Another argument for the PSR

The PSR is the Principle of Sufficient Reason, the most controversial premise of the LCA which we have defended here previously. We will here provide another argument for the PSR. That is, for the claim that for every contingent thing (or perhaps indeed every single thing, contingent or not) has a sufficient explanation.

The argument I intend to motivate is this: we should extend reasoning principles as far as possible, until we have a good reason. The PSR is a principle we use in many areas, and so we should extend it to all objects unless we can come up with a good reason why we should not.

Now we all know how we apply the PSR in physical situations. There is currently light hitting my eye, as an explanation I posit a computer monitor in front of me as an explanation. An apple falls from a tree, and we posit gravity. Celestial objects move across the sky, and we posit heliocentrism. In none of these cases do we say “perhaps there’s no explanation”, we always immediately begin looking for one. If there’s some phenomenon we can’t find an explanation for, we conclude that we aren’t smart enough, or our equipment isn’t precise enough. We assume that there is one we just haven’t found.

So now we might be tempted to say “The PSR only applies to physical phenomena”, and then we wouldn’t be forced to admit that God exists. And there may be some cause for this since intuitively, physical objects are the kinds of things which seem like they’re causally closed. But maybe other kinds of phenomena (if they exist at all) are “spooky” and not causally closed, so maybe there’s no PSR there.

Let’s consider another domain then: ethics. Take the famous trolly problem: suppose it turned out to be the case that it was morally wrong to pull the lever to save five while condemning one. Suppose this was morally impermissible. And an interested interlocutor would ask “Why?” Suppose we answered, “It just is, there’s no reason”. Is that an acceptable answer? Clearly not. And in fact many ethicists have spent their lifetimes looking for answers to such ethical question: what is right and what is wrong, and why are those things right and wrong. Again, there is the presumption of explanation.

Now a third domain: mathematics. We observe some mathematical phenomenon, and we ask “why”. That “why” often comes in the form of a proof, or at least a sketch of a proof. Often the “why” is actually hidden in the proof, almost as if the author of the proof went to great effort to obscure the deep intuition. But sometimes it’s on the surface. And this doesn’t only apply to theorems, we can ask why a theorem is true, but we can also ask why something more general is the case. Here’s one such question: why does the sum of the series of inverse square numbers involve a pi term? Pi has to do with circles, but this doesn’t appear to be related to circles. And indeed, there is an explanation.  This kind of question is often asked by mathematicians, why is something the case? And often the answer is intuitively satisfying, deep, and can lead to new ways of thinking about problems. Much of mathematics, rather than hunting for proofs of theorems, is hunting for these more intuitive, conceptual explanations of a more general class of phenomena.

Now we go back to our PSR. It holds in the domains of physics, ethics, and mathematics. Our natural, everyday reasoning assumes that the PSR holds when we consider physical objects, abstract objects (such as numbers), and moral facts. So how might we restrict it? If we say “All physical, ethical, and mathematical phenomena have sufficient explanations”, but that seems extremely arbitrary. And again, we normally want to expand principles until we have a good reason not to. What good reason do we have for restricting the PSR to these classes of phenomena, but not others?

And we can take this argument even further. We can follow Della Rocca, and point out that unless you can give a sufficient reason for that restriction, you’ve begged the question. I covered that particular argument in the original post on the PSR, but it is worth reiterating because I think it is indeed a strong one.



Common Objections to the LCA

In our previous three posts here, here, and here, we have gone through a brief summary of Leibniz’ Cosmological Argument. And of course, many objections are likely to arise, mostly from misunderstandings of the argument. Here I would like to briefly respond to some of those common objections.


What if the universe had no beginning?

You’ve got this argument confused with another argument. My argument says nothing about the universe as a whole, and only needs one contingent object to succeed. My argument also says nothing about anything “beginning”. This argument would work just fine if the universe had no beginning.


What explains God?

