Among the many problems plaguing the Principle of Sufficient Reason (PSR), perhaps Peter van Inwagen’s is best known (cf. An Essay on Free Will (Oxford: Oxford University Press, 1983) pp. 202-204. But there is also William Rowe’s earlier version in The Cosmological Argument (Princeton, NJ: Princeton University Press, 1975) ch. 2. J. Bennett has a version of the argument in A Study of Spinoza’s Ethics (Indianapolis: Hackett, 1984), p. 155 ff. The earliest version I know of is in James F. Ross, Philosophical Theology (Indianapolis: Bobbs-Merrill, 1969) 298 ff.).
Hud Hudson offers a clever solution (cf. ‘Brute Facts’, AJP (1997), 77-82). Let’s state van Inwagen’s objection briefly. We assume that (i) the items which require a sufficient reason are true propositions, (ii) true propositions are what provide sufficient reasons, (iii) the ‘sufficient reason for’ relation is the entailment relation and (iv) contingently true propositions do not contain their own sufficient reason. Here is the principle.
Principle of Sufficient Reason
For any true proposition, x, there exists a sufficient reason, y, such that,
(1) y is a true proposition
(2) Necessarily, if y, then x
(3) If x is a contingently true proposition, then y is neither identical to x, nor a contingent conjunct of x.
A Reductio Argument Against PSR
(1’) Let P be the conjunction of all contingently true propositions.
(2’) P is a contingently true proposition. From 1
(3’) There is a true proposition S which is the sufficient reason for P. Fr. 2, PSR
(4’) S is either contingently true or necessarily true.
(5’) S is not necessarily true. From 3
(6’) S is contingently true, From 4’, 5’
(5’) follows from (4’) and the fact that S is sufficient reason for P only if S is true and S entails P (by (iii) above). If S were necessarily true, then P would be necessarily true. But P is contingently true, so S is not necessary true. We are now very close to a contradiction.
Observe that S is contingently true only if S is a conjunct in P (by (1’)). But since S is the sufficient reason for P, S is not a conjunct of P (by PSR, clause 3). Contradiction!
Hudson notes that this reductio argument against PSR depends on the assumption that every true proposition is either contingently true or necessarily true. But suppose you are a friend of Genuine Modal Realism (GMR). GMR denies that every true proposition is either contingently true or necessarily true. In addition to contingently true propositions and necessarily true propositions, there are true, necessarily false propositions. It might be worthwhile to consider an example from unrestricted composition. Consider the object composed of you and all of your counterparts (given some counterpart relation). Name that object Multiworld. It is true that Multiworld exists, but it is false that he actually exists and false that he possibly exists, since no particular world contains all of the parts that compose him. The proposition that Multiworld exists is a true, necessary falsehood.
Hudson’s Solution
But notice what else follows from necessarily false propositions. We have a proposition S that will do the work that is required by the principle of sufficient reason! Since S is true, it satisfies condition (1) in PSR. Since S is not a contingent truth, it also satisfies condition (3) in PSR. Finally, since S is a necessary falsehood, it satisfies condition (2): S entails the contingent conjunction in P. So there is an S that is a sufficient condition for P!
This is a pretty cool solution to van Inwagen’s problem for PSR. But there is one serious worry. There is no need to identify reasonable or plausible candidates for S since any old true, necessary falsehood would do the work required by PSR. Suppose, for instance, we dub the mereological sum of your left hand and a single counterpart of your left hand in another possible world ‘Howard’. The proposition in S’ is a true, necessary falsehood.
S’. Howard exists.
S’ is a true, necessary falsehood and S’ fulfills all of the conditions in the Principle of Sufficient Reason above. But does the proposition that Howard exists really explain the conjunction of all contingently true propositions? It is hard to see how it could. We might be tempted to conclude instead that PSR needs some additional conditions rulling out any old true, necessary falsehood as the explanation of all true, contingent propositions. Here’s the obvious additional condition.
v. Actual falsehoods cannot explain actual truths.
