Molinists urge that we can avoid necessitarian conclusion–the conclusion that there is just one possible world–if it is true in some worlds that God is not able to actualize the best world. This is false. The necessitarian conclusion follows from the plausible principle that God must actualize the best possible world, if there is a best possible world. I don’t think it’s difficult to show that there must be a best possible world, so I leave it as an exercise. Here’s the proof contra the Molinist.
1. Necessarily, God actualizes the best possible world. Basic Principle
2. God is essentially omnipotent, omniscient, omnibenevolent & necessarily existing (all as a matter of absolute necessity). Assumption.
3. w is the best possible world. Assumption
4. God actualized w in w. From 2,3
5. It is true in w that necessarily, God actualized w. From 1, 4.
6. Necessarily, God actualized w. From 5, S5
7. w is the only possible world. From 6
8. Necessitarianism is true. From 7.
The Molinist will ask how it could be true that (8) holds, since there are worlds from the point of view of which God is not able to actualize the best world w. The answer is that, if there is a best world, and if it is necessarily from the point of view of that world that God could not actualize any other world–that is, if (1) is true–then there are no worlds with the properties the Molinist describes. Molinists can avoid this result only if he rejects (1). But what happens if we reject (1) and there is a best world?
1′ It is not necessary that God actualizes the best possible world.
2′. God is essentially omnipotent, omniscient, omnibenevolent & necessarily existing (all as a matter of absolute necessity). Assumption.
3′. w is the best possible world. Assumption
4′. God actualized w in w. From 2,3
5′. It is true in w that, possibly, God actualizes a worse world w’. From 1′, 4′.
6′. It is true in w that, possibly, an essentially perfect being to actualizes a worse world w’. From 5′.
The Molinist might try to mitigate the problem with (6′) by asserting that, in the best world w, God cannot actualize a worse world without the help of rational creatures. But (6′) is still not credible. A perfect being is intuitively not even possibly able to weakly actualize a worse world. Why would his essential perfection be consistent with his being possibly able to actualize a worse world when it is intuitively not consistent with his being able to actualize a worse world?
I conclude that Molinism gives us no reason to abandon (1). It rather just assumes, incredibly, that (1) is false. The proof is slightly more complicated, but we can reach the same result with the assumption in (1”)
1”. Necessarily, God cannot actualize a world w’, if w’ is less valuable overall than another world he can actualize w. Basic Principle
Note that (1”) is true in the best world w, and the quick result is that there are no other worlds. Here’s the short proof.
1”. Necessarily, God cannot actualize a world w’, if w’ is less valuable overall than another world he can actualize w. Basic Principle
2”. God is essentially omnipotent, omniscient, omnibenevolent & necessarily existing (all as a matter of absolute necessity). Assumption.
3”. w is the best possible world. Assumption
4”. It is true in w that God cannot actualizes a worse world w’. From 1”
5”. It is true in w that God cannot actualize a better world w”. From 3”.
6”. Necessarily, God actualizes w. From 4”, 5”, S5
7”. Necessitarianism is true. From 6”.
Hi Kevin,
No, I don’t assume that there is a best world. I think it’s not difficult to show that there is one, if you accept a principle of recombination that permits us to combine any worldstages of any worlds with one another. Let S be the set of all possible worlds, whatever the cardinality. Lewis says there are at least bethtwo worlds, maybe there are more. Hard to know. But whatever the number, it is the cardinality of S. Now consider a world W composed of the best worldstages of every world in S. W is also in S. Indeed, W is the best world in S. Of course, W is an infinitely large world, perhaps composed of infinitely many epochs–perhaps infinite in both directions–past and future.. But that presents no obvious metaphysical worry.

“Now consider a world W composed of the best worldstages of every world in S”
But ho do we know that such combination doesn´t entail a contradiction?
December 7, 2014 — 14:02 
” Of course, W is an infinitely large world, perhaps composed of infinitely many epochs–perhaps infinite in both directions–past and future.. But that presents no obvious metaphysical worry”
I’m not so sure about that. Isn’t that an actual infinite? If we suppose actual infinities are possible, I think we’ve created more problems for God than we’ve solved. But maybe I’m missing something.
December 7, 2014 — 17:38

No. It would take a long winded explanation, but an actual infinity is something that is infinite in number. God is “infinite” in many ways, but not in number.
December 8, 2014 — 4:45


It’s not an actual infinite unless the world is actual. But that aside, I’m unmoved by Craig’s arguments against actual infinites. I can’t see why anyone considers them cogent. I. For all anyone knows, the universe is infinitely large; that’s a empirical dispute for physicists. It’s certainly not going to be settled by an a priori argument. But aside from that, there are infinitely (uncountably) many numbers, infinitely large sets, etc. For what it’s worth, I also find no problem with the possibility that someone counts to infinity, though this is a bit tougher to be convincing about.
