Chisholm's Paradox/Transworld Identity, S5 and the PSR

 One criticism of the PSR which hasn't been discussed that much is the following: 

Assume S5 (Which is not at all needed for the Paradox but it certainly makes our lives far easier); we can now construct Chisholm's original Adam and Noah Paradox (of Transworld Identity) - to quote Stanford since I cba:

"Chisholm’s Paradox, presented in Chisholm (1967), begins innocuously enough. Suppose that individuals are identical across possible worlds such that de re modal claims like “Fred could have been taller” are true only in case there is some possible world where the very same individual, in this case, Fred, is taller than he is in the actual world. Now, consider that two actual individuals, Adam and Noah, could have had slightly different qualitative properties. For example, Adam, instead of dying at age 930, could have died at age 931. Similarly, Noah, instead of dying at age 950, could have died at age 949. If Adam and Noah can tolerate these incremental “changes” to each of their qualitative profiles, it seems that had they been a different way than they actually are, they could have tolerated even further incremental changes.

Now, if we allow incremental possible changes to the ways that Adam and Noah could have been and accept the transitivity of identity, we are committed to a finite series of incremental changes that ends in a possible world where Adam has all the qualitative properties Noah actually has and Noah has all the qualitative properties that Adam actually has. This is because the relevant iterated modal claim “Adam could have been such that he could have been such that he could have been such” is, by our initial assumption, true in virtue of one and the same individual, Adam, existing at different possible worlds. So, if Adam and Noah could be incrementally different and the individuals they could have been could also be incrementally different, we must accept that Adam and Noah could “swap” their respective qualitative properties. And, if so, there is a maximal possibility that differs from actuality only in haecceitistic terms—that is, it differs only in terms of which individuals instantiate which qualitative profiles."

Essentially, the main thing to maintain is that given Chisholm's Paradox, Adam and Noah would only differ non-qualitatively, hence only haeccetistically. Therefore, Identity is non-qualitative/Haecceitism is true.

We can construct a similiar argument from Cover and O'Leary-Hawthorne (Kaplan also brings this up):

Suppose that all the truths about any possible world could be captured by such general propositions [that is, by those not involving nonqualitative thisnesses]. In supposing this, it may help to imagine a being - an omniscient Being, say - that surveys all logically possible states of affairs and conceives of each possible world in terms of a book or list of general propositions of quantificational form [for instance, 'There is an individual having suchnesses F and G and .. .'l And suppose now that one were to ask this being: is there anything that exists, or that could exist, which is essentially red, that is, red at each possible world where it exists? It seems clear enough that our imagined being would not only be unable to answer this question, but moreover would be unable to make much sense of it. Nothing within any list nor any comparison among them can serve to ground the truth or falsehood of the statement 'There is something that is essentially red.' For if the full truth at all worlds is general, there will be no determinate fact of the matter whether the thing that is F and G and H ... in world W is, or isn't, the thing that is F and G and H ... in world W*. In short, purely general propositions look to contain no resources for tracking a particular object across lists or worlds: the concept of trans world identity, and with it the traditional de re modal notions of essence and accident, have been lost. [ ... ] The lesson to be learned is that in order to make sense of trans world identity claims, one needs to make room for singular propositions".

Essentially, if we were to accept Transworld Identity in any case, we would require some notion of Non-qualitative essence/Haecceity. A few other arguments have been given among these lines in the literature, but this should suffice.