Another Solution
We know that S cannot be a necessary truth, since P is contingent. We know that S cannot be a conjunct of P, since a conjunct of P does not entail P. And we know that S cannot be P, since contingent propositions cannot explain themselves. So, let S conjoin all the members of P and all of the broadly logical truths. S then satisfies everything required by PSR.
My Solution
For simplicity of exposition I assume there’s no ontological difference between states of affairs and their corresponding propositions. Let S be the proposition that necessarily, God actualizes the best feasible world. And let P be the best feasible set of weakly actualizable (w.a.) contingent propositions at W. So, necessarily, God actualizes P at W. This is consistent with it being true that necessarily, God actualizes P’ at W’, where P’ is the best feasible set of w.a. contingent propositions at W’. It is unnecessary for the argument, but I would add that each possible world is the best feasible world at itself. It follows that for each world W, W includes the best feasible set of contingent propositions P at W, and so God actualizes P at W. This is exactly what we want, since it is true at each possible world that God weakly actualizes that world. We need a sufficient reason for each such actualization.
Myself, I deny that a sufficient reason is a logically sufficient condition, i.e., I deny (2). A sufficient reason need only be a sufficient explanation, and explanations can be enough even when they are not logically sufficient.
The Molinist solution is clever. One problem that remains, however, is to explain why the Molinist conditionals hold. I don't think Molinism is compatible with the PSR.
Bibliographic addendum: The observation that Molinism is not compatible with the PSR was made by David Manley at a dinner with Al Plantinga, me and some others, while he was a first year grad student at ND.
Did I assume Molinism? Not as far as I can tell. But suppose I assume that there are some true CFF's (that's definitely not assuming Molinism). It is a mistake to think that the indeterministic events that CFF's cover--whether free actions or not--do not have explanations satisfying PSR. What they don't have are contrastive explanations.
I'm guessing that you have in mind some notion of libertarian freedom that isn't grounded in indeterminism--as Kane's version is--and that somehow precludes such explanation.
"It is true that Multiworld exists, but it is false that he actually exists and false that he possibly exists"
Which proposition, exactly, is supposed to be the true, necessarily false proposition? Is it
S = Multiworld exists
If so, then either
(A) 'exists' here is unrestricted and so S is true, and so S is *not* necessarily false.
or
(B) 'exists' is restricted to the world under consideration and so S is false and necessarily false.
I don't see a true, necessarily false proposition here. (To be honest, I don't think I understand what such a proposition would be.)
Which proposition, exactly, is supposed to be the true, necessarily false proposition? Is it
S = Multiworld exists
Yes.
If so, then either (A) 'exists' here is unrestricted and so S is true, and so S is *not* necessarily false.
No, S is true, but not true at any possible world. So S is necessarily false (i.e. false at every world). Not every true proposition is true at some world, if Lewis is right. There exist things that do not exist at any world. These include objects whose parts are in several worlds, and so do not exist (not fully) in any world. It might be a good idea to think of God in this way, though I haven't thought about that much.
I'm confused about a couple of things.
I have two questions concnerning the portion of the post titled 'Another Solution'.
First, you say, "We know that S cannot be a conjunct of P, since a conjunct of P does not entail P."
It's not true, in general, that no conjunct of a proposition entails that proposition. It might be right that, with respect to P, it couldn't be that a conjunct of P entails P. But, why think that?
The reason, I take it, that S must not be a conjunct of P is not that no conjunct of a proposition can entail that proposition, but that no contingent conjunct, p, of a proposition, q, can explain the truth of q in the way that a sufficient reason is supposed to do. That, I guess, is why we have condition (3) in (PSR); and the claim that S is a conjunct of P violates that condition, not condition (2).
Second, you say, "So, let S conjoin all the members of P and all of the broadly logical truths. S then satisfies everything required by PSR."
Any proposition that has as a conjunct some contingent truth is itself contingent. So, if S is a conjunction of all of the contingent truths, plus some logical truths, then S must be contingent. But, P is the conjunction of all of the contingent truths. So, S must be a conjunct of P. But, then, S does not satisfy condition (3) of (PSR).
Finally, I don't understand the proposal in the section titled 'My Solution'.
On your view:
S is the proposition that, necessarily, God actualizes the best feasible world.
