## Monday, February 23, 2009

### Was Lewis wrong or a relativist about counterfactuals?

David Lewis persuasively argued that counterfactuals are sensitive to context. As a consequence, Lewis claimed, counterfactuals don’t obey rules that other types of propositions do, like antecedent strengthening, hypothetical syllogism and contraposition. (From the fact that, were I to strike the match, it would light, it does not follow that, were I to strike the match and were I underwater, it would light.)

Just how is context relevant? Let’s make two distinctions. First, distinguish between a counterfactual sentence, “P > Q”, and a counterfactual proposition, {P > Q}. (I can’t quite figure out how to use the less than sign for some reason, as is typical to denote a proposition, so I’ll use curly brackets.) Second, distinguish between relativism and contextualism. According to relativism, a given proposition {P} might be true in one context, but false in another. (Note: I’m speaking of the proposition; one and the same proposition can be true in one context but false in another.) According to contextualism, a given sentence, “P”, might express one proposition in one context and a different proposition in another context.

I should note two things about these definitions. First, I don’t know if they are the standard uses of the terms “relativist” and “contextualist”. But they sound appropriate to me, so I’ll use them here. Second, relativism and contextualism are independent. One could deny both, accept one but not the other, or accept both.

There are at least two ways context might be relevant to counterfactuals: 1) In determining the truth conditions for a given counterfactual proposition; 2) In determining which counterfactual proposition a given counterfactual sentence asserts.

Suppose that Lewis was a contextualist but not a relativist about counterfactuals. Context determines when a given counterfactual sentence expresses a given counterfactual proposition, but the truth conditions are fixed for counterfactual propositions. Were that Lewis’ view, then he would be wrong about the failure of, say, weakening with respect to counterfactuals. That’s what Berit Brogaard and Joe Solerno argue in “Counterfactuals and Context” (Analysis, 68(1), 2008). After all, when examining an argument for validity, we don’t allow context to shift from premise to premise or between premises and conclusion. Suppose I utter the words “I am hungry,” and you utter the words, “Therefore, I am hungry and tall.” If validity didn’t require us to hold context fixed, we’d have a counterexample to and introduction. Yet all of the supposed counterexamples to, say, antecedent strengthening, involve a shift in context. Moral: If Lewis is a contextualist, he was wrong to think that antecedent strengthening, hypothetical syllogism and contraposition are invalid.

Suppose we hold fixed, then, that Lewis believed these arguments invalid (and that he didn’t hold a false belief!). Then Lewis must have been a relativist about counterfactuals. Or is there some other option?

1. As far as I can see, Lewis was both a contextualist and a relativist about counterfactuals (to use your distinction). Suppose you have determined what counterfactual proposition a certain utterance of a certain counterfactual sentence expresses in a given conversational context. In order to determine whether that proposition is true, there is still the question of which worlds are closer to the actual world and in many places Lewis seems to suggest that different contexts call for different similarity measures (and so possibly different truth-values for the same proposition).

Consider the classic "If Caesar had been in command in Korea, he would have used to the atom bomb" and "If Caesar had been in command in Korea, he would have used catapults". Lewis seemed to think that in some contexts the first one is true and the second false, and in some contexts the second true and the first false (presumably there are also possible contexts in which they could be both true and contexts in which they could be both false) but the reason why he thought that is not that the two sentences above can express different propositions in different contexts but that in different contexts we used different similarity measures to assess the truth-value of the same propositions.

2. Hi there!

I'm not sure I'm fully grasping the background to Brit and Joe's argument.

In particular, I'm not sure about their account of the "standard" view. The view I thought was Lewis's, at least, is the following. First, there's a closeness ordering over worlds. As Gabriele says, it might be a context sensitive matter. But let's focus on one particular context, and so one particular closeness ordering. Then the Lewisian truth conditions (near enough) say that "A>B" is true at w iff all the closest A-worlds to w are B-worlds. The reason antecedent strenthening fails (even holding fixed the closeness ordering) is that the nearest A&B-worlds may be further away than the nearest A-worlds. If so, C might be true at all the latter; but false at all the former. If so, we have "A>C" true at w, but "A&B>C" false at w. No contextual jiggery-pokery needs to be going on to do this.

