December 20, 2013

Jacob Ross on the PSR

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. 7-8, 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:

  1. For every true contingent proposition, there is an explanation of why that proposition is true. (Assumption for reductio)

  2. Any conjunction of true contingent propositions is itself a true contingent proposition.

  3. The truth of a conjunctive proposition cannot be explained by one of its conjuncts.

  4. There is a conjunction of all true contingent propositions.

  5. A true contingent proposition can only ever be explained by another true contingent proposition.
  6. Therefore,

  7. The conjunction of all true contingent propositions is an unexplained true contingent proposition, contrary to (1).

Now Ross's strategy is to deny (4). This is a well-known 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 fine-grained (hyperintensional) conception of propositions is needed here. So far so good. But here's the part I'm puzzled by:

suppose we adopt [a fine-grained] 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 well-developed 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 Hume-Edwards 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 non-member 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 regress-stopper 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 self-contradictory, at least in any obvious way.

(Cross-posted at The Prosblogion.)

Posted by Kenny at December 20, 2013 7:03 AM
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Why Do We Ask Why?
Excerpt: Several of the essays in The Puzzle of Existence argue, in one way or another, that no non-trivial answer can be given to those who ask why there is something rather than nothing. This may be because the question is somehow confused or mistaken, as in ...
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Comments

I hope it's okay if I share my own reaction to Ross's chapter.

I disagree with how Ross handles talk of 'kinds'. He seems to presuppose that any two items each of which satisfies a given predicate thereby belong to the same kind. But that presupposition is by no means clearly true and is arguably clearly false. Take the predicate 'sui generis', i.e., 'of its own kind'. If any two things are each sui generis, then Ross's presupposition implies that they belong to the same kind, which is inconsistent. (If no two things are each sui generis, then why not?)

It's interesting, too, that the Argument 4 Ross criticizes also makes the same uncritical presupposition in step I5: in this case, that 'being' denotes a kind of being, when surely it can't! The same goes, mutatis mutandis, for N5 from Argument 5. I think the usage of 'kind' that Ross and those arguments employ strays so far from ordinary usage that it would better to use a different word that doesn't smuggle in our intuitions about genuine kinds.

Posted by: Steve Maitzen at March 5, 2014 7:43 AM

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