Now, take the conjunction, P*, of all of the contingently true propositions. Notice that the conjuncts of P* won't (all) be indexed to worlds. They won't be propositions like the proposition that Mike is tall at w. Where 'w' names some world, those are necessary truths. So, the conjuncts of P* are just regular (non-world-indexed) propositions like that Mike is tall.
Now, I don't understand what you want to say about P*.
Do you say that S is the sufficient reason for P*? Then, it must (by condition (2)) necessarily entail P*. But, then, contra our assumption, P* isn't contingent. What am I missing?
Hi Mike,
As far as I know, Lewis (and everyone else) always maintained the following: a proposition is true/false if and only if it is true/false at the actual world. Hence, S is true/false if and only if S is true/false at the actual world.
"[On a modal realist account,] there exist things that do not exist at any world."
That's true, provided that we are equivocating on the word 'exist'---using it unrestrictedly in the first instance and restrictedly in the second. (See 'On the Plurality of Worlds', section 4.3, where Lewis discusses this explicitly.)
It's one thing for there to be individuals that do not exists at any world; it's quite another for there to be true propositions that are not true at any world.
Any proposition that has as a conjunct some contingent truth is itself contingent.
That can't be right. p & ~p is not contingent.
So, if S is a conjunction of all of the contingent truths, plus some logical truths, then S must be contingent. But, P is the conjunction of all of the contingent truths. So, S must be a conjunct of P.
It is not clear in the specification of P whether it conjoins any conjunctions that themselves conjoin necessary truths or whether P contains itself as a conjunct. Such conjunctions would be contingent truths. The reason it is unclear is because such conjunctions would be logically equivalent to contingent propositions already in P. If it does contain such conjunctions, then this solution won't work.
Do you say that S is the sufficient reason for P*? Then, it must (by condition (2)) necessarily entail P*. But, then, contra our assumption, P* isn't contingent.
S entails that God actualizes P* at W* since P* is the best feasible set of weakly actualizable contigent propositions at W*. The best feasible set of weakly actualizable propositions varies from world to world.
As far as I know, Lewis (and everyone else) always maintained the following: a proposition is true/false if and only if it is true/false at the actual world.
Dustin, that's not true for Lewis. The following two inferences are invalid for friends of Lewis's GMR.
1. P is true
2.:. P is actually true
1'. P is true
2'.:. P is possibly true
It's one thing for there to be individuals that do not exists at any world; it's quite another for there to be true propositions that are not true at any world.
No denying it. You would agree, though, that there are such individuals as you describe just above, right--individuals you describe as not existing in any world? You would agree that it is true that there are such individuals as you describe, right? So, it is true that there are individuals that do not exist in any world. But if such an individual does not actually exist, then it is not actually true that he exists. It is, in short, true but not actually true that there are such individuals. In any case, for Lewis, there definitely are such truths. Hudson spells this out in more detail in his piece, if you're interested.
"That can't be right. p & ~p is not contingent."
Fair enough. What I should have said is that any true proposition that has as a conjunct some contingently true proposition is itself contingent.
If that's right, then S is a contingent truth. Because P is the conjunction of ALL of the contingent truths, I can't see why S wouldn't get in.
"S entails that God actualizes P* at W* since P* is the best feasible set of weakly actualizable contigent propositions at W*. The best feasible set of weakly actualizable propositions varies from world to world."
So, this is where I'm really getting lost.
What we want is some proposition, S, which meets the conditions for being a sufficient reason (by (PSR)) for P; where P is the conjunction of a bunch of simple (non-modally indexed) propositions like - that Shaq is tall.
You claim that S = necessarily, God actualizes the best feasible world.
But, if which world is the best varies from world to world, then condition (2) is not met. It is not the case that, necessarily, if S, then P. At a world, w', distinct from our world, w, God weakly actualizes a different set of propositions, P'. But, S is still true at w'. So, the unmodalized conditional (If S, then P) is false at w'. So, S does not meet condition (2) of PSR.
It wouldn't help, as far as I can tell, to modify S in the following way:
S* = Necessarily, God actualizes the best feasible world and, at w, w is the best feasible world.