December 8, 2014 — 7:46
I was thinking more of Aristotle or Aquinas (or Duns) than Craig. As you say, I probably made a mistake, since this is only a potential infinity…but I still feel like something is wrong there. But then again, you would probably not agree even if I knew what that was, if you think that way about infinities, so the point is moot (for me at least, since I have no desire to debate a professional philosopher on a topic of which I have limited understanding).
December 8, 2014 — 12:41
If you have a good reason to believe that there are no actual infinities, I’d love to hear it. Whether there are or not seems to me an empirical matter, not a philosophical one.
December 8, 2014 — 12:46 
I’ll get back to you on that when I can be sure I can respond to the question more intelligently than I feel I could at the moment.
December 8, 2014 — 14:00



Jakub,
You ensure such worlds are consistent in the same way that you ensure that any world is consistent. How is it possible that you are short at one time and tall another? Well, either you assume presentism (so you exist only at the present) and there’s no conflict; or you assume that different parts or stages of you exist at different times, but no two stages at the same time. Similarly for everything else. I’d assume that no two world stages overlap with respect to anything except things like universals. Other abstract objects don’t exist in any stage.


Jakub,
The consistency of worlds does not entail eternalism. As I said, there are lots of ways to do this. But yes, eternalism seems the most credible view to me.
December 8, 2014 — 7:48

Mr. Almeida,
I think the reason Molinists think “it is true in some worlds that God is not able to actualize the best world” is precisely because most Molinists deny that there is a best possible world. So to leave it “as an exercise” is to guarantee you’re not making an argument for your most controversial premises (1 and 3). You say you “don’t think it’s difficult to show that there must be a best possible world.” I think the majority of Molinists will find this to be your biggest sticking point. I, for one, find it quite unlikely that there is a best possible world. It’s much more likely that there are a myriad of equally valuable possible worlds. A classic response goes like this: what is the “best” number of trees to exist in the best possible world? 1000? 1 million? 2.3452345326 quadrillion? It’s pretty hard to see how that sort of a thing would even be qualifiable (even by God). I think it’s likely that there isn’t a “best” number of trees. But if there isn’t a “best” number of trees, then any number of worlds whose properties are identical in all other ways than the number of trees they contain (and any properties that are necessarily changed by the change of the treenumber property) could be equally valuable overall. If there are a minimum of two equally valuable worlds but that contain a different quantity of trees (or whatever else you’d like to substitute), then it follows that both premises (1) and (3) fail. Thus necessitarianism doesn’t follow.
Hi Scott,
Thanks for the thoughtful comment! Yes, I’ve heard these sorts of arguments before; they are all (less controversial) versions of Plantinga’s “one more dancing girl” argument. Before I address that, I don’t think people become Molinists because they believe there’s no best world. They become Molinist because they need a theory of providence and sovereignty that does not upset libertarian freedom. Molinists believe it doesn’t matter if there is a best world, since God is not in general able to actualize it. Leibniz’s Lapse was just his failure to notice that God might be unable to actualize the best world or even, for that matter, a morally perfect world.
Anyway, you’ll notice above (Dec 7th, 9:35) a small toy proof for the existence of a best world. I’ll repost it here, and add some commentary.
If you accept a principle of recombination that permits us to combine any worldstages of any worlds with one another, we can show that there is a best world. Let S be the set of all possible worlds, whatever the cardinality. I assume there is such a set. Lewis says there are at least bethtwo worlds, maybe there are more. Hard to know. But whatever the number, it is the cardinality of S. Now consider a world W composed of the best worldstages of every world in S. W is also in S. Indeed, W is the best world in S. Of course, W is an infinitely large world, perhaps composed of infinitely many epochs–perhaps infinite in both directions–past and future.. But that presents no obvious metaphysical worry.
Now, suppose you add, “but there’s a better world, W+ that includes W and W’s duplicate W“. The mistake here is to assume I somehow missed W+. W+, if its a world, is already in S, so it’s already been accounted for. It’s best stages are a part of W. And the same goes for any other world. By hypothesis, S includes all of the (probably uncountably infinite) worlds there are. W is composed from all the worlds there are, including itself.

Interesting discussion. Let me comment something:
” Leibniz’s Lapse was just his failure to notice that God might be unable to actualize the best world or even, for that matter, a morally perfect world.”
AFAIK, according to medievals, (logically) possible is everything that doesn´t contain contradiction. And God´s omnipotence rests in that that God can do everything that is logically possible. But you offer a position that some possible world is unactualizable for God.