The way we have used the word “God” is by meaning “The non-contingent object”. But given our definition for contingent, this means “The object that does explain itself”. So if you ask “What explains God?”, you are asking “What explains the thing that explains itself?”. The answer is obvious: God does.


How do you know there are contingent things?

Consider a simple fact: things fall down. The first scientists asked: why do things fall down? They needed an explanation. The fact that things fell down wasn’t self-explanatory. And they found an answer, coming up with a theory of gravity. But then again: why do things have mass? The fact that things have mass requires and demands an explanation. It is contingent. And we built the Large Hadron Collider looking for that explanation.


You’re just defining God into existence!

What I am doing is inferring the existence of something by looking at the effects it has. For example, I might look at a clock and infer the existence of a motor behind the arms, because it is making those arms move. Am I defining the motor into existence by doing this? No I am not.


This only proves a deist God, not the Christian God!
True, this is not a sufficient argument for Christianity. It gets us to theism, but we need further arguments to get to Christianity. But it’s a step in the right direction, ruling out atheism.


This is a God of the gaps argument!

What I am doing is inferring the existence of something by looking at the effects it has. A God of the gaps argument goes something like “We can’t explain this thing, therefore God did it”. I am not doing that at all. Instead, what I’m doing is arguing that God is the only possible explanation for something. Suppose I have a car that works. Am I right in inferring the existence of a motor inside the car? Is that a motor of the gaps argument? No.


Believing the PSR commits us to denying libertarian free will/accepting necessitarianism

This doesn’t bother me much, since I am a Calvinist and therefore a compatibilist, and I am a modal necessitarian. However I do need to maintain that God is totally free, so I have to engage with it to some degree. A good argument can be found here, it is reasonably well explained and I will not reproduce it.


We should only believe things we can test, how did you test this?
I reject the claim that we must test every claim. I only think we should test scientific claims. If you can test this, go ahead, but I think it is fundamentally impossible. Just like it’s fundamentally impossible to test whether the square root of two is irrational. But that doesn’t mean the proofs that the square root of two is irrational fail, nor does it mean that Leibniz’ cosmological argument fails. The simple fact is that logic works, and we can use deductive logic to work out truths from true premises. If you think my premises are false, or my arguments for why they are true fail, then feel free to tell me why. But if you think my premises are true, then you must accept the conclusion, it’s the result of simple and easy to follow logic.


The necessary thing is the universe/big bang/laws of physics

That’s a reasonable suspicion when we get up to (4), but falls flat after (5). We not only prove that there is a necessary object, but we prove that it has all the properties we normally think of God as having. And none of the suggestions above for the necessary object have these properties.  We cannot merely attach the description “necessary” to whatever we please, we must discuss what properties the necessary thing must have.

LCA Point 5: The Necessary Object is God

This is our third post in a series on Leibniz’ Cosmological Argument. You can find the first post here and the second here. The full argument is:

(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 will be examining…

(5)               This necessary object is God.

This is much like the first point, in that it’s not obvious and requires some argumentation. First, let’s talk about what it means to be a necessary object. A necessary object is an object that explains its own existence. It does not “depend” on any other object to exist. Using the possible world terminology we introduced last post, a necessary object is an object that exists in every possible world. 

So what properties can we deduce about the necessary object? Well it’s clearly not material, as material objects depend on matter to exist and are contingent. In fact, it’s not composite at all, since composite objects depend on their components to exist. So the necessary object must be entirely simple.

Whatever necessarily exists must always exist, since the fact that it necessarily exists is true no matter what time period you are in. So the necessary object is everlasting.

The necessary object must be unchangeable. Suppose that the necessary object were to change. That change must either be caused by the necessary object itself, or something else. It cannot be caused by something else, because that would make the state of the necessary object contingent on that thing that caused it. So if it changes, it must cause that change itself. If something changes itself, either part of it changes another part, or the whole changes the whole. Since the object in question has no parts, the whole necessary object must change the whole necessary object. But if this were the case, it would have already been the thing it was going to change into. So it cannot change.

