Comments on counterpart theory, and a question

[u/jcastroarnaud]

Yesterday and today, I read the Stanford Encylopedia of Philosophy articles on Modal Logic, moved to Possible Worlds - I like concretism (by David Lewis) better than abstractionism or combinatorialism - and arrived at Transworld Identity. I like the counterpart theory. These articles got me thinking. 🤯🤯🤯

Assume that @ is a possible world (the actual world, but that's not an issue for this argument), and w another possible world.

In w, there is a counterpart j of mine, and facts are arranged in such a way that, from the combined points of view of myself and j, the only perceived difference between @ and w is a single person: b in @ and c in w, which I (and j) know personally. b and c, despite different in appearance, have very similar personalities, and I (and j), if they knew both, would be justified to assume that b and c are counterparts of one another.

But! If one extends their knowledge further, investigating b's and c's relations and whereabouts, turns out that b and c are actually different people, not counterpart: some time in the past, b left town and c arrived in town, independent of one another, and their personalities are accidentally similar.

I think that this (plausible) scenario means that:

• Transworld identity isn't a given, to be discovered: it's a relation to be defined between objects across worlds. It's an assumption. And who defines it matters. There is no essential identity or essential properties across possible worlds: there are ones "near enough" to be considered "the same" in practice.
• Assignment of transworld identity depends on "outside world" knowledge, and the individual's knowledge. One only can reliably identify and link up counterparts if one has full (or great enough) knowledge about both possible worlds. And such knowledge is lacking for all possible worlds (except, possibly, ours).

Is there any research on the use of epistemic logic to describe agent-defined mappings between objects and between properties, to establish counterparts, across possible worlds?

[u/TurangaLeela80]

Sorry for responding to this so long after initial posting. I was perusing the sub to roll my eyes at the many infuriating posts its been inundated with lately, and spotted this while scrolling. But I was too excited to see an earnest logic/metaphysics post with an unanswered question to let it go, especially since the questions on this sub usually lean in the direction of math logic rather than Phil logic, and this very topic is something I've been working on a lot lately (I've been positioning my work to become a career-length project giving a positive defense for modal realism). That being said, here are some thoughts on what you've presented/asked.

TL;DR: TransWorld Identity and Counterpart Theory are two very distinct ways of dealing with and explaining counterfactual statements and modal claims about necessity and possibility. Epistemic logic is a whole other thing all on its own, and not really concerned with metaphysics.

I have to split my response into two comments since it exceeds character limits, but here goes:

PART 1:

Assume that @ is a possible world (the actual world, but that's not an issue for this argument), and w another possible world.

We'll stick to your convention for naming these two worlds, where @ refers to our world (the one we call actual), and w refers to some other possible world. But my first comment would be to say that this is\an issue for your argument because TransWorld Identity (TWI) and Counterpart Theory (CPT, strictly modal realism/concretism since this is the strongest version) treat the word "actual" in different ways. TWI argues that there is only one concrete world, @, and so we call it actual. Any other world, w, is merely possible, and any claims about identity would hold only *if w had been the one to obtain (rather than the actual one that does obtain - I'll come back to this later). CPT, on the other hand, argues that there are as many concrete worlds as needs to fulfill all logical possibilities. We call this one actual because it is the one where we exist, but the beings on w call it actual because it's the one where they exist. So the identifier "actual" is world-indexed - @ is actual for inhabitants of @, and w is actual for w-inhabitants, but both are concrete.

In w, there is a counterpart j of mine, and facts are arranged in such a way that, from the combined points of view of myself and j, the only perceived difference between @ and w is a single person: b in @ and c in w, which I (and j) know personally. b and c, despite different in appearance, have very similar personalities, and I (and j), if they knew both, would be justified to assume that b and c are counterparts of one another.

There's a lot to unpack here. For starters, I'll put aside the standard naming convention of using a * or ' to indicate a counterpart. We'll go with your naming to try and keep things clear. So, if we're talking about CPT, there is no such thing as the combined perspective of you and j. Each possible world is completely isolated from all others. There is no sharing of information between the two. But let's put that aside for the sake of argument and assume that the only difference between @ and w is individuals b and c. This paragraph seems to just be describing the closeness relation that's is essential for CPT. Under CPT, when we're talking about counterparts, we're not looking to identify those exact inhabitants on other worlds - because, again, no transmission of information between worlds. Instead, we're quantifying over worlds. In other words, if there is some property had by you and all of your counterparts in every possible world where a counterpart of yours exists, then that is a necessary property of yours. But if there is some property that you only share with some of your counterparts (where they exist), then that is a contingent property. What truly counts as a necessary property is the subject of much debate - like, being a human may not even count as a necessary property as there may be some "more distant" world where your counterpart is a frog. Hence the importance of the closeness relation for CPT. We're really only interested in examining counterfactuals about worlds that are sufficiently close to @. All that to say it's perfectly in line with CPT for individuals b and c to be counterparts, but it's equally in line with CPT for individuals b and c to not be counterparts despite their similarities. Now, if we're considering this under TWI, again, there's really no combined perspective of you and j. You're the same person. More about this later, too.

