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Delia Graff Fara (Princeton) is presenting "Counterparts within Actuality." The two invited commentators for her paper are Ted Sider (Rutgers) and Joseph Melia (Leeds University).
Posted by tnadelhoffer on May 13, 2007 at 11:56 PM in Metaphysics | Permalink
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A few thoughts. Sorry if they're cryptic or vague...
1. What about defining transworld entities as certain counterpart-interrelated classes of possible individuals (though not maximal, given the intransitivity of the counterpart relation), and then doing standard kripke semantics with the transworld entities? You'd want to have an intransitive accessibility relation that would somehow match the intransitivity of the counterpart relation. One question is how to get that to work. Another issue is that you wouldn't have contingent identity or contingent distinctness this way. But maybe contingent identity and distinctness are bad ideas in the first place. I'm inclined to think that contingent identity is a bad idea (I don't mean the kind you get from multiple counterpart relations --- that I'm happy with) but I'd rather keep contingent distinctness if I can. But the argument at the end of my comments suggests that it's hard to do that if you add an actuality operator.
2. I just noticed that ACT seems not to care about accessibility. Forget about counterpart theory, just think intuitively: the following two sentences seem equivalent:
<> <> Ex(Gx & ACT (Fx) )
Ex (Fx & <> <> Gx)
(If you're worried about contingent existence, consider instead these two sentences:
<> <> Ex(Gx & ACT [Ey (y=x & Fx)])
Ex (Fx & <> <> (Gx & Ey y=x))
So it looks like, when an occurrence of ACT occurs inside a number of iterated modal operators, it doesn't matter whether the actual world is accessible from the world of evaluation. I started, then, wondering about what this means for a counterpart-theoretic account of ACT. The standard clause for ACT, namely: translating ACT PHI(y) at w as: "there exists at @ a counterpart, x, of y, such that PHI(x)", is in essence requiring that the actual world be accessible from the world of evaluation, which is wrong as we just saw. So how should the clause for translating ACT be changed? You can't replace the reference to the counterpart relation with a reference to the ancestral of the counterpart relation -- maybe *every* possible individual stands in the ancestral of the counterpart relation to every other.
3. A thought about Melia's idea of "resetting". What you want to do is "reset" if a variable is "originally introduced in the actual world" (as in: Ex <> Act Fx, for example.) You don't reset if the variable is introduced in some other world (as in: <> Ex ACT Fx, for example.) We then face Williamson's point, that the following are intuitively equivalent:
Ex <> ACT Fx
Ex <> Ey(y=x & ACT Fy)
Now, you might try to respond to Williamson by saying that we don't just reset if the variable "started" in the actual world; we also reset if the variable can be "traced back" to a variable that started in the actual world, via chains of "="s. But (and here's the point): the chain might not be via "="s; other predicates have the same effect. e.g. "is a member of all the same sets as".
Ted Sider |
May 15, 2007 at 07:57 PM
Notice that there seems to be an analogous problem for standard modal semantics with the familiar clauses for ACT. On that semantics, “Fx & <>ACT~Fx”, is always false. So, “DGF is a philosopher but she could actually have been a mathematician (and not a philosopher)” is false. But so is, “DGF was born in 1970 but [given haecceitism] she might actually have been born sometime after 1970.”
Joe Salerno |
May 16, 2007 at 11:19 AM
Interesting points and I'm not sure what to say.
On your 3. I agree that those examples show that the when and the where of resetting looks very difficult – it’s not clear how a nice recursive definition is going to go.
Incidentally, on Williamson’s objection, are we being asked to find the *formal* sentences
Ex <> ACT Fx
Ex <> Ey(y=x & ACT Fy)
*intuitively* having the same truth-value? When I put the second in English I find it hard to parse. Or is there a kind of intuition for those trained in logic (which I kind of see but am unsure whether I am duty-bound to respect) that says it’s meant to be a constraint on the logical formalism of QML+ACT that the two should have the same truth-value?
I’m not sure why you’re so pessimistic. Those final examples, involving actually distinct things that are possibly identical, look like everyone’s problem. In fact, they even make me wonder whether we should always expect a clear translation or whether there are contextual features that prompt me to reset the value one way or the other. Given
Ex <> Ey(y=x & ACT Fy)
I do see some pressure to reset the value of the variable y under the ACT back to the value of the initial x. But given
<>Ex (x = a & x = b & ACT Hx)
I’m at a loss about what to say. I am at a loss even at the level of the modal sentences of English that we want to analyse. I’m told that Ted is Happy, and asked whether it’s possible that there be something identical to Ted which is actually happy. I want to say yes – because Ted *is* happy. I’m told that Ted is Happy and Joe is Sad, and I’m asked whether it’s possible that there be something identical to both Ted and Joe which is actually Happy. Suppose I allow that the two could be identical – they’re so similar after all – but when asked what would be actually true of this thing, what properties could fill in the H of the above, I don’t feel there’s a right answer. Is it Ted’s properties that it actually has or Joe’s? I can see that, if we had been particularly focussing on Ted, we might want to reset back to Ted. If we had been particularly focussing on Joe, we might want to reset to Joe. But just given the bare sentence I’m left wanting to be thrown a bone here – alone, neither answer seems justified or right.
What the counterpart theorist can offer is various couterpart theoretic sentences of the relevant English sentences making it explicit which of the two actual objects one should ‘return’ to. So perhaps the counterpart theorist may say that, as far as the English sentences go, it’s not clear which thought exactly we have in mind. (For what it’s worth, I’m reminded of the situation where we have subscripted actually operators and diamonds to deal with non-rigid uses of actually – the English isn’t clear which kind of actually operator we have in mind, or which ‘possiblity’ we’re being sent back to by an Actually operator. But you can make these kinds of distinctions with quantification over worlds.) So could he turn this around in his favour?