Where 'w' names our world, S* still fails to meet condition (2). S* is true at every world, but P is not true at every world. So, the unmodalized conditional (If S*, then P) is false at some world. So, S* does not meet condition (2).
It wouldn't help, either, to modify S so that it quantifies over worlds.
S** = Necessarily, God actualizes the best feasible world and, for any world, w, w is the best world at w.
Again, S** doesn't meet condition (2). The relevant unmodalized conditional is false at some worlds.
Maybe you're thinking that the conjuncts of P are modally indexed so that - that Shaq is tall - doesn't get in, but - that Shaq is tall at w - does get in. In that case, condition two is satisfied by S, but only because P isn't the conjunction of contingent truths. P is a necessary truth that has as its conjuncts a bunch of necessary truths.
So, I'm really not sure how it's supposed to work.
You claim that S = necessarily, God actualizes the best feasible world. But, if which world is the best varies from world to world, then condition (2) is not met. It is not the case that, necessarily, if S, then P. At a world, w', distinct from our world, w, God weakly actualizes a different set of propositions, P'. But, S is still true at w'. So, the unmodalized conditional (If S, then P) is false at w'. So, S does not meet condition (2) of PSR.
If it is necessary that God actualizes the best feasible world, then it is necessary that God actualizes the best feasible world at W, for each W. There are lots of feasible worlds at each possible world--lots of worlds God might have actualized instead. An analogy might jog an intuition. Suppose it is true that, necessarily, you purchase the best available ice cream cone. At each baskin-robbins, the set of available cones varies. It follows that, necessarily, at each store B you purchase the best available cone at B.
Instead of speaking of actualizing worlds at worlds--which can be confusing--let me speak of actualizing worlds under feasiblity conditions.
1. Necessarily, God actualizes the best feasible world.
2. Necessarily, for each set of feasibility conditions F (determined by the CFF's that obtain), God actualizes the best world W under F. (From 1).
3. Necessarily, God actualizes the best world W1 under F1. (2, instantiation)
4. S is part of the best feasible world W1 under conditions F1.
5. Necessarily, God actualizes W1 and S under conditions F1.
Hope that helps.
Hi Mike,
"In any case, for Lewis, there definitely are [true, necessary falsehoods]."
Do you have a citation? (That is, a citation aside from the 'in personal conversation' footnote in Hudson's paper. I'd hate to charge Lewis with such an absurd view based simply on one piece of hearsay.)
Lewis talks about such impossible, yet existing, transworld individuals in OPW, pp. 210-220, esp. p. 211. Hudson commends the first 'Postscript' to
'Counterpart Theory and Quantified Modal Logic' in Phil. Papers, Vol. I, pp. 39-40.
But note Lewis's account of possible truth.
Possibly P if and only if at some world W, P is true at W
Here 'at W' restricts the domain of quantification of quantifiers in P to the parts of W. Since you seem to agree that there are objects that do not exist at any world--transworld objects--you seem to agree that the quantifier in 'there are objects that do not exist in any world' is not restricted to the parts of any world. But then it is true that there are objects that are not possible.
"Here 'at W' restricts the domain of quantification of quantifiers in P to the parts of W"
This is incorrect. P here is a proposition, not a sentence. So it simply doesn't make sense (not for Lewis, anyway) to talk about 'restricting the quantifiers in P'.
Maybe this will help. We need to distinguish between the following:
1. At W, x is wholly located within W.
2. At W, x exists.
Provided we read 'exist' in (2) as unrestricted, (2) can be true while (1) is false. For example, even though it is not true at the actual world that Multiworld is wholly located within the actual world, it is true at the actual world that Multiworld exists (again, in the unrestricted sense of 'exists').
Maybe this will help. We need to distinguish between the following:
1. At W, x is wholly located within W.
2. At W, x exists.
Provided we read 'exist' in (2) as unrestricted, (2) can be true while (1) is false
The phrase 'at W' restricts the quantifier in 'there is an x' to W. So, you cannot read it the way you suggest.
This is incorrect. P here is a proposition, not a sentence. So it simply doesn't make sense (not for Lewis, anyway) to talk about 'restricting the quantifiers in P'
I can't follow that. We are specifying the conditions under which it is true that there is an x at W. I have no idea what you mean by saying that there is no quantifier in there is an x at W.