What is true then?a) God is not almighty
b) unactualizable possible world entails contradiction and so isn´t possible at all
c) possible world is not meant in logical sense (which would seem strange to me)
d) something else?December 9, 2014 — 5:16
Jakub,
The argument in Plantinga’s Free Will Defense is designed to show that it might be impossible for God to actualize a world W despite the fact that W is a possible world. The basic idea is that God might need the cooperation of libertarianfree agents in order to actualize W and, as a matter of contingent fact, fail to get that cooperation. If these agents are libertarianfree, the argument goes, God cannot force them to cooperate without sacrificing their freedom.
December 9, 2014 — 8:31

Hi Michael,
The assumption that there is a set of possible worlds entails, under usual set theory axioms, that some statements about the number of possible concrete, personal entities, etc. (in the sense of cardinality), be false. For example:
P1: For every cardinal number x, there is a possible world at which there are x and no more than x concrete objects.
P1′: Like P1, but “persons” instead of concrete objects.
If P1 is true (which is incompatible with Craig’s claims against infinities, or similar ones, but that’s another issue) then let’s say that there is a set of all possible worlds PW.
Then, there is a power set PS(PW) as well.
For every cardinal z one can define a function Fz from the set of cardinals smaller than or equal to z into PS(PW), Fz(x) = { W: W is in PW and #{Concrete objects that exist in W } < x or = x }.
For every cardinal z, Fz is injective, so the cardinal #(PS(PW)) is equal to or greater than the cardinal of the set of the first z cardinals. For sufficiently large z, a contradiction follows.
A potential objection is that perhaps the term "concrete object" is not precise enough for the task at hand, and there are possible objects such that there is no fact of the matter as to whether they're concrete. But that is unclear, and also, one can use other categories, like "particles", or "electrons", or "agents with subjective experiences", or something else, and a claim that none of the categories is sufficiently precisely defined would need to be argued for.
Perhaps, it would be simpler to reject P1, P1', etc., but that too would need some argumentation, it seems to me.

Thanks Angra,
I guess I’m not sure what role the power set of the set of worlds S is playing here. The power set of the set of all worlds is larger than the set of all worlds, of course, but it does not entail that there are more worlds than are in S. The cardinality of the set of all worlds will depend on metaphysical assumptions about the nature of worlds, whether there can be distinct indiscernible worlds, etc.; the number of spatiotemporal objects that a world might include will also depend on the nature of worlds. Suppose you think worlds include spacetimes essentially. Then the number of concrete objects in any world cannot exceed the points of spacetime. But maybe I’m not addressing your point.
December 10, 2014 — 18:26
Thanks for the reply, Michael,
I used the power set in order to construct a class of functions (one for every cardinal z), on the assumption that P1 is true, and that there is a set of all possible worlds (and a power set). The idea was to prove that P1, alongside usual set theory axioms, entails that there is no set of possible worlds. I’m not sure what part of my post you find unclear, though. Is it the proof I give, or why I bring that up in this context?
Your reply about spacetimes does address my point, because if the number of concrete objects in any world cannot exceed the points of spacetime, then P1 is false, blocking the conclusion that there is no set of all possible worlds.
However, it seems to me that the hypothesis that the number of concrete objects in any world cannot exceed the points of spacetime may not be left as an assumption in this context, and requires some argumentation.For example, it might be suggested that unembodied persons (ghosts, angels, etc.) are possible, and that the following is true:
P2: For every cardinal number x there is be a possible world W(x) at which the number of unembodied persons is exactly x.
I’m not saying that P2 is true. Rather, I’m saying that you’re making an argument with an assumption that – alongside usual set theory axioms – entails that entails that P2 is not true (The hypothesis that there is a set of possible worlds, plus usual set theory axioms, entails that P2 is not true, which can be shown by a construction like the one I used in the previous post).
So, it seems to me that in order to use that assumption, you should also argue that P1 (and P2, and similar propositions) are not true, or at least that the conjunction of one of them with usual set theory axioms is not true, or give some reason against the applicability of set theory axioms, etc.
I hope that clarifies the point I was getting at.
If the part of my point that was unclear is the proof of the entailment (i.e., the proof that the hypothesis that there is a set of possible worlds plus usual set theory axioms entail that P1 is false), please let me know and I will try to write it more clearly.
December 11, 2014 — 17:23

Thanks Angra,
I don’t think I assume that P2 is false. I don’t say anything about the number of inhabitants of possible worlds, I don’t think. I grant that the number of worlds might be any cardinality you like, you choose it. I do say that there is some cardinality for the set of all worlds. And I do say that, in that set, is a world that is best. The last claim is based on a principle of recombination that assumes that any worldstage can be combined with any other.
