Leibniz sporting some seriously impressive locks
In a previous post on the Kalam Cosmological Argument (KCA), I mentioned the Principle of Sufficient Reason (PSR) in defence of the second premise of the KCA. The PSR traditionally hasn’t had much to do with the KCA, but the more I think about it, the more powerful I believe it do be. As history would have it, there is a cosmological argument that relies more heavily on the PSR and therefore affords me the opportunity to defend it more at length. This argument was proposed by the philosopher Gottfried Leibniz (1646-1716), but here I will defend a more modern version of the argument as detailed by philosopher Alexander Pruss (see recommended reading section below). The form of this argument is the following, with the PSR expressed in the first premise.
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 being
5. This necessary being is God
The defence of premise (1) is lengthy on its own, so this post will be dedicated to defending only it. A future post will cover the rest of the Leibnizian Cosmological Argument (LCA).
Every contingent fact has an explanation
As mentioned above, this premise is a restatement of the PSR. In order to defend this premise, I have to define some terms. If a being or event is contingent, this means that it is possible for that being or event to not have existed / occurred. This is opposed to a necessary being or event, which by necessity must have be or have occurred – it is said to occur in every possible world, that is, in every possible way the world could be. By “fact” I mean a true proposition, like “the sky is blue”. By the word “explanation” I mean the common usage of the term, something like “a reason for why something is, or a reason for why an event has occurred”. For p to be an explanation of q, then p must also be true – in other words, a proposed explanation which is plainly false is not an explanation at all.
So why think that the Principle of Sufficient Reason is true? There are a number of reasons, which I’ll explain below.
Without it, knowledge is impossible
Knowledge is generally thought to be “justified true belief”. In other words, I know something if my belief is both true and I’m justified in believing it. However, if the PSR is false, I am not justified in believing anything. If the PSR is false, all my beliefs could have occurred for no reason at all. What’s more, it’s hard to see how I could be justified in thinking that such a situation (my thoughts appearing ex nihilo – from nothing) is unlikely. Likelihoods are judged based on our understanding of how the physical world works – i.e. it is unlikely that the moon will crash into the Earth in ten minutes because of what we know about gravity. If we say the PSR is false, then we have no basis whatsoever to think that our beliefs coming into being for no reason at all is unlikely. Therefore, if we hold this belief (that the PSR is false) along with all our other beliefs, we have lost the justification of all our beliefs. The whole exercise becomes self-contradictory and self-defeating.
We can’t have recourse to the best explanation
If the PSR is false, we can never really say what the best explanation of a certain phenomena is. Say we have a trial where a man is convicted of murdering their mother-in-law by stabbing. We have his fingerprints on the murder weapon, along with an obvious motivation (being his mother-in-law after all). Usually, one would weigh up all the possible options and assess the probability or likelihood of each of them. The most likely option is that he killed his mother-in-law, the least likely option is that he was framed by his father-in-law who wanted to kill two birds with one stone, so to speak (if my mother-in-law ever reads this, let her know that I hardly ever have homicidal thoughts about her). But what if the PSR is false? We now have a third option – that the knife ended up in the mother-in-law multiple times for no reason at all. What’s the likelihood of such an option? As discussed above, we have no way of saying how likely this is or not. If such were the case, we would be obliged to empty all our prisons – after all maybe that convenience store money just teleported itself into my garage for no reason, your honour.
Why should we believe Principle of Sufficient Reason to be false?
Really, why would anyone doubt the PSR apart from trying to avoid the outcome of cosmological arguments like this one? It is so hard to believe that the PSR is false that we would struggle vociferously against that proposition in practice – imagine a unicorn popped into existence into your bedroom tonight. What do you think you’d consider to be more likely: 1. That you were dreaming or hallucinating 2. That some strange race of alien unicorns had invented cross-galaxy teleportation or 3. that the unicorn popped into existence from nothing, for no reason at all. My guess is that it wouldn’t be 3.
As a matter of fact though, some philosophers have tried to show the PSR to be false, so I need to address those arguments here in case they come up in any of your discussions. Fair warning, the philosophy gets a little dense here, so if you are satisfied with the above points and already are basking in the warm afterglow of understanding that the PSR is indeed true, feel free to skip to the next premise.