But maybe we can wrap this up. Here's what DKL actually says,
"It is possible for something to exist iff it is possible for the whole of it to exist. That is, iff there is a world at which the whole of it exists. That is, iff there is a world such that, quantifying only over parts of that world, the whole of it exists. That is, iff the whole of it is among the parts of some world. That is, iff it is part of some world - and hence not a transworld individual. Parts of worlds are possible individuals; transworld individuals are therefore impossible individuals" (OPW 210-220)
Note that nowhere in the quote from Lewis does he mention true, necessarily false propositions. That's an implication that Hudson is trying to draw out of his view that there are 'impossible individuals'. But, as far as I can see, that simply doesn't follow. Moreover, it would certainly be a (devastating) mark against Lewis's view if it did follow!
"I have no idea what you mean by saying that there is no quantifier in there is an x at W."
Quantifiers are linguistic items such as 'there is', 'there are', 'there exists', etc. The sentence 'There is an x at W' contains a quantifier. The proposition that there is an x at W does not contain a quantifier. Propositions, for Lewis, are simply sets of possible worlds. Sets of possible worlds, unlike sentences, do not contain quantifiers.
But yes, we probably should wrap this up. I'm sorry that we couldn't see eye-to-eye! I think that some disputes are more easily resolved over a beer than over a blog.
I actually don't see any looming devastating mark against Lewis, so long as we keep distinct 'actually true' and 'true'.
All Hudson wants to say is that there exist individuals that exist in no possible world. So, take the claim in (1).
(1) Z exists
where Z is some transworld individual. Keeping in mind Lewis's truth conditions for 'possibly Z exists', it is true both that (i) Z exists and (ii) it is impossible that Z exists. It expresses a true impossiblity. That seems pretty cogent to me.
Thanks for the quantifier lesson...:)
Mike:
Granted, if a CFF has a true antecedent, an explanation can be given of the truth of the CFF (note, though, that if the explanation is non-contrastive, then one can just use the same non-constrastivity move to refute van Inwagen altogether) by explaining the event in question. But how could you give an explanation of the truth of a CFF with a false antecedent?
But how could you give an explanation of the truth of a CFF with a false antecedent?
Since they're counterfactuals, they all have false antecedents, right? I must be misunderstanding you. In any case, what explains what they would freely do is presumably some statistical law governing indetermnistic events at the relevant worlds in which the antecedents are true. If pressed, one might defend the view that the laws explain both the frequency of A's and the frequency of ~A's, when each have some chance of occurring given C.
But I admit that there are deep worries about truth-condiitons for counterfacutals (of any kind) in indeterministic worlds.
That's a nice move. I've made this move in the case of concrete indeterministic events, but hadn't thought to make it for counterfactuals. I am not sure I am convinced, though. It seems more plausible for events. The idea of explaining things that lack truth-grounds seems odd. It's like positing some kind of a stochastic process prior to God's decisions, where the stochastic process explains the CFFs. But what kind of a stochastic process produces results that don't have truth-grounds? Or produces results that have whatever weird kind of truth-grounds CFFs have?
The idea of explaining things that lack truth-grounds seems odd. It's like positing some kind of a stochastic process prior to God's decisions, where the stochastic process explains the CFFs
Suppose libertarian free actions supervene on indeterministic micro-events. We have something like Kanean libertarianism. I think God would know what would happen were Smith in circumstance C in the same way that God would know what would happen were this piece of radon allowed to decay for 20 seconds. Both are governed by the prevailing statistical laws, given some history H.
Let L be the laws of our world.
Suppose that God never creates a world governed by L. Nonetheless, on the Molinist kind of view, there are CFFs about what indeterministic events would occur were God to strongly actualize a world governed by L--when, given history H this piece of radon would decay, etc. But what explains these CFFs? L? But L does not actually obtain. So are they explained by the laws that would hold were their antecedents to hold?
Alex,
You say: "I don't think Molinism is compatible with the PSR."
And the famous grounding objection is that on Molinism, there are some truth-makers missing.