In Brit and Joe's discussion, the view they describe as "standard" is something like the view that closeness is a matter of holding fixed a range of contextually determined facts. I'm not quite sure how to turn this into an analysis of "x is closer than y to z", which is what is needed to feed into the semantics, but I can sort of see what they mean. Basically, this proposal would divide worlds into two cases (by the lights of w): those that share the relevant facts with w, and those that don't. And if closeness is that coarse-grained, you're not going to get the sort of examples I described above.

But whether or not this deserves the name "the standard view", it's certainly not Lewis's position. His view is that closeness-to-w is a pretty fine-grained relation---something like degrees of similarity to w. And in the "Time's arrow" paper, he gives a pretty detailed recipe about how he wants to flesh that out.

It looks to me that the "sharing contextually relevant facts" view of counterfactuals is more like the "contextually strict conditional" view of counterfactuals, which Lewis (very briefly) mentions and sets aside in the first(?) chapter of "Counterfactuals".

All this is quite compatible with counterfactuals being context-sensitive in some ways---just not in ways that undermine the logic.

I'm not sure whether this makes him a "relativist" in the sense of the post. Fixing the context of utterance of the counterfactual, we can read off from the semantics and the similarity ordering whether the counterfactual is true or false in world w. If you think of a proposition as a function from worlds to truth values, we've thereby fixed a proposition. By varying the context of utterance to one where the relevant similarity relation is different, the semantics may deliver a different proposition (in the sense of function from worlds to truth values). So on this way of reading Lewis, he's a contextualist. Gabriele: do you think that diagnosis is wrong? Or maybe we're using "proposition" in different ways?

3. Thanks, Gabriele and Robbie. I'll see if I can get Brit or Joe on here to defend their argument.

With regard to propositions, now that Robbie has reminded me that a proposition is a function from worlds to truth values, rather than a set of worlds, it seems obvious Lewis was a contextualist (in the sense of the post) and need not be a relativist.

4. Jonathan

If you look at Counterfactuals p.93, it seems that whether the system is relativist or contextualist depends on how the truth conditions are stated:

"My formal statements of truth conditions in section 1.3 took the form P > Q is true at a world i according to a system of spheres \$ if and only if ... To get down to truth at a world simpliciter, I had to remove the relativity at the cost of introducing vagueness by saying that the system of spheres was supposed to be based on comparative similarity." So if the truth conditions are stated in terms of systems of spheres, then relativism. If the truth conditions are stated in terms of comparative similarity of worlds, then you get truth simpliciter, and thus plausibly, contextualism.

5. Hi Jonathan,

I was thinking that the function from worlds to truth values and the sets-of-worlds approach are interchangable: the set of worlds induced by a function being those that are mapped to the true by the function; and the function induced by a set of worlds being one that maps a world to the True iff it is a member of the set (and otherwise, maps a world to the false).

Relativists like Andy Egan think of propositions somewhat differently to this (as mappings from centred worlds to Truth or Falsity). But I can't see as yet any motivation to introduce this machinery to deal with counterfactuals.

all best
R

6. Robbie,

I think I was using 'proposition' in such a way that the position Jon calls relativism could (at least in principle) be true (something along the lines of what some philosophers of language seem to think of propositions). If one interprets 'proposition' as you do (or, in an even more traditional Lewisian fashion, as a set of PWs), then the position Jon calls relativism would seem to be trivially false. By definition, One and the same proposition cannot have different truth-values at the actual world. The actual world is either world to which the function assigns TRUE or it's one to which it assigns FALSE.

7. I'm posting the following comment on behalf of Lee Walters, who had troubles with the word verification (if anyone is experiencing the same problem could you please let me know?)

"You write “David Lewis persuasively argued that counterfactuals are sensitive to context. As a consequence, Lewis claimed, counterfactuals don’t obey rules that other types of propositions do, like antecedent strengthening, hypothetical syllogism and contraposition. (From the fact that, were I to strike the match, it would light, it does not follow that, were I to strike the match and were I underwater, it would light.)”

The two embedded claims here are correct, but the second is not a consequence of the first. The way Lewis takes account of context is in the various similarity relations that we employ to order possible worlds. Once this is fixed, context plays no especial role. Strengthening and the rest fail as a consequence of Lewis’s semantics within a context. Take some ordering that counts worlds where my match is dry as closer than worlds in which my match is wet, then plausibly “if I were to strike my match it would light” is true whereas “if I were to soak my match in water overnight and strike it, it would light” is false. This is not a result of s shift in context but a result of Lewis’s variably-strict semantics. That the worlds we consider in assessing different counterfactuals change, is the result of the different antecedents of those counterfactuals, given a context.