I guess I don’t see clearly how you prove that there is no set of possible worlds. Do you mean to prove that there is no set of all possible worlds? What puzzles me about the proof is that if S is the set of all worlds (assume), the P(S) is not a set of worlds at all. It’s just a set of sets. There are no more possible worlds in P(S) than there are in S,; in fact, there are fewer. So, how does a proof about PP(S) show anything about possible worlds? PP(S) includes no possible worlds, as far as I can tell.

Michael, thanks for the clarification. Now I see that the part that was unclear was indeed my proof. I will try another variant of the proof, which I think is perhaps clearer.
I will slightly modify P2, to make it (I think) clearer, but I can use the other one (except for the typo).Specifically, I will assume the usual axioms of set theory (including power set and choice), and from those axioms and the following premises, I will reach a contradiction (I will use usual theorems that follow from those axioms, else the proof would be too long).
For any set A, by #A I mean the cardinality of A.P: There is a set of all possible worlds.
P2′: For every cardinal number x greater than zero, there is at least one possible world W, such that the number of unembodied personal agents at W is exactly x.Let PW be the set of possible worlds. Let PS(PW) be the power set of PW.
For every cardinal number z > 0, let C(z) be the set of cardinal numbers smaller than z.
Let z1 be a cardinal number such #C(z1) > #PS(PW) (it can be proven that there is such a cardinal).Let us define a function F, from C(z1) to PS(PW), as follows:
F(y) = { W: W is in PW and #{Unembodied persons that exist in W } < y or = y }
Then, F is a function (i.e., it's welldefined, since those are all sets) and injective – it’s injective because of P2′.
Since there is an injective function from C(z1) into PS(PW), it follows that #C(z1) ≤ #PS(PW), contradicting the assumption that #C(z1) > #PS(PW).
So, it follows that under usual set theory axioms, P and P2′ are incompatible.
December 11, 2014 — 19:21
That’s very interesting. I guess I would reject P2′. But only because I have no idea whether there are so many disembodied persons that the set of all disembodied persons exceeds in cardinality the power set of all worlds. Second, even if there are (quantifying unrestrictedly) that many disembodied persons, why think that any world could include all of them? You could run the same argument with spacetime points or particles of matter, but why think that any world includes all particles of matter whose set exceeds in cardinality the power set of all worlds? It’s interesting to think about, but I don’t see a reason to believe that there are such huge worlds.
Michael, I’m not saying that P2′ is true (by the way, if P2′ is true, there is no set of all possible unembodied persons). But on the other hand, I wouldn’t assert it’s false, either.
Maybe it is false, but I don’t think it’s obvious. Why wouldn’t such huge worlds be possible?
Moreover, the argument does not need that P2′ is true. P1 is enough, and less demanding.
Maybe P1 is false as well – for all I know – , but as in the case of P2, it seems to me that would require an argument, since you’re not only refraining from asserting that P2′, P1, etc., but you’re using a hypothesis that implies they’re false, and it does not seem obvious that they are false (or more precisely, that implies they’re false if some axioms are applicable, but it’s also not obvious that they are not).
Then again, if the Molinist also holds Craig’s views on infinite – or something like that , then that particular reply is not available to her. Or maybe you could try to make your argument without assuming that there is a set of all possible worlds.
I think I’d need a reason to believe either P1 or P2′ is true. It’s easy to fall into this belief: well, there are very, very large cardinals, so there’s likely to be concrete objects of that number too. Or, perhaps, ‘i should believe that there are concrete objects of that size unless I’m shown otherwise’. Impossibilities don’t in general wear their impossibility on their sleeves. I have no difficulty believing that there exist such large cardinals, it is another matter to believe that there is (quantifying unrestrictedly) a correspondingly large number of concrete objects. By ‘concrete’ I simply mean causally efficacious, so disembodied objects/persons can be concrete. It might be that all possible worlds (and all possible concrete objects) do not form sets, but a class of some sort. But I’m not inclined right off to go this route.

I agree you’d need a reason to believe that P1 is true (P2′ entails P1), but I would say that you’d also need a reason to believe P1 is false as well. So, I’m not saying one should believe P1 is true, but I’m saying that without a good argument, one shouldn’t believe it’s false, either.
Consider, for example, Craig’s claim that actual infinities are impossible (Craig uses “actual” in this context in a sense different from the sense in “actual world”. Personally, I would prefer a different terminology, like “proper infinity”). It seems clear to me one shouldn’t believe that Craig’s claim is true without a good argument in support of it (and I see no such good argument). It’s not some sort of default position. But similarly, I think should one shouldn’t believe the claim that an arbitrarily large numbers of concrete objects is impossible (i.e., that P1 is false) without a good argument in support of it.
That aside, there are other propositions that entail that there is no set of possible world (as before, under usual set theory axioms), and I don’t see one may assume they’re false, either.
How about the following example?