The Humean imagination argument
Philosopher David Hume (1711-1776) suggested the PSR was false because of his notion that the cause and effect of some event could be separated conceptually, and therefore, there appeared to be no necessary connection between the two. In other words, if one could imagine some effect occurring without a cause, then it follows that this is possible and therefore the PSR is false. By my reckoning, here is how the argument would look:
6. Whatever can be imagined is in reality possible
7. I can imagine an effect without its attendant cause
8. Therefore the imagined effect can occur without a cause
I think (6) is plainly false. But in addition to that, I think the argument is invalid. In order for it to be valid, (8) should actually be:
8a. Therefore the imagined effect can occur without its attendant cause
In order for (8) and not (8a) to be reached, premise (7) should be:
7a. I can imagine an effect with no cause
(7a) is very much doubtful. I can imagine a brick popping into existence, but to imagine this occurring with no cause would require me to imagine it without any of the immeasurably imaginable causes – a ghostly brick maker, alien race A with teleportation technology, alien race B with even better teleportation technology, angels, demons, etc. That is beyond anybodies imagination, and therefore (7a) is false, along with the Humean imagination argument.
The Van Inwagen modal argument
Philosopher Peter Van Inwagen has devised a reductio ad absurdum of the PSR using modal logic. A reductio ad absurdum argument is one in which the premise that is being defeated is included as a premise to the argument in such a way as to lead the argument into some clear absurdity, thus showing the premise to be incorrect. Modal logic is logical argumentation involving concepts like possibility/contingency and necessity. Pruss (in the recommended reading) expresses this argument in 13 premises, but I’ll try to explain it more simply while still getting to the main meaning / recommendations. For the argument, let p be the conjunction of all contingent truths (so all things that are contingently true). This could be, say, all the true propositions about the universe.
9. No necessary truth can explain a contingent truth
10. No contingent truth can explain itself
11. The PSR is true (for the reductio)
12. q, the explanation of p, is itself a contingent truth (from (9) and (10))
13. But then q is member of p (p is the conjunction of all contingent truths)
14. q then explains itself, but it can’t given (10), therefore we have an absurdity
So in less formal terms, if we have all the contingent truths (p), and we try to explain it by another contingent truth (q), then q becomes a part of p and then is the explanation of itself, which is a problem for contingent truths (more on what is possible for necessary truths later). So what’s the problem with (9) to (14)?
(9) is the biggest problem. What is the intuition behind it? For something to be a necessary truth, it must be true in every possible way the world could be. An example of a necessary truth is 2+2=4 – it is true in every possible way the world could be, or could have turned out. So even if the world collapsed back in on itself in some huge black hole after the big bang, it would still be the case that 2+2=4 (along with all the other truths of mathematics). The problem that (9) attempts to address is that if a necessary cause q was present in every possible world, then, so the argument goes, the effect p would also be present in every possible world. But then the truth of p would be necessary, rather than contingent (contingent means that there are some possible ways the world could be that don’t include the contingent truth), hence (9).
So (9) is actually dependent on another sub-premise:
(15) If it is possible for q to be true with p false, then q does not explain p.
(15) applies to a necessary cause q and a contingent truth p, according to the argument against the PSR. Reformulating (15) in another way gives:
(16) If q explains p, then q entails p
(Note: (15) and (16) are taken verbatim from the recommended reading)
The word “entails” means to follow necessarily from – so, if q, then p will necessarily occur. If we can show that (16) is false, we can show that Van Inwagen’s objection fails. One counter example is immediately obvious from modern science which involves statistical effects. Take, for instance, the decay of a certain type of atom. When an unstable atom decays, it releases some form of radiation (in particle or electromagnetic form). The thing is, according to quantum theory, there is no way to say precisely when an atom will decay – the only thing that can be said is the statistical likelihood any given atom will decay within a certain time. So let q be equal to “the laws of nature are operative and we have a newly created Tritium atom” and p be “the Tritium atom decayed within 10 years” and lets substitute those in (16):
(16a) If the laws of nature are operative and we have a newly created Tritium atom, and this fact explains that the Tritium atom decayed within 10 years, then the laws of nature and the existence of the Tritium atom means that the Tritium atom will decay in 10 years necessarily
(16a) is false as the laws of nature can be operative and the Tritium atom could have decayed in, say, 20 years, not 10. Yet q in this case surely is a reasonable explanation of p. Therefore (16) is false and so is Van Inwagen’s argument.