Brogaard and Salerno are correct that we must hold context fixed when assessing arguments, but they are wrong to think Stalnaker and Lewis’s counterexamples to strengthening do not do so. They misconstrue the role of the factual background for Lewis. B&S think that if it is part of the contextually-determined factual background that my match is dry, then this fact is to be held fixed when considering any counterfactual, so that whereas “if I were to soak my match in water overnight and strike it, it would light” comes out as vacuously true. But this is not the role factual background plays for Lewis. The factual background is not a set of facts to be carried around form world to world when assessing counterfactuals – if it were all genuine counterfactuals would be vacuously true. Rather the factual background is/determines the similarity relation; it is this that must be held fixed and it is in the example above. It is no more a shift in context, than is Nathan Salmon’s view that the worlds we consider when we iterate modalities differs from the worlds we consider when we consider uniterated modalities (Salmon rejects transitivity of the accessibility relation so P can be possibly possible but not possible). In both cases, which worlds we consider depends on the proposition under consideration.

For those interested, a slightly longer version of this defence of Lewis can be found in draft form here

http://www.ucl.ac.uk/~uctylwa/papers/Brogaard_and_Salerno.pdf"

8. Hi Ghislain,

I think we need to keep different senses of "relativity" apart. In the compositional semantics for all sorts of things, we often need to know about the truth value of a given sentence relative to a string of parameters (context, world, time, system of spheres, info state, whatever).

To get a notion of truth simpliciter for a sentence, we have to have a way of "deparameterizing"---picking out some privileged string of parameters, such that the sentence is true iff it is true at that privileged string.

The contextualist thought, I believe, is that if we start with an utterance (or sentence type as uttered in a context c), we have all the information we need to deparameterize. Thus, for "There are talking donkeys" as uttered in c to be true simpliciter, we require that the sentence be true wrt c, the world of c, the time of c, the system of spheres fixed by c, the info state of the speaker in c, etc.

Relativism (at least as I understand it) thinks that context alone won't do all the deparameterizing job. So for example, relativism about epistemic modals says that "It might be that p" is true simpliciter, if it true with respect to the c, the world of c, ... and the *information state of the assessor*.... Since the context of utterance doesn't fix who the assessor of the utterance is, there's no longer an unambiguous notion of truth of S as uttered in c.

It looks to me like in the quote you mention, the "relativity" that Lewis is talking about is simply a matter of not yet having filled in the parameters. His proposal of how to deparameterize is to appeal to the comparative similarity relation. To discriminate between contextualism and relativism proper, we'd need to know whether the context of utterance alone fixes the comparative similarity relation, or whether we need to bring in e.g. context of assessment.

(Another way of putting this: you can reformulate Lewis's system in various equivalent ways: giving clauses for counterfactuals relative to a system of spheres, or to a three-place relation with appropriate formal features; or to a "selection function". In each case, the question will be: what's the *correct* system of spheres, relation, or function. And the story is that the right one is that which matches up to relations of objective similarity).

Now, maybe I'm using a technical notion of "relativism" different from that intended in the initial post (though I think they match up, once we spell out, as Egan does, what is to count as the "proposition" expressed by a sentence that has relativistic truth conditions in the sense just given). But I do think we need to give some more content to the notion of relativism than compositional clauses for this or that term being "relative to" a string of parameters---for most everything is "relative" in that sense (e.g. indexicals---compositional clause relative to the context parameter; contingently true sentences---compositional clause relative to a world parameter).

9. This comment has been removed by the author.

10. Hi Gabriele,

Sure.... but I wasn't sure what the *positive* view of the nature of propositions that you had in mind was, such that Lewis ends up counting as a relativist. I didn't see any obstacle to going with the old-fashioned definition, in this particular case.

But I think maybe we can express the view without having to get into issues about what is or isn't a proposition. Here's the thought I was having. Suppose that from the sentence and the context of utterance, we can unambiguously associate a sentence with a function from worlds to truth values. If that's all agreed upon, I'm not seeing any real sense in which the theory is "relativist".