Let’s define an equivalence of propositions:
For every two propositions P and Q, P is equivalent to Q if and only if (necessarily, P is true if and only if Q is true). In terms of possible worlds, Q and P are equivalent if they hold in exactly the same possible worlds.
Let eq(P,Q) mean “P is equivalent to Q”.P3: For every cardinal number x, there is a set S of propositions, such that #S>x, and for every two propositions P and Q in S, ¬eq(P,Q).
The assumption that there is a set of possible worlds, under usual set theory axioms, entails that P3 is false (I offer to prove it, if you like). But it’s not obvious to me that P3 is false, or in other words that there is a set of equivalence classes of propositions.
December 12, 2014 — 18:11
I think we disagree about the dialectical position of denying P1P2′. Both of those propositions clearly express extravagant metaphysical claims. The rejection of these claims is, to my mind, the default position. For the very same reason, I cannot show that the principle of the uniformity of nature is true (nor can anyone else). But it would be bizarre to suspend judgment on whether it holds; we’d need some good reason to deny the principle. Similarly again I cannot show that any number of bizarre hypotheses are false: deceiving demons, brains in vats, the universe beginning two minutes ago, etc. There’s no chance of showing that these are not true. But it is again bizarre to suspend judgment on them. So, I guess I have no qualms about rejecting P1 and P2′, until I’m given some evidence to think either might be true. I’m not sure what to say about P3, since propositions just are possible worlds (though probably not every set of worlds is a proposition). As I mentioned above, there are any number of ways of running this argument from P1 – Pn: for instance, maybe for any cardinal number there are that many particles of matter. But that is an extravagant metaphysical claim. My default position is to believe that view is false, not to suspend belief on it.
But setting that dispute aside, I don’t think it would negatively affect the argument to accept all of P1Pn and hold that the collection of all possible worlds forms a class.
Michael,
Yes, we disagree about that. I don’t think that P1 is any more extravagant than the propositions:
Q1: There is a cardinal x, such that necessarily, the number of concrete objects is less than x.
Q1′ [equivalent to Q1, accepting possible worlds]: There is a cardinal x, such that for every possible world W, the number of concrete objects in W is less than x.
Similarly, I don’t think that P3 is any more extravagant than:
Q3: There is a set S of all equivalent classes of propositions.
Under usual set theory axioms, the hypothesis that there a set of all possible worlds entails Q1, Q1′ and Q3.
That said, I tend to agree that removing the assumption that it’s a set would negatively affect the argument. On the other hand, I’m not convinced it works. Among other worries, I don’t know whether the principle of recombination is true, for a number of reasons.
For instance, one may ask:
a. What if the best worldstages of W1 and W2 overlap in time and space? (I think even patching principles that avoid spatiotemporal overlapping may be suspect, but spatiotemporal overlapping is clearly a potential problem, in my view).
b. What if there are infinitely many worlds with overlapping best stages?
Angra,
I’m not sure I understand (a) or (b) well. I would reject (on independent grounds) that there are any worlds that share stages or parts. So, concerning (a), I’d say that the best world includes intrinsic duplicates of S and S’ of those worlds (assuming that S and S’. I’d say something similar for (b). Possible worlds do not overlap with respect to world stages or anything else (there are exceptions for universals and (sort of, but not really, for numbers, sets, God, and so on). The options available are not just widely permissible overlap or complete worldboundedness. There is partial overlap (worlds might overlap only with respect to certain objects), quasioverlap (worlds might “overlap” in the sense that some objects exist from the point of view of those worlds, but do not exist in those worlds), worlds might include parts of a single transworld objects or transworld continuants that do not exist (completely) in any world. If, say, we turn out to be transworld continuants, then we do not exist in any world (or not completely in any world), and the continuants are the same from the point of view of each world. These are decisions that have to be worked out on the basis of which view best solves the outstanding problems.
Michael,
That’s interesting. If don’t understand (a) or (b) well, then maybe I don’t understand your argument for a best possible world well.
But perhaps, the following will clarify the sort of objection I have in mind.
Let’s say that BW is the best possible world, that, in W1, at t1 Alice does X, whereas at t1, in W2, Alice does Y, and Alice can’t do both Y and X. Maybe X=¬Y, but it does not have to be like that. For example, we may stipulate that X is helping the victims of an earthquate in Haiti by carrying out some activities right there – i.e. in Haiti – and Y is helping the victims of Ebola in Africa, as a doctor. Alice is human, and she can’t be in Haiti and in Africa at the same time (if we relativize this to temporal reference frames, the point remains, only more complicated).
So, what if Alice’s activities at t1 are part of the best world stages of both W1 and W2? (I’m not sure how you’re using “world stages”, though. It’s not entirely clear to me. In a sense of the expression, world stages are parts of an object that exists in more than one world, but that does not seem to be how you’re using the expression. Please let me know if I’m getting that part wrong).
