QuestionsWhy is there something rather than nothing?If every contingent fact has an explanation, the totality of contingent facts is explained by a necessary being
Why is there something rather than nothing?There is a reason

If every contingent fact has an explanation, the totality of contingent facts is explained by a necessary being

The cosmological argument from the principle of sufficient reason (Pruss)

Alexander Pruss born 1973Philosopher and mathematician who defends the principle of sufficient reason and cosmological arguments.
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What it claims

There exists a necessary being that acts, and it explains why there are contingent things rather than nothing.

Why

No contingent fact can explain all contingent facts without going in circles: a necessary being is needed.

The same idea through history
Samuel Clarke1705Clarke argues that an infinite series of dependent beings has no reason to exist, without a necessary being.Gottfried Wilhelm Leibniz1714Leibniz asks why there is something rather than nothing and looks for the ultimate reason outside the series of contingent things.
Alexander Pruss2006Pruss applies the principle of reason to the conjunction of all contingent facts and derives, by elimination, a necessary being that acts.
In short

"If every contingent fact has an explanation, the totality of contingent facts is explained by a necessary being" is an argument by Alexander Pruss (The Principle of Sufficient Reason: A Reassessment, 2006, 2006) on the question "Why is there something rather than nothing?" (answer: there is a reason). Its claim: There exists a necessary being that acts, and it explains why there are contingent things rather than nothing. According to AskPhilosophy's logic check (Z3 solver), the argument is valid only if one grants a premise the author leaves unstated (P4). AskPhilosophy presents 3 objections, 3 of them with a documented reply, and the original text behind each premise, checked word for word.

The Principle of Sufficient Reason: A Reassessment, 2006
Valid with an implicit premise

In a 2006 book the philosopher and mathematician Alexander Pruss defends the principle of sufficient reason (PSR): whatever is the case has a reason why it is the case, at least for contingent truths, those that could have been otherwise. He draws an argument from it in several steps. Take the conjunction of all contingent truths, which he calls the "Big Conjunctive Contingent Fact". It is contingent, so it has an explanation. But this explanation cannot cite any contingent being, law or initial condition, since these are part of what has to be explained. What remains is a necessary being that acts. A caveat: Pruss himself notes that this leaves two questions open, whether this being is the God of theism and whether the PSR is true. The first half of the book defends the PSR and the second answers objections; several of these appear below.

P1Principle of sufficient reason: every contingent truth has an explanation.
P2The conjunction of all contingent truths is itself contingent and true. So it has an explanation.
P3This explanation cannot go through any contingent being, nor through the laws of nature or initial conditions if these are contingent, since all of that is part of the conjunction: it would be circular. An infinite chain of partial explanations does not explain the whole either, since explaining each element does not explain the totality.
P4 · implicit premiseThe only possible explanations are those of a necessary being that acts, of a contingent being or fact, or of an endless chain of such facts. If P3 rules out the last two, the first remains.
Therefore there exists a necessary being that acts, and it explains why there are contingent things rather than nothing.

click a premise to reject it

If you accept every premise, logic forces you to accept the conclusion. So the debate is about the premises.
Checked by a logic solver: the premises cannot all be true while the conclusion is false.
Without the implicit premise: Without P4, the computer finds a case where the principle of reason holds, the contingent whole has an explanation of a kind not examined, and no necessary being exists.
Valid with P4. Without it, an explanation of a third kind could be imagined. Pruss examines other explanations (scientific, reductive, circular) and rules them out one by one; the possible weak points are therefore P3 and above all P1, which the book defends over several chapters. Calling this being God requires one more step.
Analogy. A family story in which each person was raised by another, without end. Each is explained by the previous one, but "why are there families at all?" stays unanswered as long as the explanation cites someone in the family. The image is ours.

Objections

3

Each objection is a conversation: click to see who replies and where the debate stands.

Peter van Inwagen 1983 · attacks premise 1

If the conjunction p of all contingent truths has an explanation q, then q is itself contingent, so one of the conjuncts of p. It would end up explaining itself, which is absurd. So the principle of reason would be false, or would make everything necessary ("modal fatalism").

Pruss replies
Alexander Pruss 2006 · Pruss's reply
Pruss, building on an argument of Davey and Clifton (2001), disputes the very existence of this conjunction. The collection of all contingent truths is not a set: there is no set of all cardinal numbers, and van Inwagen's argument assumes we can talk about any subconjunction.
Where the debate stands (our summary)The disagreement is about whether the totality of contingent facts can be explained without the explanation being part of it. Pruss answers with set theory, but grants that van Inwagen's argument might be made to work by restricting the conjunction; he then answers with the free explanation of a necessary being. His critics hold that the restricted version of the argument stands. No broad agreement.
David Hume 1779 · attacks premise 3

In a chain of causes, each part is caused by the one before. Asking afterwards for the cause of the whole is an arbitrary act of the mind: explaining each particle explains the collection (a principle later taken up by Edwards).

a defender replies
see the argument
Alexander Pruss defender of the argument · 2006
Pruss argues that the Hume-Edwards principle is false. It assumes that explaining the elements suffices to explain the whole, whereas explanation does not add up (Gale): explaining why each of two men is at the street corner does not say why they are there together.
Where the debate stands (our summary)Each side holds that the other assumes what has to be proved: for Hume the cause of each part exhausts the question; for Pruss it leaves unanswered the fact that these parts exist together. A core point that is unsettled (our summary).
Alexander Vilenkin 1982 · attacks premise 1

Quantum cosmology models, such as Vilenkin's, describe a universe created by tunnelling from a state with no space and time, with no initial condition. Read this way, they suggest that a universe can appear with no prior cause, which would contradict the principle of reason.

a defender replies
see the argument
We have not yet found a direct reply by Pruss in the texts.
Alexander Pruss defender of the argument · 2006
Pruss adds that the dispute between a theist physicist and an atheist physicist about such a model is not a disagreement about physics but a philosophical one: they agree on the model and differ on whether it describes all of reality.
The debate goes on (our summary) Vilenkin wrote before Pruss. In his book (chap. 4, § 4.5), Pruss answers this kind of model: physicists' intuition only makes probable a possible world where the physical universe arises without a physical cause, which is compatible with the PSR, which does not say that the causes of physical phenomena are always physical.
Where the debate stands (our summary)The disagreement is about the reach of physical models: do they describe all of reality, or only its physical part? Physics itself does not settle this point (our summary).