Leibniz famously claimed that, once we have endorsed the Principle of Sufficient Reason, “the first questions we will be entitled to put will be – Why does something exist rather than nothing?” The answer to this question, he further claimed, “must needs be outside the sequence of contingent things and must be in a substance which is the cause of this sequence, or which is a necessary being, bearing in itself the reason for its own existence, otherwise we should not yet have a sufficient reason with which to stop” (“Principles of Nature and Grace,” sects. 78, tr. Latta). In his contribution to The Puzzle of Existence, Jacob Ross argues, on the contrary, that the PSR entails that one never reaches “a reason with which to stop.”
Consider the following modal collapse argument, which is somewhat simpler than the version Ross discusses:
 For every true contingent proposition, there is an explanation of why that proposition is true. (Assumption for reductio)
 Any conjunction of true contingent propositions is itself a true contingent proposition.
 The truth of a conjunctive proposition cannot be explained by one of its conjuncts.
 There is a conjunction of all true contingent propositions.
 A true contingent proposition can only ever be explained by another true contingent proposition.
 The conjunction of all true contingent propositions is an unexplained true contingent proposition, contrary to (1).
Therefore,
Now Ross’s strategy is to deny (4). This is a wellknown move in the dialectic around the argument from contingency for the existence of a necessary being, which has its roots in Kant. But Ross has interesting things to say about two points: first, what reason can be given for denying (4)? Second, what are the metaphysical consequences of accepting some version of the PSR (such as (1) of the argument) while denying (4)?
On the first point, I’m afraid Ross is a little unclear. He starts by arguing that, since explanation is a hyperintensional notion, a finegrained (hyperintensional) conception of propositions is needed here. So far so good. But here’s the part I’m puzzled by:
suppose we adopt [a finegrained] account [of propositions] and regard propositions as consisting in, or at least representable by, an ordered series of constituents corresponding to the constituents of the sentences by which they would be expressed in a canonical language. On such an account, for every proposition, there will be a corresponding set of the constituents of this proposition. And a conjunction will have its conjuncts as constituents. And so it follows that for every proposition, there will be a set that includes all of its conjuncts (p. 84).
Following this, Ross adverts to an argument of Pruss’s for the claim that the collection of all propositions is a proper class, and shows how to excise a certain controversial assumption (that for any cardinality k, possibly there are exactly k many concrete objects) from that argument. From this argument, he concludes that there is no ‘Grand Conjunction,’ i.e. that there is no such proposition as the conjunction of all contingent truths.
Here’s why I’m puzzled. Ross’s conclusion follows directly from his conception of propositions. Indeed, it follows directly from Ross’s conception of propositions that propositions have at most countably many constituents, for an ordered series (at least in the standard mathematical sense) can have at most countably many elements. So the first puzzle is why Ross presents this argument for the existence of a proper class of contingent propositions without noting that all he actually needs is uncountably many of them. The second puzzle is that Ross gives no argument in favor of his particular notion of a proposition, and in his exposition he says things like “suppose we adopt” and so forth. Then at the end of the section, he concludes that there is no Grand Conjunction. In other words, it appears that Ross begs the question: he asks us to grant a certain supposition from which his conclusion trivially follows, namely, that the existence of a conjunctive proposition requires the existence of the ordered series of its conjuncts.
I think the best response to be made on Ross’s behalf is this. He does provide arguments (compelling ones, even) in favor of adopting some hyperintensional conception of propositions. Now, there simply aren’t a lot of welldeveloped hyperintensional theories of propositions on the market. So the opponent of Ross’s argument needs to articulate some alternative hyperintensional conception of propositions if she wants to hold onto the existence of the Grand Conjunction. This seems fair enough to me, but then I was already somewhat skeptical of infinite propositions.
After arguing against the Grand Conjunction, Ross considers some other principles that might be thought to create problems, such as the modal collapse problem, for the PSR. These principles are all designed to say the some basic fact about contingent beings – e.g., that there are some of them – can only be explained if there is a necessary being. Ross rejects the HumeEdwards principle and endorses the following claim:
(K4) For any set S of beings, the proposition that there exists at least one member of S can be explained only by a proposition that appeals to the existence of beings that are not in S (p. 89).
Ross notes that, since there is no set of all beings (sets are beings, and there is no set of all sets), (K4) cannot be made to yield the contradiction, there is a being that is not a being. On the other hand, though, it is extremely plausible to suppose that there is a set of all concrete contingent beings and, by (K4) this set must be explained by some nonmember of it. This might sound at first like it would be nice for the theist; unfortunately, if there is a set of all concrete contingent beings and God exists, then surely there is a union of the set of all contingent concrete beings with the singleton {God}. Bad news.
If (K4) is restricted to sets of contingent beings then, together with the PSR and the claim that there is a set of all contingent concrete beings, it entails the existence of a necessary being; if it’s not restricted to sets of contingent beings, then it requires a proper class of beings standing in explanatory relations to one another (no regressstopper can be introduced). Ross holds that, because of skepticism about the possibility of necessary things explaining contingent things, the defender of the PSR has cause to be skeptical of the claim that there is a set of all contingent concrete beings (p. 93). Thus, Ross thinks, the defender of the PSR should grasp the second horn and believe in a proper class of contingent concrete beings and an infinite regress of explanatory relations.
Much in Ross’s essay is clearly turning on the assumption that the existence of contingent beings cannot be explained in terms of a necessary being. This is an assumption most defenders of the PSR have rejected. However, Ross provides a quite interesting exploration of the kind of view one might be driven to if one endorsed this assumption while also endorsing the PSR, and he shows that such a view need not be selfcontradictory, at least in any obvious way.
(Crossposted at blog.kennypearce.net)
Some more thoughts.
A. The following seem plausible to me:
1. Every true proposition is grounded in a conjunction of true fundamental propositions.
2. If q explains r and p grounds q, then p explains r.
3. There is a conjunction of all true fundamental propositions.
By 3, let r be the conjunction of all true fundamental propositions. This is a contingent proposition. By PSR and 12, there is a conjunction of true fundamental propositions that explains r. So we don’t escape the need to explain a conjunction by a subconjunction. (On my view, the fundamental propositions include some necessary ones, and the subconjunction will consist entirely of necessary propositions, which then will explain the contingent r.)
I suppose Ross will deny 3.
B. Suppose that there is a proper class C of all contingently true propositions. Let r be the proposition that every member of C is true. This is a contingent truth. Let q explain r. If q is contingent, then q is a member of C. But it is not much less odd to suppose that r is explained by a member of C than to suppose that a conjunction is explained by a subconjunction.

Professor Pruss, I’ve been meaning to ask you this for quite some time…in the essay you coauthored with Richard Gale, you posit the existence of a BCCF, and correct me if I’m wrong here defend it against the criticisms of Davey and Clifton by saying that the validity of a proposition should be given an “innocent until proven guilty” status. But the BCCF is plausibly infinite, and an infinite conjunction is more counterintuitive than a finite one. Given that, shouldn’t a proponent of the BCCF give arguments for its validity as a conjunction?
(Again, please forgive me if the question sounds too ignorant!)
Hassan
September 28, 2014 — 5:26
Maybe the “ordered series” that Ross is talking about doesn’t have to be countable