain itself. For example, we might say “a cat exists”. Is that self-explanatory? Can we coherently ask “why does a cat exist?”. In the case of my cat, explanations may include: me and my brother asked my parents for one, and also the cat has parents, and also the cat is composed of molecules, and also the species “cat” evolved. These are all partial explanations for the contingent fact “my cat exists”. Here, a contingent fact is any fact like this, any fact X that has an explanation Y, where Y and X are not identical.

This definition is a bit vague, and purposefully so. There are multiple conceptions of precisely how we cash out contingency, and I want my argument to be general enough to cover all of them. But if you are after a more specific definition, try this one: a contingent fact is a fact that is true in some possible worlds, but not all possible worlds. There are some worlds in which there is no cat (or no matter), and some that include a cat. Note that I am not talking about a multiverse here, some worlds contain one universe, some contain multiple, some contain none. A possible world is a way that reality could have logically possibly been, but isn’t. A possible state of affairs that could have attained, but didn’t. If this is a new idea for you, perhaps study this SEP article. We will occasionally make use of this definition during our argument, but I will attempt to stay as general as possible.

Some of you are necessitarians and reject possible worlds. I am. If that is you, then we will need a different notion of contingency. I intend to publish my thoughts on that once we have completed the entire LCA series.

The actual premise is relatively easy. If it’s true that “x is a fact” and “y is a fact”, then it’s true that “both x and y are facts”. So we can construct a true statement such as “x is a fact and y is a fact and……..” and so on until we’ve covered every contingent fact. This fact that we’ve constructed is contingent because all of the incorporated facts are contingent. If any of them could possibly be different, then so could the constructed fact. In some other literature, this fact is called the BCCF (Big Collected Contingent Fact).

There is a minor concern here that the BCCF could be self-referent. That is, the BCCF includes the BCCF . Some of you will be familiar with Russel’s Paradox, which relies on this kind of self-reference. So there are two solutions, I think either works. Either we say that this isn’t a set, and we call it a “collection” or something, and then we aren’t bothered by self-reference. Or we construct the BCCF by including every contingent fact that isn’t the BCCF, we include every other contingent fact. This is a relatively minor issue, it is in a sense just nitpicking. But it seems important to include it so people don’t get grumpy at me.


(3)               Therefore, there is an explanation of this fact.

This follows from (1) and (2). Every contingent fact has an explanation due to the PSR, so the fact we just constructed has an explanation

(4)               This explanation must involve a necessary object.

Let’s suppose it isn’t true, suppose the BCCF is explained by a contingent fact. Given the PSR, then this explanation still has to exist. We’re supposing it’s not necessary, which means it must be contingent. But if it’s contingent, then it’s part of the fact that we’re trying to explain.

This means that the explanation is its own explanation. It doesn’t depend on anything else to be true. This means it’s not contingent, and is instead necessary. So by reductio, the explanation for the constructed contingent fact must be necessary.

Some complain that I’ve equivocated between “fact” and “object” here. But this is not a big problem, like the self-reference above. Every fact refers to at least one object, and for every object X we have the fact “X exists”. We can travel between “facts” and “objects” freely. I choose the term which best primes the intuition of the person reading it.

This will conclude the middle section of the LCA. Next time, we will investigate what the necessary explanation is, we will work out what properties and attributes it must have, and end up concluding that it is God.

Laying the Groundwork for the LCA: The PSR

The Leibnizian Cosmological Argument is one of my favourite arguments for God. The LCA can be summarised in this way:

  1. Every contingent fact has an explanation.
  2. There is a contingent fact that includes all other contingent facts.
  3. Therefore, there is an explanation of this fact.
  4. This explanation must involve a necessary object.
  5. This necessary object is God.

Today we are only going to discuss point 1. And this will probably not be our only discussion of this point, as there are many levels of counter arguments and responses to those that we will need to discuss at some point. This premise is called the Principle of Sufficient Reason.

A more general formulation (Taken from the SEP) is given as: For every fact F, there must be an explanation why F is the case. There are several good arguments for accepting the PSR, some of which I will provide now.

First, if we do not accept the PSR, I would argue that we must accept some unfortunate consequences. I believe that I’m currently sitting in front of my laptop typing things into it. I believe this because I can see it. Because there are photons bouncing off my laptop (or emitted from the screen) and entering my eyes. But if the PSR is false, then there’s no reason to think that anything actually caused those photons to exist. Not just that I might be a brain in a vat being fed sensory information, or deceived by an evil demon like Descartes might suggest, but that there may be no explanation for the sensory information at all.

If we don’t take the PSR, then we can’t look at facts and try to work out the best explanation. Sherlock, for example, takes in a lot of details and provides usually a good explanation for why the facts are that way. But he never includes in his reasoning the option that there’s no explanation. Neither should we. We should look for explanations, and so we must always assume that there is one.

If the PSR is not true, why don’t we see lots of violations of it? If I saw a soccer ball materialize in front of me, I’d probably look for an explanation. But if the PSR weren’t true, there’d be no reason to look for an explanation. It could just be a brute fact that the soccer ball exists there. No explanation for why it is there.

Which brings me to the next argument: even if there’s not always an explanation, we ought to believe that there is one and look for it. Consider the example of the theory of evolution: what is the explanation for the variation of species? Normally, we’d say something like evolution via random mutation and natural selection. We’d justify that claim by pointing out the large number of observations that confirm it. But how do these observations confirm it? They confirm it via the PSR: we believe that evolution is true because it is the best explanation for our observations.