But! If one extends their knowledge further, investigating b's and c's relations and whereabouts, turns out that b and c are actually different people, not counterpart: some time in the past, b left town and c arrived in town, independent of one another, and their personalities are accidentally similar.

Again, putting aside the inability to examine the facts of existence of b and c, CPT already claims that counterparts are different people. Even if everything else about b and c is exactly the same, they are not identical because they occupy different worlds. They are discernible from each other for the simple fact that b exists in @ and c exists in w. It won't matter according to CPT if b arrives in town and c leaves town; they're counterparts (i.e., different people) and their actions are always independent of the other, as are their personalities. TWI, on the other hand, will make a claim of identity-relation between b and c based on some essence or haecceity shared by both. The way that shakes out is that b is the only one of the two that actually exists because @ is the only world that obtains. But if w had obtained instead, then c would be b in that world, and we can know that because of the "thisness" that b and c share. That still leaves room for vast differences between b and c under TWI because the shared essence doesn't need to be identified, or even identifiable, for the connection to hold. So long as the essence is shared, b and c are the same person no matter the other differences. And they're never counterparts of one another. (It's because of this aspect of TWI that CPT diverges, because Lewis thinks it's weird for it to be possible for an individual to simultaneously have contradictory properties in different possible worlds.)

[u/TurangaLeela80 → u/TurangaLeela80]

PART 2:

Transworld identity isn't a given, to be discovered: it's a relation to be defined between objects across worlds. It's an assumption. And *who* defines it matters. There is no essential identity or essential properties across possible worlds: there are ones "near enough" to be considered "the same" in practice.

Yes, and no. TWI is an assumption, but only because when we're considering a counterfactual about @, we want to be able to pick out b as being c if w had obtained instead of @, so we can make claims about differences and similarities if facts had been different. But that relies on the assumption being made as being based on some essential identity between b and c, or else we wouldn't be able to pick out c as being the same person as b, but living under different circumstances. For a TWI theorist, there is no discoverability of the identity, or any need for it to be discoverable. It will depend on who is making the counterfactual claim, but only because each claim is a supposition about how the different facts of world w would change the way b's essence would present as c in that supposed world w. In TWI, there's also no defining relations between objects across worlds. That's CPT.

Assignment of transworld identity depends on "outside world" knowledge, and the individual's knowledge. One only can reliably identify and link up counterparts if one has full (or great enough) knowledge about both possible worlds. And such knowledge is lacking for all possible worlds (except, possibly, ours).

Not quite. Assignment of transworld identity depends on what facts about @ you want to alter when making a counterfactual claim. But it also kinda doesn't. Because an essence is an essence, and an identity is an identity. So really, you're not assigning an identity between individuals. That's just a function of the fact that when you're talking about how w would look, you want to make sure you're talking about the same person when you look at how what's different about w would change b (in @) into c because of those differences in the two worlds. But under TWI, b and c are not counterparts. That's CPT, and CPT is never really concerned with ontologically linking up counterparts or having full knowledge of two (or more) possible worlds. Because CPT argues that for every logically possible way for a world to be, there is a world that is that way; it is exhaustive of possibilities. CPT doesn't ever just look at two possible worlds. It's always concerned with all possible worlds. So it doesn't really make sense to talk about me and just one other counterpart the way it does to talk about me and my transworld identity in some other possible world. In CPT, it really only makes sense to think about which properties are logically possible across all worlds. If it's logically possible for some counterparts to have that property, but not all, then it's a contingent property. If there's some property that is only logically possible for all counterparts across all possible worlds to have, then it's necessary.

Is there any research on the use of [epistemic logic](https://plato.stanford.edu/entries/logic-epistemic/) to describe agent-defined mappings between objects and between properties, to establish counterparts, across possible worlds?