We may assume also that her activity in Africa in W2 and her activity in Haiti in W1 are equally good.
What does Alice do at t1 in BW?
Or are you saying that she does something at t1 in BW, and then there is another spacetime in BW where she does something else, etc.? I see potential difficulties either way, but please let me know.
Right, I think I understood you this way. My last post addressed this point. Alice is not in two worlds, since (as I said) worlds do not overlap with respect to objects like Alice (at best the distinct worlds include Alice duplicates or, more weakly, Alice counterparts). Worlds do not overlap in general with respect to worldstages, either. Worlds do overlap in the ways I suggested in my last post; so I guess I won’t reiterate that. Hope that’s useful.

Michael,
Okay, but then it seems to me you’re assuming in your argument that Alice only exists in one world, and the same for each possible person except, it seems, for God (assuming here God is possible for the sake of the argument, since I’m not trying to object to that point). But that’s is a controversial assumption as well. At least, it seems to me it would need some argument in support of it.
In any case, let’s say that Alice1 and her counterpart Alice2 do as I described.
Then, what happens in BW?
Is there an Alice1 who is in Haiti, and then an Alice1 in Africa, perhaps in different spacetimes?December 13, 2014 — 16:24 
Angra,
You say,
For example, we may stipulate that X is helping the victims of an earthquate in Haiti by carrying out some activities right there – i.e. in Haiti – and Y is helping the victims of Ebola in Africa, as a doctor. Alice is human, and she can’t be in Haiti and in Africa at the same time.
In BW what happens is that in one worldstage S of the best world W, A1 does X and in another worldstage S’ (in this case, S might just be S’) we have A2 doing Y. Since A1 ≠ A2, there’s no consistency worries. But it can look like worries might arise another way: it could be that A1prevents an event E and A2 helps people who suffer from the occurrence of event E. But again, there’s a solution, because the events are also worldbound. Event E1 and event E2, occurring in different worlds, one is prevented and the other not in different stages of WB.
You’re right that I owe an explanation for why some objects exist in more than one world and some do not.
Michael,
Thanks for the explanation.
I’ve been thinking about your hypothesis that Alice only exists in one world – and the same for each of us – and it seems to me that if your target is Molinism, you have a more straightforward argument: from that hypothesis, it follows that Molinism is false (e.g., transworld identity is impossible, except for God), regardless of whether there is a best possible world.
That aside, I have a few worries about the composition principle you propose (at least, what I understand from your post; please let me know if I got something wrong), such as:
1. You say that S may be S’, or it may not be. How would that work? I take it S might be S’ because there can be one Alice in Haiti, and another one in Africa (is that a correct interpretation?), but that raises seems to raise some worries, such as:
a. Take A1 in W1, A2 in W2, A3 in W3, etc. For a sufficient number of worlds, there is no room on Earth for all of the Alices, so at this point, the corresponding stages in BW need to be different, or at least there need to be parallel Earths. However, the procedure you gave does not say how that is resolved – i.e., it does not say which Alices get to the same Earth, and which ones get to parallel ones.
b. If A1 is in Haiti and her counterpart A2 is in Africa on the same Earth (and maybe there are other Alices), there is a good change (using a social network or something) that the two Alices, with the same name, last name, looks, etc., will run into each other. Perhaps, they will do that when they come back to their home in the US (whether they live in the same place or not; obviously, it’s more likely that they run into each other if they live in the same address, but it might still happen). If we extend this from Alice to many other people whose duplicates are on the same planet, eventually a good number of people would find they have duplicates like that. But then, that would seriously alter their behavior, and BW is no longer the superposition of different worlds, but has some different features of its own.
c. (related to b). Let’s say that Alice in Haiti and Alice in Africa meet. They have the same looks, DNA, name, and even they seem to have the same parents, Bob and Lucy, also with the same names, looks, etc. However, as it turns out Bob and Lucy didn’t have two daughters but one – and each of the Alices has the same history , so there are duplicates of Bob and of Lucy as well, generating a good number of further duplicates. A problem with all of those duplicates is that there may well not be a consistent history.
2. An alternative is parallel Earths, parallel spacetimes, or somehow different worldstages (I’m still not entirely sure what you mean by “worldstages”; you seem to mean different regions of spacetime, or different spacetimes, or something like that. Is that correct?). But that still raises the following worry: What happens to the bad events, or bad parts of the history of each world?
More precisely, in W1, W2, etc., and on each Earth if there are parallel Earths in some world, bad and good events, people, etc., all take part on a consistent history. But if you remove the bad while keeping the good, or you remove some parts of the history of a world and patch it with the history of another one (or with something else), then the line of causation is broken (it seems the result is at least many uncaused events), and – much more worringly – even the consistency of history seems to be at risk – at least, there is no guarantee that the result will be consistent. At least, I don’t see any mechanism in the composition principle you propose that would guarantee consistency.