But how did we determine that there was an explanation here? The fact is that we didn’t, and we would have no way of doing so. We assumed there was, and we looked for it. But a Creationist who responds to the evidence for evolution with “Perhaps there’s no explanation” would be rightly ridiculed. We value explanations over no explanation, even if we can’t conclusively show that there is no explanation. We ought to believe there is one, even if there isn’t.

A more complex argument comes from Della Rocca. I link his paper below, and I will give a summary (and occasionally steal parts verbatim) of his argument here. First, he establishes that in every-day reasoning, we use something he calls “explicability arguments”. Something like this: no explanation for a state of affairs means that state of affairs cannot attain. Consider this: we have a scale with a weight on either side. If the weights are equal (and the scales are fair, and there are no outside influences), we know the scale will be balanced. How do we know this? Because there is no reason the scales would be unbalanced, there is no explanation as to how that would happen, so it cannot be the case. We reject the possibility of an unbalanced scale because it has no possible explanation. Or another example: suppose we have two substances. Suppose they are identical in every way, that they have the same chemical makeup, same structure, etc. One dissolves in water. We know that the other will dissolve in water too. Why? Because there is no reason why it would not, if one has the disposition to dissolve in water, how would the other fail to have this disposition? If they are identical, nothing could ground this difference, so we reject the possibility of them behaving differently.

In fact, it seems like avoiding inexplicability is a main motivator to naturalism or physicalism or materialism. We want to avoid believing in things that can’t be explained (such as the supernatural). The naturalist says that if it cannot be explained naturally, it does not exist. Again, they affirm the PSR in this context.

If we can use these arguments in general, then the PSR follows easily. Clearly we want to take a limited PSR in some local contexts. But can this kind of reasoning apply in general? Someone who denies the PSR might claim that it applies to some situations, but not others. But we claim that there is one example where we use inexplicability arguments where we can’t appeal to a local PSR without doing so arbitrarily and question-beggingly. And it is precisely the case in question in this argument.

What is it in virtue of which something exists? The existence of each thing that exists must be explicable. When we have causation, we ask why it is that this is a case of causation. So when we have something that exists, we ask why it is the case that this thing exists. The denier of the PSR attempts to draw a line somewhere, and explain why we can use a PSR in some contexts, but not in the existence context.

The denier of the PSR must draw this line in a principled, non-arbitrary way. This is because to draw the line in an unprincipled, arbitrary way is to say that there is no explanation or no reason why the law is drawn in this place. But to say that there is no explanation is to say that the PSR is false. And surely people cannot be allowed to assume the PSR is false when they are trying to argue against the PSR. That would be circular, I may as well assume God exists when trying to argue that God exists.

So of course, this line must be drawn in a principled, non-arbitrary way. And of course there is no such way. If you and I want to use the kind of explicability arguments above, then you and I need to come up with some reason why they work in some cases and not others. And unless we do come up with such a reason, we must accept the full PSR.

Further reading:

Introduction to Cosmological Arguments

In the history of theism, cosmological arguments have been some of the strongest and most widely used justifications for theistic belief. They are very old arguments, some form of the argument was even put forward by Aristotle. In this article I will not put forward any particular cosmological argument, but I will go through the general pattern of cosmological arguments.

Cosmological arguments derive their name from the Greek word “cosmos” which means “world”. The general idea is that we look at some feature of the world, combine it with a logical principle that we call the Principle of Sufficient Reason (or some similar principle), and deduce the existence of God. While some forms of the argument make claims about the entire universe (such as WLC’s famous defence of the Kalam argument), not every cosmological argument considers the universe as a whole. For example, Leibniz’ argument only considers a single contingent object, and Descartes’ argument deduces God from the existence of thoughts about God. So when presenting or criticising these arguments, don’t fall into the trap of always thinking about the universe, just because WLC made that particular argument famous.

So what is it about the world that we can observe? Here are the features that some of the arguments consider (the list is far from exhaustive):

  • Aquinas: Change
  • Descartes: Thoughts about God
  • Leibniz: Contingency
  • Kalam: Things beginning to exist

 

And here are the various principles or forms of the PSR that the arguments use:

  • Aquinas: Things are changed by things external to them
  • Descartes: Thoughts are invented, told to us by someone else, or about something real
  • Leibniz: All contingent things have explanations
  • Kalam: Everything that begins to exist has a cause

 

And each of these attempts to infer from their observation and their principle that God exists. Aquinas, therefore, argues that there is an unmoved mover, Leibniz argues that there is a non-contingent thing that explains contingent things, Kalam argues that there is something outside the universe that caused the universe. Descartes’ case is a bit more complex, where he first rules out inventing the idea of God and shows that using the “someone else told us” explanation only pushes the problem back a stage.

And then the argument goes on to attempt to prove that the thing they deduce, perhaps pre-emptively called “God”, has all the attributes that we normally assign to God. Aquinas shows that God is unchanging because He must be pure actuality and no potentiality, Descartes shows that God is perfect because the idea of perfection can’t have come from anywhere else, Kalam shows that God exists outside the universe to cause it, Leibniz shows that God is all knowing and all powerful because He saw all possibilities and could have created any. They all provide long and detailed explanations of each of the divine properties.

Whether or not these arguments succeed is a matter for further blog posts, Leibniz’ argument is my favourite and I will probably provide an in-depth defence of it at some point. But this gives you a general idea of how cosmological arguments work, with a particular observation, a particular principle relating to that observation, deducing God, and then deducing the properties of God.