Contrast relativists about knowledge, or epistemic modals, or whatever: they think that sentences as uttered in c don't fix one such function from worlds to truth values; rather, they pick out different such functions relative to different contexts of assessment.

So a more careful wording of my question would be: given that the sentence+context determines such a set of worlds, why should the theory count as relativist?

(Of course, I can imagine *defining* a notion of proposition as e.g. functions from systems of spheres and worlds to truth values. And then we could say that Lewis is a relativist in a sense that sentences are true or false, at a world, only relative to systems of spheres. But then I do think that the burden would be on one in favour of that theory to justify the labeling of that formal beasty a "proposition".)

Does that sound right, or am I misunderstanding your position?

11. We actually don't object to Lewis's account but only to "a common variant of Lewis’s (1973) account".

12. Let me clarify what our position is.

1) Our argument is not an argument against Lewis but an argument against what is thought to be a consequence of a common account of counterfactuals that does allow for context-sensitivity in evaluating conterfactuals (and which does NOT assume an objective similarity metric). The idea behind the common account is that we need to keep certain background assumptions fixed in order to know which worlds are closest or even relevant to the evaluation. So what counts as the correct similarity metric depends on context. Here is an example from Jackson (or at least I think it's Jackson's example).

(A) If I were to jump from the 10th floor of this building, I would die

(B) If I were to jump from the 10th floor of this building, I wouldn't die

(A) and (B) can both be true depending on which background facts we keep fixed. How so? Well, if we suppose that things outside the window are just the way they are now (there is no safety net etc), then the first counterfactual is true (and the second false). If, on the other hand, we take it to be true that if I were to jump from the 10th floor of this building, there would be a safety net, then the second counterfactual is true (and the first false). That is, if we hold facts about my personality fixed, we get one truth-value, and if we hold facts about the outside fixed, then we get a different truth-value.

It's these kinds of examples that force us in the direction of the common account (and hence away from an objective similarity metric).

Now, let's move onto the argument from our Analysis paper.

2) Consider:

If I were to jump from the 10th floor, then I would die
If I were to jump from the 10th floor and the outside is completely different from the way it actually is, I would die

Suppose we keep the outside fixed when evaluating the premise. Then the premise is true. Then when we move onto the conclusion, we could go to a further away world in order to evaluate the conclusion. But we could also take the background fact (viz the fact that the outside is the way it actually is) to be something that is kept fixed in the context. If we do that, then the conclusion is vacuously true.

That is our approach. It's not an objection to us that Lewis doesn't do it this way. And it's not an objection to us that one can do it differently. We need to be told WHY Lewis's way is better than ours.

Contextualists who hold that there are counterfactual constraints on knowledge needn't reject Closure. Consider:

(A) I know I have hands
(B) If I know I have hands, then I know that I am not a handless brain in a vat (via closure)
(C) So, I know that I am not a handless brain in a vat

Suppose that one follows DeRose in taking Sensitivity to be a requirement on knowledge. Then it would seem that we get a counterexample to the above argument.

In the closest worlds in which I have no hands, I do not believe I have hands (true because the closest worlds are worlds where I lost my hands in an accident. So sensitivity is satisfied)

In the closest worlds in which I am a handless brain in a vat, I DO believe I have hands (true because that's what one does in BIV worlds. So sensitivity is not satisfied)

Contextualists like DeRose get out of this predicament by taking the counterexample to involve a context-shift. In evaluating the premise we suppose that the relevant worlds are worlds where I lost my hands in an accident. These are close worlds. So in evaluating the conclusion we should look at the same range of worlds. But I am not a handless brain in a vat at any of those worlds. So it is vacuously true that if I had been a handless brain in a vat, then I wouldn't believe I had hands. So, I know (if only tacitly) that I am not a brain in a vat.

We can widen the relevant range of worlds to include BIV worlds. But if we do that, then it is false that in the closest world in which I have no hands, I do not believe I have hands (this is false because some of the closest worlds now are worlds where I don't have hands but where it looks like I do because I am a BIV). So, I do not know that I have hands.

So our approach has an advantage. If we do not take this approach, then we cannot easily make the DeRose move when responding to the skeptic.