Now Leibniz presents an argument that the necessary object has understanding, a will, and power. He argues that it has understanding, as it can survey all possible worlds it can create. It has a will, as it selected one possible world. And it has power, as it actually created that world.

Is this argument reasonable? Consider first the understanding argument. Can the necessary object survey all possible worlds? A possible world is a world that could exist. If such a world contains any contingent objects, then the necessary object must exist. And if it doesn’t contain any contingent objects, and only the necessary object, then the necessary object must still exist.

Our necessary object explains all contingent objects. That means it must in some way contain information about those objects. And it contains information not only about contingent objects that exist, but also all possible contingent objects, since it would also explain them. And clearly it contains information of itself, since everything does. This kind of containing information is understanding.

Does it have a will? Of all the possible worlds, it chose one. Is simply choosing one possibility out of many having a will? Probably not, since my computer also does this and does not have a will. Instead, it seems more reasonable to say that having a will, or maybe a free will, is choosing an option apart from any outside compulsion. My computer chooses what it was programmed to choose, and so doesn’t have a will in this sense. But the necessary object is not compelled by anything external to it, and its choice comes entirely from within. So it seems it has a will.

And power? This one is more clear: it did in some sense create the world. It chose this possible world, and actualised it over other possible worlds. That is power.

Since the understanding, will, and power are directed towards all possibilities, they are infinite. The necessary being understands all possibilities, can will to create any of them, and has the power to carry out that will, whatever it may be.

And since choosing is to judge that the thing you choose is the best thing among the alternatives, and since the necessary object has full knowledge (knowledge of all possible worlds), it judges which is actually the best among infinitely many alternatives. This means that it is in a sense infinitely good.

Another argument can be made for a more general agency of the necessary object. As far as we understand explanations, there are three types: scientific, conceptual, and agential. The necessary object is clearly not a scientific explanation, since it cannot be material, due to simplicity. Further, science only explains things in terms of contingent things, or at least it has in every case we know of.

Nor is it a conceptual explanation. Among the contingent things we find substances, the stuff that other things are made from. Dualists will argue that the soul is a different kind of substance to matter, for example. Matter/energy is the substance that physical objects are made of. But the activity of a substance cannot be conceptually explained by the activity of something other than that substance. A conceptual explanation can tell us why things behave the way they do, in terms of what they are. But a conceptual explanation cannot give an account of why they are in the first place. So a conceptual explanation is insufficient for the big contingent fact.

So the only option remains is an agential explanation: an explanation in terms of some agent. So the necessary thing must be an agent in some sense.

We can also demonstrate uniqueness: every property the necessary object has must be a property it necessarily has, by a similar argument to the simplicity argument above. So if there are two necessary objects, they have the same properties. But two objects with identical properties are actually just one object. So there is only one necessary object.

At this point, we have proven that there exists a necessary object, which has infinite knowledge, infinite power, is infinitely good, is simple, eternal, unique, immutable etc. I know no name we could give this object other than “God”. And of course we have not yet arrived at Christianity. But I claim that after proving that this God exists, we may go looking for it in the world.

We find this: there exists a religious tradition spanning thousands of years who claim to worship something with all of these properties. They record centuries of interactions with this thing, who behaves exactly as we’d expect God to behave, including giving and fulfilling prophecy. And in the end we see the man Jesus who comes claiming to be God come in the flesh, who behaves as we’d expect God to behave, with a supremely good moral character, who fulfills prophecy given over the last few thousand years. I believe Him.

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” was created by God. 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 BCF or BCCF (Big Contingent Fact, or Big Collected Contingent Fact).

There is a minor concern here that the BCF could be self-referent. That is, the BCF includes the BCF. 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 BCF by including every contingent fact that isn’t the BCF, 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 BCF 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, but so far there’s no proof of it.

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.