## The Principle of Disjunctive Causation and Sufficiency.

1. X is sufficient for Y if and only if, if X then Y.
2. C is sufficient for AvB (Principle of Disjunctive Causation)
3. If C is sufficient for AvB, then C is sufficient for A.
4. Therefore, C is sufficient for A.

Premise 3 is supposedly the problem, but I think it shouldn’t be. If C is sufficient for explaining a disjunctive state of affairs, then presumably it can explain any state of affairs on which the disjunction is true. Sure, something may be left out (that darn resilient contrastive problem again), but I’m still putting off dealing with that for now, and simply aiming to clarify how the Principle of Disjunctive Causation is supposed to play an explanatory role. If it works, then it very clearly does get one out of van Inwagen’s problem, since we can imagine that C is a necessary truth, and that A is a contingent truth, and yet C is clearly sufficient for explaining A (if the above argument is sound), ergo a necessary fact can sufficiently explain a contingent fact (just in case it is possible for a necessary fact C to cause a disjunctive state of affairs).

[Edit: This post obviously has a glaring difficulty, which is that premise 3 is clearly false given how sufficiency was defined in premise 1. I dealt with this in the comments so I thought I’d just leave the post as is, as a record of my mistake. However, I’ve been asked to change the post, and I think it might be worth doing in order to avoid future objections on the blog and off. So, let me be clear, this argument fails. I think maybe it could be reformulated if the first premise read as follows: “X is a sufficient explanation of Y if and only if, both, if ~X then ~Y, and, X is the cause of Y.” I say that X is the cause of Y in addition to (~X⊃~Y) because neither conjunction nor even entailments properly track causal relations.]

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### 11 Responses to The Principle of Disjunctive Causation and Sufficiency.

1. “If C is sufficient for AvB, then C is sufficient for A.”
By 1, C is sufficient for A iff if C then A; but C causes AvB.

I think by definition we identify a cause by whatever is explanatorily relevent to the question. iow, explanatory efficacy picks out the cause instead of the cause picking out the explanation. It seems like you’re going the latter route. iow, I think in saying something is a cause, it presupposes that it’s an explanation.

I’m unsure of saying if C causes AvB, then C causes A (if A happened). Maybe another example using transitivity can give us reason to be careful when extending causes past their original formulation.
Say A causes B, and B causes C. Does that mean A causes C?
Jack places a bomb at Suzy’s door intending to kill her. Suzy’s friend Ray comes by and disables the bomb. Jack is the cause of the bomb placing. The bomb placing caused Ray to disable it in order to save Suzy’s life. That means Jack is the cause of the saving of Suzy’s life. Hooray Jack!

• Jack was in no way the cause of Ray’s actions.

C is sufficient for AvB, and C is the cause of AvB if and only if C is the cause of at least one of the disjuncts. Suppose that C is the cause of AvB by being the cause of A. Then C has caused A, and C is the explanation for any situation satisfying AvB (given how we’ve defined ‘sufficiency’). We both suppose that to cite something’s cause is to explain it. You’re objection is that C is not the ‘sufficient’ cause of A given how we’ve defined sufficiency. I think you’re on to something here. So it seems C is not the sufficient cause of A, even while being the cause of A, and C is not the sufficient explanation of A, even while being the explanation of A. I wonder if there’s any room for saying that C is not the sufficient cause of A, even while being the cause of A, and that C is the sufficient explanation for any state of affairs satisfying AvB (one of which is the state of affairs on which A&~B). In that case, it would seem that AvB would be explained, and it would be explained by C’s causing A, but we’re not sure that any situation satisfying AvB is itself sufficiently explained. That’s an interesting paradox. C is the sufficient explanation of AvB, and must be the sufficient explanation of AvB by being the sufficient explanation of any state of affairs satisfying AvB, but C isn’t the sufficient explanation of any state of affairs satisfying AvB.

That’s a good criticism. Obviously something’s wrong either with the PDC, or the definition of sufficiency (or both). I’m inclined to think the problem is with how I defined sufficiency here. Here’s a suggestion:

X is a sufficient explanation of Y if and only if, both, if ~X then ~Y, and, X is the cause of Y.