In part, these questions are tied to the fact that I’m not sure whether many of the objections here are an objection to counterpart theory itself, as a versatile way of disambiguating and making precise various intuitive modal claims of English, or whether the obejctions really focus on Lewis’ original recursive translation procedure – showing that there’s no easy way of translating between QML+ACT and counterpart theory. Since there are already delicate issues about how we translate from English to QML and QML+ACT, it’s pehaps no surprise that we should sometimes have a hard time translating from English to counterpart theory. But if the focus is really on the relationship between two more formal systems, and whether there’s a recursive translation procedure between the two – I’m a little less certain what the upshot for counterpart theory is if the two systems turn out to be incommensurable at a certain level. Would we expect modalist systems and counterpart theoretic systems to be intertranslatable?
Joseph Melia |
May 16, 2007 at 01:21 PM
I am hardly a fan of counterpart-theoretic analyses of modality, but I
wonder whether Lewis has resources to deal with the problem posed by
Prof. Graff Fara that haven't been put on the table.
Is it entirely ruled out, for instance, that Lewis leave the
translation clause for ACT alone, and instead appeal to
context-sensitive constraints on the counterpart relation? As
Prof. Graff Fara notes, Lewis held that which counterpart relation was
operative was a context sensitive matter. Lewis might claim in this
mood that use of ACT imposes restrictions on the counterpart relation.
In particular, a use of ACT imposes the constraint that nothing
numerically distinct from any actual thing is "similar enough" to be
its counterpart in the actual world. This expedient introduces a
non-qualitative element into the explanation of the counterpart
relation; but I think that was always in the cards, given the role
Lewis allows for match of origins, spatial relations to other things,
or cultural role in counterparthood, e.g. in (1986, p. 8). So, when
we wonder whether DGF might have been an 18er, we use a relatively
liberal counterpart relation; when we wonder whether DGF might have
ACT been an 18er, or is ACT an 18er, we use a relatively restricted
counterpart relation. So, Lewis can affirm in one breath that DGF
might have been an 18er. Taking a pause, he may then deny in the
next breath that it's possible that DGF ACT be an 18er.
The envisioned response doesn't come near the additional problem of
the divergent interpretations of apparently equivalent sentences noted
by Prof. Sider. But, as also noted by Sider, there is some reason to
suspect that counterpart theory was already committed to
distinguishing such sentences.
May 16, 2007 at 04:59 PM
Forgive the following garbled thoughts.
Once we grant the a priori possibility of "duplicate" worlds (D-worlds), e.g. worlds where the universe consists of two qualitatively identical halves, and that I might have existed in a D-world, problems arise for Lewis's counterpat theory (LCT) even if he does not relax the counterpart relation to allow actual objects to have many actual counterparts. For then it is a priori true that there is a world in which I have two counterparts.
Then, (1) and (2) are true in LCT (assuming that names get treated as free individual variables), but (3) is false:
(1) (x)(x=m --> <>Dxm)
(1) affirms that everything identical with me might have been in a different half of the universe than me. (1) is counterintuitive, but so is the result that (1) and (2) do not entail (3).
Lewis does not get out of the woods by disallowing names into his logic, for we would still get (4) coming true and (5) false:
(4) ExAy(y=x --> <>Dyx)
(4) is counterintutive, as is the result tha (4) does not entail (5).
Does any of this make sense?
Murali Ramachandran |
May 18, 2007 at 10:49 AM
Nice point - would this be a problem for Lewis’ original theory, since he allows that one thing can have two counterparts at a world?
But is the upshot, then, not that there’s particularly a problem with the actually operator, but that there’s a problem with how identity gets treated? In some contexts – when we translate a sentence and are given that x = m, we may want to ensure that x and m have the same counterparts at other worlds. That’s not to muck about with the counterpart relation itself, it’s just to translate the modal sentence so that x and m have the same counterpart.
That is, though, to allow flexibility in Lewis’ original translation scheme – and maybe in a similar way to the ways suggested to deal with the actually operator: when we have an identity holding between two different variables, there are issues as to, when we translate the sentence into counterpart theory, we ensure that the counterparts of identical things are identical, or we allow them to come apart. I suppose one could go two ways – this just shows that counterpart theory is doomed, independently of all the difficulties with the actually operator. Or we might claim that the suggestions being made to deal with the Actually operator are not so very ad hoc – because they had to be made to deal with these kinds of problem.
Joseph Melia |
May 18, 2007 at 02:59 PM
I apologise if the following thoughts do not focus on Delia's worries about actuality, but I do think there are more general problems with counterpart theory which arise from the allowing an object to have more than one counterpart at a world.
While LCT has the problem I mentioned in the previous note, Forbes' CCT has the undesirable consequence that (6) and (7)come out true (given the existence of D-worlds):
(6) <>(m=m & ¬(m=m))
(7) affirms: I and myself might have existed in different halves of the universe.
And my earlier versions of counterpart theory have the consequence that I might not have lived in the *same* half of the universe as myself (<>¬Smm).
These problems diasappear if one disallows objects having more than one counterpart at *any* world (not just the actual). But it is difficult to see how such a restriction could be justified if the counterpart relation is grounded on comparative similarity alone.
The paper at the url below presents a counterpart theory where the counterpart relation is not grounded on similarity but is 'stipulated' in Kripke's sense.
Thoughts welcome. And I am really sorry for hijacking the discussion.
Murali Ramachandran |
May 20, 2007 at 03:34 AM
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