On the other hand, if you don’t remove anything from history and you copy all of the worlds in one, there is no particular reason to think that one will be the best. Even in the Alice case, she’s in Haiti helping the victims of an earthquake, and her counterpart in Africa helping Ebola victims, etc., but then, there is also Ebola and earthquakes, and victims, etc. Why would that be the best world?
Michael,
I’d like to add some further details on the issue of Molinism and transworld identity. I suppose it might be argued that middle knowledge of counterfactuals does not require transworld identity, and a Molinist might come up with a different way of treating counterfactuals. I’m not sure about that (as long as they accept possible worlds at least), but in any case, it seems to me that actual Molinists (at least, all I’m familiar with) accept transworld identity.
In particular, it seems to me the Molinist is committed to the view that Alice has the same essence in W1 and W2. But going by your hypothesis about possible worlds, she does not – either there are no essences, or Alice1 and Alice2 have different essences; either alternative is incompatible with the views Molinists are committed to.
So, I think a Molinist is almost certain to reject your hypothesis that Alice only exists in one world. But if you manage to establish that hypothesis, you don’t need to take the long route of arguing that there is a best possible world, and from there, that Molinism entails necessitarianism. Instead, you can go directly from “Humans only exists in one world” to “It’s not true that there is transworld identity, transworld depravity, etc.”.
Angra,
All good questions. Note that I did not say that either S or S’ would be a part of any best world: those are your examples, cited for another purpose. There is a good question about the laws of nature that might obtain in the best world and how they might obtain. One natural route is to view (deterministic) laws as exceptionless regularities (not necessities) determined by the behavior of objects, not the other way around. So, the laws that obtain in the best world will be the best system of regularities on display there. Perhaps there will be only statistical laws, with lots of exceptions, if the best world is not deterministic. One worthy alternative is to replace worldstages with historical epochs corresponding to each of the worlds whose value is on balance positive. So, imagine a world in which there is just one epoch after another, each epoch mirroring or duplicating a possible world that is on balance good; as one epoch ends and closes out, another begins. It would be an historically interminable world. But it is another way of constructing a world from (this time, very large) world stages. Another way to construct a best world is with four dimensional hyperspace (Hud Hudson does this). So, you have a series of the best spatially three dimensional universes stacked up, side by side by side…, in a single possible world. I’m not crazy about Hudson’s approach, but it is another way to construct a best world.
Incidentally, I think you’re right that Molinists do not assume that objects are worldbound. But that’s not an implication of Molinism. It’s a feature of the historical accident that most contemporary Molinists are Plantingan modal realists.
Michael,
Fair enough, you didn’t say those specific events would be a part of BW, but you said that the BW was composed by the best stages of other worlds, so it seems to me that would include stages of the actual world and similar ones – which has Ebola, earthquakes, etc. Maybe there is a way around that, but I think in any case if you intend to prove that there is a best possible world, you would have to give a more detailed procedure to construct it.
With respect to the alternative of replacing world stages with historical epochs corresponding to each of the worlds whose value is on balance positive, I see some potential difficulties, like:
1. Suppose we do that and we get BW(1). Let’s say that there are two epochs, E1 and E2, such that they’re both on balance positive, but E1 is better than E2. Wouldn’t it be better if we replaced E2 with another copy of E1?
I suppose it might be argued that repeating good epoch is not as good as adding different ones. But even if that is sometimes the case, it would also depend on the degree of difference between the goodness of E1 and E2.
2. Given that the world has infinitely many such epochs, one can always add copies, and it’s not clear at all that the resulting world would be any worse. For example, let’s say that after and before any epoch, we add one copy of it. Why would the result be worse?
3. One may simply swap epochs, and I see no good reason to think that a world in which E1 happens before E2 is any better than one in which E2 happens before E1 (your argument requires a single best possible world BW. If there are infinitely many worlds that are equally good and better than any other world, the conclusion does not follow).
4. You offer a number of different procedures to look for a best possible world. But how do we know that one of the methods gives a world that is better (or the same world as) the world that we get from the other method? It might be that different methods yield equally good worlds, but different ones.
As for the question of whether objects are worldbound, it may be that presentday Molinists do not assume that (and in fact believe the opposite) because they’re Plantingan modal realists, but on the other hand, it may be that [some] they already believed that objects weren’t worldbound before they became Plantingan modal realists. I don’t know. Maybe it depends on the Molinist.
Generally, it seems to me that the most common view on possible worlds is that human people are not worldbound. The view that we are seems unusual, and it seems to lead to conclusions such as:
N1: “Necessarily, if Barack Obama exists, he wins two presidential elections”
N2: “Necessarily, if Jorge Bergoglio exists, he is elected Pope.”