• I’m skeptical of the classifying explanations as if they pass this determinate threshold of sufficiency. Some explanations have more empirical content (by ruling out states of affairs) than others. Some explanations predict novel facts. Some explanations have more virtues: testability, background knowledge, past success, simplicity, ontological economy, and informativeness. I rather think of good explanation in degrees rather than as a binary.

In the case of Suzy causing her disjunctive state of lying or telling the truth, citing her as the cause only explains who is in the state of lying or telling the truth. So far, no reasons are invoked as to why she is in the state of lying or telling the truth.

• Prediction of Libertarianism: that Buridan’s paradox would 1) never be verified, and under the right conditions 2) be falsified.

Libertarianism would, then, explain more than it’s competitors (compatibalism et al).

[Edit: it may not explain more in the ‘Buridan-ian case’ than positing randomness, but given the choice between randomness and Libertarianism, Libertarianism may still be a preferred explanation given other considerations).

2. When I brought up Buridan’s ass, I wasn’t thinking about it in relation to Libertarianism. If anything it seems to be more a problem for compatibalism. But I actually don’t see it as a major problem for either side. The idea that I was thinking of was that for God every choice is a choice between incommensurable choices on Pruss’ view, which is similar to a Buridan situation. In our lives it seems we don’t face many Buridan situations, let alone constantly being in a Buridan situation.

3. “Premise 3 is supposedly the problem, but I think it shouldn’t be.”

I’m almost certain I’m misreading the notation here, so you can clarify where I’m going astray.

If I have too many beers and start reading apologetics blogs, then I make sarcastic comments on them OR 9/11 was an inside job. (true conditional!)

Since the conditional is true, does P3 mean if i get drunk and go on the internet tonight, this is sufficient for 9/11 being an inside job?

• I gestured towards the fact that Pruss addresses this in this section of the book. You can find his answer there, and come back here if you’d like to discuss it.

• 1) You didn’t mention Pruss or any book in this post, and (genuine, non-sarcastic sorry) I don’t read all of your posts, so

2) after this comment I went and read all (three) posts tagged with The Principle of Disjunctive Causation, and discovered only one that directly identified a book by Pruss, however

3) that one post didn’t appear to be discussing premise 3 at all, so

C) could you tell me if Pruss even advances P3, or if it’s an original hypothesis of your own? Regardless

C2) could you at least give a summary of the argument against my objection, or a page citation where my objection to P3 is addressed, if in fact it is dealt with at all?

• I apologize, I was reading your comments on my email, and not on the blog. I thought you were responding to this post: https://thirdmillennialtemplar.wordpress.com/2013/10/01/the-principle-of-disjunctive-causation-and-libertarian-free-will/

There I mention that “Pruss runs through three clever counter-arguments against the principle, and diffuses them all pretty easily.”

I then misinterpreted your trouble with premise 3 as one of the three problems he addresses.

Premise 3 in the argument above is clearly wrong, as Hugh made clear in the comments. So, my argument clearly fails.

Sorry for being so dismissive. I am just really busy.

• Also, just for fun, here’s what Pruss writes on page 144 (which I mistook on memory and a cursory reading of your comments to be an address to your problem):

“A better counterexample is the following. Let p be the proposition that my arm moves up. Let q be the proposition that there are aliens in the Tau
Ceti system. Consider the disjunctive state of affairs of its either being the case that (p&q)-or-(p&∼q). My willing to raise my arm causes this state of affairs to be actual. However, I do not cause either disjunct, for there either are or are not aliens around Tau Ceti. If there are, then I could only have causedp&q, and I certainly did not do so, since I did not cause there to be aliens around Tau Ceti. But neither have I caused there not to be aliens around Tau Ceti, so the horn of the dilemma according to which the Tau Ceti system has no aliens is no more tenable.
In response, observe that it is true that that I raise my arm entails that (p&q)-or-(p&∼q). But that my doing A entails p does not mean that I bring it about that p. That I raise my arm entails that 2+2=4, but I do not bring it about that 2+2=4.”

• To be crystal:

It really does look like p3 is false just by consulting the truth tables for [p->(qvr)] and (p->r).