However, we can show this to be the case in an even more interesting way. If beings can have free will, then that also makes (16) false. How does this work? Let’s say that q in this instance stands for “Fred’s favourite ice-cream flavour is banana” and p stands for “Fred chooses a banana flavoured ice-cream at the store”. q is a good and true explanation for p. But does this mean that q necessarily leads to p? In other words, is there no possible way the world could be if q is true but p isn’t? Yes, there is. Fred could have really wanted a banana ice-cream as it is his favourite but, because his daughter prefers strawberry and wanted to share, he freely chose strawberry instead (note that if he had chosen banana regardless of his daughter, q would still have been a true explanation of p). Therefore (16) is also false with respect to the free choices of agents (note that God is typically considered an agent with total freedom of His will).
The indeterminacy of quantum mechanics
In the quantum world, events can only be predicted with probability calculations. As in the example above, the time it takes for any particular atom to decay cannot be predicted with certainty – in other words, we can’t say that atom X will decay in precisely 5 years time, only that atom X has, say, a 25% chance of decaying within that time (note that these probability predictions are extremely precise and experimentally demonstrated by quantum theory – they are not “random”). Does this fact defeat the PSR? No, at least not the PSR in the form required for cosmological arguments. Leibniz had a stronger form of the PSR that resulted in (16), which, as discussed above falls afoul of quantum theory. This stronger form involves logical entailment – if q explains p, then necessarily if q occurs so will p. However, this strong version of the PSR is not required for cosmological arguments or the sound operation of reason. Philosopher John Haldane says that all is required is “an ‘explanation enough'” – in other words an explanation that truthfully captures some aspect of the causal picture. As mentioned above, the explanation for a quantum event such as the decay of an atom at a certain time can consist of the experimental set-up plus the properties of atoms and the laws of nature. This type of explanation is completely sufficient for the Leibnizian cosmological argument, and for the proper operation of reason.
Therefore, quantum indeterminacy is also not a threat to the PSR.
The taxicab objection
One final objection that I will address is that the PSR described as “Every contingent fact has an explanation” is somewhat ad-hoc and is only set up exclusively for contingent facts so that a necessary fact (or a necessary being, i.e. God) can enter the picture later to form a cosmological argument. The philosopher Arthur Schopenhauer compared the PSR to a taxicab, you call it when you want it (i.e. when dealing with contingent facts) and then get rid of it when you’re done (i.e. you don’t apply it to necessary facts / beings, which is ad-hoc). The objector may ask, why not express the PSR in the following form?
(17) Every fact has an explanation
It turns out that this restriction isn’t ad-hoc though, as (17) isn’t obviously true. For starters, it isn’t clear how the necessary truth 1=1 is to be explained. It is an expression of the law of identity, but how can we explain the law of identity? It isn’t at all clear – perhaps it is self-explanatory. Likewise, say we take the fact that a necessary being exists – does this need to be explained? The atheist would probably say yes, but I’d offer the following. If we take God to just be existence, Being Itself (from which everything else derives its own being), which is the classical definition of God flowing from St Thomas Aquinas’ arguments, then God’s essence (what God is) is the same as His existence. Such a being can’t cease to exist, in every possible world such a being would exist. Again, it is unclear that the existence of such a being can in principle be explained, in the same way that the necessary truth 1=1 can’t be explained.
The atheist may claim that, somehow, the universe also explains itself, that its nature is such that it includes necessary existence. However, as far as any of us can tell, the whole stuff of the universe is contingent – it seems entirely plausible that there are possible worlds in which the universe doesn’t exist, especially seeing that every element of the universe (even space and time) is clearly contingent. If, therefore, it is possible for the universe not to exist, its essence (what it is) is not the same as its existence, and it does not explain itself. This however, is a digression and will be discussed more in the future post on the Leibnizian cosmological argument.
In summary then, we have very good reasons to accept the Principle of Sufficient Reason, as defined above. This post should cover you against a significant array of the common objections to the PSR – so good luck.
Alexander Pruss’ version of the Leibnizian argument, from which this post draws heavily, can be found in the following excellent compilation – The Blackwell Companion to Natural Theology
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