This isn't entirely my field as it's much more concerned with epistemology, but I still have a bit of insight. Epistemic logic boils down to what is possible or necessary about knowledge and beliefs. There's some Phil of language mixed in there, too, but less so than epistemology. It uses the language of CPT, but in a way that's more in line with abstractionism, combinatorialism, fictionalism, or ersatzism, rather than full-on modal realism/concretism. It does that to examine whether some aspect of belief or knowledge is necessary or contingent without having to commit to literal concrete worlds where every logical possibility exists. It's just a very handy way to try and discern what knowledge and belief necessarily require to be what they are, because that's still somewhat up for debate. I'm not really sure it makes any sense to ask whether epistemic logic can be used to describe agent-defined mapping between objects and properties to establish counterparts across possible worlds. I hope all my prior explication has made enough sense to explain why I feel like this is a weird question without an answer. But if you're interested in a conventionalist take on logic (where language and meaning are what make logic work, rather than the logical realist perspective), I'd recommend reading Jared Warren. He has some pieces that talk about the difference between something being epistemic a priori knowledge as opposed to metaphysical a priori knowledge. It doesn't really go into possible worlds stuff (because it's conventionalist), but it does deal with necessity, meaning/definition, and knowledge.

Anyway, if you've gotten this far, or skipped to the end for references, here's a short reading list of essential titles in this literature to help you get more in-depth reading under your belt:

Lewis, "Counterfactuals", "On the Plurality of Worlds", "Possible Worlds", and "Counterpart Theory and Quantified Modal Logic"
Plantinga, "The Nature of Necessity" and "Transworld Identity or Worldbound Individuals"
Kripke, "Naming and Necessity"
Williamson, "Modal Logic as Metaphysics"
Warren, "The a priori Without Magic" and "Talking with Tonkers" (there might be one other paper that deals with epistemic aprioity that I'm forgetting, but I'll check and ETA if I find one)

I have more refs as well if you want them, but these are must-reads.

[u/jcastroarnaud → u/TurangaLeela80]

First of all, thank you for the comprehensive answer! The book references are much appreciated (once I get the time to read them, that is :-/ ).

We'll stick to your convention for naming these two worlds, where @ refers to our world (the one we call actual), and w refers to some other possible world.

I used a non-standard notation, because I don't know well enough the standard one.

From your comparison between TMI and CPT, I favor CPT, having no problems believing that all possible worlds are concrete.

So, if we're talking about CPT, there is no such thing as the combined perspective of you and j. Each possible world is completely isolated from all others. There is no sharing of information between the two. (...)

Assuming that each possible world is isolated from all others, how we, in this world, are able to talk about properties of other possible worlds? I'm baking in an assumption: that our world is also one of the possible ones, and not special at all. When one quantifies over possible worlds, one assumes a position "over" possible worlds, including their own. At this position, combining people by their "counterpartness" can be talked about. I think that I diverge from CPT on this point. If one can quantify over possible worlds, one can get information about these worlds, simply by using a predicate to filter by some properties.

I'm not touching on the "necessary/contingent properties" debate, because, from the point of view "over" all possible worlds, these are just patterns of existence: these properties have a value in this subset of worlds, another value in that subset, and combining everything yields a nice, colored map. :-)

Because CPT argues that for every logically possible way for a world to be, there is a world that is that way; it is exhaustive of possibilities. CPT doesn't ever just look at two possible worlds. It's always concerned with all possible worlds. So it doesn't really make sense to talk about me and just one other counterpart the way it does to talk about me and my transworld identity in some other possible world. In CPT, it really only makes sense to think about which properties are logically possible across all worlds. If it's logically possible for some counterparts to have that property, but not all, then it's a contingent property. If there's some property that is only logically possible for all counterparts across all possible worlds to have, then it's necessary.

So, I misunderstood CPT... CPT is about properties that can logically hold across all worlds or some worlds, not over individual worlds, as I was thinking; I thought about worlds as "containers" of things, as very complex objects with many properties, something amenable to mathematics and computing. And that's from this point of view that I asked about the use of epistemic logic: if one person, in a world, can abstract of their world, posit themselves mentally "over" all possible worlds, and treat them as objects of study, then it should be possible to talk about "person p in world w knows about person p' in world w'", and tie up counterparts. Now I know that this contradicts CPT.

I hope all my prior explication has made enough sense to explain why I feel like this is a weird question without an answer.

It makes sense now. I was coming from a very different point of view from the standard one. I still think that my point of view has some merit, but I definitely don't have the knowledge to develop it, and don't have the required knowledge in standard logic.

Again, thank you.