To sum up,
1. The truth-makers problem. Prior to creation, the actuality of God and all necessary states of affairs cannot ground the truth-values of counterfactuals of freedom.
2. The explanation problem. As you say in your book on the PSR (ch. 1.1):
(1) The proposition F (about what a person would freely do in non-actual circumstances where the person in question is herself non-actual) is such that if it were contingent and true, then its obtaining could not be explained. Explanations are nomological (i.e., scientific) or personal. But any scientific explanation would cancel LIBERTARIAN freedom of the person, and the personal explanation is not available because the person does not exist yet, and the explanation in terms of God's intentional action would, again, cancel libertarian freedom.
(2) But all contingent true propositions have explanations.
(3) Therefore, F is necessary or false.
I asked a Molinist what he thinks about these problems. His reply:
"I would say that a true counterfactual of the sort in question is true in virtue of what the person would freely do in the relevant circumstances. I guess that this would count as a "person" rather than "nomological" explanation. This is the sort of explanation we typically give of non-deterministic free actions. As for the claim that this cannot be because the person in question does not exist at certain times when the proposition is true, I'm not impressed. There are presumably true contingent future-tense propositions about what certain now non-existent individuals will do at various future times (-- if the objector denies this, then we have a fundamental disagreement that does not have to do specifically with Molinist counterfactuals.) The explanation for the truth of such propositions presumably is that the person in question will freely do such-and-such at the relevant time. Whether or not we can know such truths ahead of time or so much as entertain them is irrelevant to their truth.
Quite frankly, I am a bit weary of arguments that try to stick a dagger in the heart of Molinism. I'm convinced that no such arguments exist. This is not to say that Molinism is the only alternative (it is not) or that it is the most plausible alternative (it may or may not be, depending on what other assumptions one makes about freedom and providence). I would like to see exactly what alternatives the others espouse instead."
So, as for the truth-makers problem, the Molinist says that (i) the truth-maker is God (because what else ground could there be prior to creation?), or (ii) it has no truth-maker. This is my interpretation of what the Molinist wrote to me: "I would say that a true counterfactual of the sort in question is true in virtue of what the person would freely do in the relevant circumstances. [= (i)?] ... As for the claim that this cannot be because the person in question does not exist at certain times when the proposition is true, I'm not impressed. There are presumably true contingent future-tense propositions about what certain now non-existent individuals will do at various future times [= (ii)?]"
As for the explanation problem, the Molinist says that the premise (1) is false because the COUNTERFACTUAL F is self-explanatory. The Molinist wrote: "The explanation for the truth of such propositions presumably is that the person in question will freely do such-and-such at the relevant time." For instance, even you, Alex, similarly hold that true CATEGORICAL propositions about free intentional actions, like "Peter freely and intentionally did A for the reason D," though contingent, are self-explanatory.
Finally, I believe you would opt for Banezianism instead of Molinism, right?
Mike and Alex,
Let me press on a very basic question (sorry if you've answered it here already, but I guess you haven't).
Assuming the thesis that every contingent true proposition has a truth-maker, and that some sentences express CONDITIONAL OR CATEGORICAL future-tense, true, contingent propositions about INDETERMINISTIC events (for instance, "if we shall irradiate the piece of radon, it will decay in 10 seconds," "the piece of radon will decay in 20 seconds", "he will kiss her freely in a week", "if he will kiss her freely, she will slap him freely", "if she would slap him freely in the forthcoming month after kissing her freely, he would kiss her freely again"),
Which kinds of entities are the truth-makers for such propositions?
Is it God? But how could it be God?, one naturally asks. But the answer could be: just somehow, though we don't know how exactly, right?
Or is it something in the FUTURE part of space-time?
So are they explained by the laws that would hold were their antecedents to hold?
Yes, it has to go more or less that way. When we say that the CFF's are true, what is meant is that if T is actualized--where T includes the laws of the relevant world-and in T you are created at t, then you would do X. So, yes, if God actualizes me in a world in which God also strongly actualizes laws governing indeterministic events, then we have an explanation of what I would do. That's the general idea, though obviously it would be nice were it put more precisely.