How does this relate to the PSR? Well, Chisholm has made this interesting observation in his original paper with the Paradox:

"There is a certain ambiguity in "discernible" and in "indiscernible". The two Adams could be called "discernible" in that the one has the property of being Noah in the other world and the other does not, and similarly for the two Noahs. But in the sense of "indiscernible" that allows us to say that "Indiscernibles are identical" tells us more than merely "Identicals are identical," aren't the two Adams, the two Noahs, and the two worlds indiscernible? Could God possibly have had a sufficient reason for creating W' instead of Wn? If W' and Wn are two different possible worlds, then, of course, there are indefinitely many others, equally difficult to distinguish from each other and from W' and Wn. For what we have done to Adam and Noah, we can do to any other pair of entities. Therefore among the possible worlds which would seem to be indiscernible from this one, there are those in which you play the role that I play in this one and in which I play the role that you play in this one. (If this is true, there may be good ground for the existentialist's Angst; since, it would seem, God could have had no sufficient reason for choosing the world in which you play your present role instead of one in which you play mine.) " I think it's important to note that, Pruss brings up a similiar yet very distinct problem regarding "Qualitatively identical yet non-qualitatively distinct worlds" in his book on the PSR and very briefly in "Actuality, Possibility and Worlds" - The problem focuses on the Qualitative identity of each World while this Problem does the opposite. What sufficient reason would God have between two merely non-qualiatively distinct Worlds? The idea is just that, if me and your qualitative characters could've been exactly identical, yet we could've differed non-qualitiatively (Or in other words, I could've had all of your qualitiative properties and you could've had mine - while I'm still "me" and you're still "you"), then God wouldn't have a sufficient reason to decide which one of us would play which role in creation. Hence, we run into some clear form of Brute Contingency under Theism. One could appeal to some sort of Origin Essentialism (either Moderate or Radical) to escape this issue. Obviously, Moderate Origin Essentialism wouldn't solve this issue at all, so we need some sort of Radical Origin Essentialism instead to "block" the Paradox and maintain conditions for Transworld Identity. I don't think Radical Origin Essentialism is that great of a view for numerous reasons, I'm probably going to elaborate in another post on why but here are a few reasons: For one, it seems like every theist has this shared intuition that God could create me, at any point before I was created. It seems weird to say God couldn't have made you, but rather some sort of counterpart, since only your parents can make "you" - you given origin essentialism. Another problem is that even two particular gametes can create more than one individual in the future (in cases of monozygotic twins, e.g.). Moreover, if we look further back in the past, to consider the possibility of Noah's existing or not existing even before the existence of his parents (and their gamete cells), it doesn't seem like there's anything which could act as a truth-maker for the claim "You could've existed", unless we appeal to mere possibilia or something of that sorts - which would motivate Haecceitism regardless. To borrow an analogy from Nathan Salmon:"although Queen Elizabeth II could not have had a totally different origin, surely she could have originated from a sperm with a difference of only one mitochondrion to the one from which she actually originated." Another problem is that we will have to trade on a chain of tenuous sufficiency of origin claims just by trying to "specify" which Individual we're referring to. More robust conceptions of ROE also utilize Leibniz's Law (alongside the converse principle which is also controversial), which could serve as a reason to dismiss the theory all-together.

Again, consider Adam. I think most theists would share the intuition that "Noah" could've been the first man. But given Radical Origin Essentialism, this is just false. God could've not created "Adam", but he couldn't have not created "Adam" as the first man. It seems very intuitive/conceivable to me that the Doctrine of Creation could've played out differently, with Noah as the first man and "Adam's Ark". I'm sure many others share this intuition with me. (Note that this itself is not a statement of Haecceitism, Noah could've played Adam's Role insofar as He could've been the first man, not that they could've swapped complete qualitative characters.) The Theist would also see very few reasons to accept this view (Except to utilize reasonably weak Theodicies) as nearly every advantage this view has, Haecceitism has aswell, the extra ontological commitment doesn't really matter as I hold that Theists are just commited to Haecceitism anyway (check my previous post about Haecceitistic Divine Conceptualism.) I think there are other disadvantages to the Origin Essentialist view which would ultimately mean Chisholm's Paradox leads to some form of Haecceitism, or in this case, even the mere acceptance of Transworld Identity. There might be a few ways for the PSR defender to push back here, which I hope to go over on another post too. But I still think this is a interesting way to attack the PSR which isn't that discussed in the literature. (Didn't have much time to write this so apologies for any poor wording or inadequate explanations)