13. Brit, I don't think that's right. For starters, what you actually claim - in a footnote - is that "For simplicity we will deal only with a common variant of Lewis’s (1973) account.
Stalnaker’s (1968) is similar, and the differences will not be relevant here." I took it the simplification was the limit assumption

Also what you say in general terms about context-sensitivity carries straight over to Lewis. that is, Lewis thinks the similarity ordering is sensitive to context. Indeed he explictly discusses backtracking interpretations in his 1979 (maybe here he underplays there importance). He also discusses the role of context in his 1981 (p.78 of the reprint), 1979 (p.53 of reprint), his 1973 paper (p.6 of reprint) and his book.

Now above and in your paper you talk about holding facts fixed, but this is only one-way to acheive the context-sensitivity and it is not a part of the standard account. This is, I guess, what Tichy does, but his account is not standard and he knows that strengthening and the rest aren't valid.

You start your paper with "We discuss what we take to be a contextual fallacy in the standard understanding of the logic of counterfactuals." and "The standard account of subjunctives – it is alleged – explains why these classical inference rules fail."

But it is the Stalnaker-Lewis semantics that is the standard account and which explains why these inference patterns fail. People like Tichy who have contetxtually strict accounts of the counterfactual don't explain why these fail because they do not on their account.

Also when discussing the standard account you highlight two features of it 1)that counterfactuals with impossible
antecedents are vacuously true and 2) closeness is contextually determined, since which worlds are relevantly similar to a given world is a contextual matter. Lewis endorses both of these.

You end your paper saying "it would be very odd if arguments with subjunctives were an exception to the rule that context remains fixed when determining validity. If it remains fixed, then contrary to what is commonly believed, contraposition, antecedent strengthening and hypothetical syllogism for
subjunctive conditionals are valid inference rules after all." And this seems to be a conlusion of wider import than that you are claiming now.

The account that you say was your focus in your paper is not one that anybody thinks is the standard account, and the standard account is not one that is touched by your paper for the reasons Robbie and I gave.

Of course, you are correct to claim that "That is our approach. It's not an objection to us that Lewis doesn't do it this way. And it's not an objection to us that one can do it differently. We need to be told WHY Lewis's way is better than ours." But in your paper you do not argue for your approach, but rather are highlighting what you take to be a contextual fallacy in the standard account. these are two very different projects.

14. Hi Brit!

Is the idea this:

(i) everyone (including Lewis) needs to allow contextual variation (in Lewis's case, in the similarity relation) in order to take into account backtrackers.

(ii) given this, there's no motivation to stop there---you can explain the other phenomena in some contextualist way.

(iii) if you're explaining the standard data in this way, you might as well abandon all talk of similarity orderings, and just work with a contextually strict conditional analysis. (I'm thinking of Gillies/von Fintel style elaborations as one way of working this out).

(iv) once we've reached that point, by the standard holding-context-fixed account of validity, the various famous "invalidities" of Lewis's logic are no longer invalid.

If that's right, then I see the project. But I do think you can't really blame people for reading the paper as targetting sonething in the Lewisian tradition, rather than something he explicitly discusses and sets aside. E.g. while I'm familiar with people thinking that antecedent strengthening fails *for the natural language conditional*, or *on the Lewis-Stalnaker account*, I haven't come across anyone thinking it fails *on a contextually strict conditional account*. But maybe that's my poor reading! And maybe you meant to target the claim about natural language conditionals explicitly, independently of theoretical glosses.

On that point, I read the footnote you cite exactly as Lee did---as about the limit assumption. Sorry if that was a mistake, but can you see where we were coming from?