N3: “Necessarily, if Pol Pot exists, he is a mass murderer”.
N4: “Necessarily, if Mark Chapman exists, he murders John Lennon”.
Those conclusions seem to follow because those things happened in the actual world, and I’m assuming those people do not exist in any other world, even if some counterpart might. Maybe you have a way around them?
Given that the world has infinitely many such epochs, one can always add copies, and it’s not clear at all that the resulting world would be any worse. For example, let’s say that after and before any epoch, we add one copy of it. Why would the result be worse?
We are not adding copies. Based on the principle of recombination, we are asking which combination of world stages (i) is best and (ii) exists. Maybe there would be lots of repetition of stages, maybe not.
Those conclusions seem to follow because those things happened in the actual world, and I’m assuming those people do not exist in any other world, even if some counterpart might
No, those conclusions do not follow from the assumption of worldbound individuals.
We are not adding copies. Based on the principle of recombination, we are asking which combination of world stages (i) is best and (ii) exists. Maybe there would be lots of repetition of stages, maybe not.
I was talking about one of the alternative procedures that you offered, which replaces world stages with historical epochs corresponding to each of the worlds whose value is on balance positive.
The procedure does not seem to be specific enough, so it’s difficult to assess some of the points, but in any case, one can raise the following issues:
a. If we’re not adding copies but asking which combination is best and exists, a question is: why should one believe that one combination is best?
For all one know, it might be that for each combination, there is a better one. Or maybe there is an equally good – or infinitely many equally good ones.
b. At any rate, one can always consider the scenarios I suggested earlier. For example, let’s say that by applying one of the procedures you propose you get some world BW. What if we, say, swap two epochs? or what if we replace a good one with a copy of a better one? Or what if we add duplicates of each epoch? And so on.
c. Similarly, one may consider the different procedures you offered. For all one knows, they may yield one (or infinitely many, with minor modifications) equally good worlds, but not the same one.
No, those conclusions do not follow from the assumption of worldbound individuals.
They do follow from that assumption plus the fact that those things happened in the actual world, as long as one considers the full length of their existence at the actual world.
That’s what I had in mind but I guess that wasn’t clear.
If that’s your objection (i.e., that Pol Pot wasn’t yet a mass murderer when he was a kid, etc.?), let me clarify with the following modification:
N3′: Necessarily, if Pol Pot exists and turns 70, he committed mass murder.
We can argue as follows:
R1: At the actual world, when Pol Pot turns 70 years, he committed mass murder.
R2: Pol Pot does not exist at any world other than the actual world.
C: In every possible world at which Pol Pot exists, when he turns 70, he committed mass murder.
Similarly (under the worldbound assumption, plus events that happened at the actual world), one may also establish:
N3”: Necessarily, if Pol Pot exists, it is impossible that he refrains from committing mass murder.
That follows (of course, accepting that possible worlds capture all possibility, else all bets are off) from the fact that Pol Pot only exists at the actual world, and he does not refrain at the actual world.
N4”: Necessarily, if Mark Chapman exists, either he already murdered John Lennon, or he is murdering John Lennon, or he will murder John Lennon.
N4”’: It is impossible that Mark Chapman lives but refrains from murdering John Lennon.
Similarly, one may establish results like:
N5: It is impossible that Ronald Reagan studies engineering. [or, for that matter, that he refrains from doing anything he didn’t refrain from doing, or that he does anything he did not do, etc.)]
If you have any objections to those conclusions, I would like to ask what they are.
Michael,
I’ve been trying to figure out other reasons you may be saying that propositions such as the above doesn’t follow from the hypothesis that humans are worldbound – i.e., that they only exist at one world , in case it’s not the objection I mentioned in the post above.
I’m guessing an alternative is that you are holding a Lewisianlike view on the matter (even if without other features of his view), according to which as long as there is a possible world W at which some counterpart of Chapman who is not Chapman refrains from murdering Lennon, then it’s possible that Chapman refrains from murdering Lennon.
That sort view seems very improbable to me (I think it gets the semantics wrong), so I think the statements in question do follow from worldboundedness, but I guess we’re just going to disagree on that if that’s what you have in mind – or something along those lines.
Is that the sort of view you have in mind?
The problem is that I don’t think it is plausible that a best plausible world exists, or at least we can’t just assume it, since it would seem to imply an actual infinite. I know that it is a matter of concern to you, since your book popped right up when I googled “no best possible world”, – and I know that Rowe has argued that if it God knew a best possible world wasn’t possible, he shouldn’t have created at all. But Rowe’s line of thinking always came off as sophistry to me, along the same lines as those parodies of the Ontological Argument you see sometimes.