15. Ok, I repeated Lee a bit more than I meant too! Sorry... typing in an airport departure lounge.

16. Try not to miss your plane while blogging this time!

17. Robbie,

I agree--if propositions are functions from pairs of worlds and contexts of utterance to truth-values (and it's a big 'if' as far as I am concerned), relativism in Jon's sense is patently false. However, my impression is that Lewis's use of 'context' was often ambiguous between context of utterance and context of assessment (so he was ambiguous about propositions being functions from worlds and contexts of utterance to truth-values and being functions from worlds, contexts of utterance and contexts of assessment to truth-values).
Suppose, for example, you utter one of the counterfactuals about Caesar in Korea. In that context of utterance, it is pretty clear "what you meant" (so some would say it is pretty clear what proposition the sentence you uttered expresses in some pre-theoretical sense of 'proposition', which is definitely not reflected by neither of the above conceptions of 'proposition') but we still can see that the proposition expressed by that particular utterance (in the sense of "what you meant") can be true or false depending on which similarity metric we adopt and that this metric might not be entirely determined by the context of utterance. In fact, we could look at the sentence you uttered in the context and still switch between the two similarity metrics and see that "what you meant" is true on one metric and false on another because in one case we keep fixed, say, the ruthlessness of Caesar, in the other his love for catapults (it's a bit like looking at the that rabbit-goose drawing). Btw, I think that it is this characteristic of counterfactuals that make non-philosophers so often agnostic about their having a definite truth-value in the first place. So if propositions are functions from ordered n-tuples whose first element is a world and whose co-domain is {true, false}, the disagreement between contextualists and relativists could still be what other arguments the function takes and, from what Lewis says, it is not entirely clear to me whether contexts of utterance are all one need in the case of counterfactuals.

Sorry this is probably too quick and unclear but I can try to make it clearer if you are interested (btw, I hope you've not missed your plane! ;-))

18. Lee:
Thanks, this is very interesting. I guess the main aim of our paper was to counter the common claim that a number of arguments which are valid for conditionals are invalid for counterfactuals. And I believe we (among others) have shown that this claim is incorrect. There is a tendency among philosophers to take counterfactual theories to entail the invalidity of these arguments. It was that minor irritant that inspired the paper. I believe we were right to claim that there is a contextual fallacy here, especially if the alternative approach is preferable. In my previous post I offered a reason to favor our approach. In any event, we do, of course, criticize Lewis but we never claimed that our approach was also Lewis's or that there is no other approach to counterfactuals than the one we propose.

Robbie:
Actually, it's not clear that (A) and (B) are backtrackers, given their future-directedness. "If I had jumped ..." vs. "If I were to jump ...". But never mind. I suppose the point can be made even w backtrackers. As for the project you outline, yes I think I can submit to that. Admittedly, your outline is clearer than anything I have ever put into print. So I owe you a mention if I ever become this clear. As for your second point, I think I responded to it in my reply to Lee.

19. Hi Gabriele,

I think I agree with what you said. One caveat: I think the case is pretty complex. E.g. some people seem to read the antecedent "Caesar fought in Korea" as "Caesar fought in the 20C US war in Korea". But a literal reading might just invoke a situation where Caesar fought in the Korean peninsula (presumably the closest such situation would be one that took place back in the day, when catapults but not atomic bombs were available). Vacillation between these two might explain divergent reactions on the basis of ambiguity in the antecedent rather than anything to do with the counterfactual.

There's also the issue about what someone has to be like to count as Caesar (or Caesar's counterpart) in a non-actual situation. I'm inclined to think that flexibility of the counterpart relation, rather than flexibility of the similarity metric, may explain some divergent reactions to the counterfactual (think of a counterpart relation that emphasizes similarity wrt knowledge and tactics, vs. one that emphasizes general tendancies; one gives you Caesar fighting in the Korean war with ancient strategies at his disposal, the other gives you Caesar with the training of a modern general). Again, this to locate our divergent reactions to the counterfactual in issues about the content of the antecedent rather than anything to do with the flexibility in the counterfactual similarity ordering.

The last thing that occurs to me about the case: aside from context-dependence (whether of contextualist and relativist form) there's also the possibility of indeterminacy in the similarity relation. And then we might expect that on one precisification of the indeterminacy, the counterfactual is true, and on another, it's false.

None of this is meant to be an objection to the view that relativism (or indeed, contextualism) is a potential explainer of reactions to the cases: it's just that I think that there's quite a lot going on in the case, so it'll be some work to sort out clean data supporting a relativistic interpretation.

I think this is pretty important, because on the sort of project Lewis outlines in "time's arrow", the room for context sensitivity is pretty limited: maybe restricted to stuff like (i) what the relative weights we should give to similarity wrt particular fact vs. similarity in respect of laws; (ii) what counts as a "large divergence" in either; (iii) whether or not approximate but not perfect similarity counts for anything. It's hard to fit in stuff like "holding fixed F" as a contextually fixed determiner of the similarity relation, given that specific view.

Of course, Lewis's particular way of cashing out the similarity relation isn't sacrosanct, so maybe the right upshot is that the best account of closeness to feed into Lewisian semantics isn't Lewis's own. (Backtrackers already pose a problem for it; and maybe Brit's cases or indeed the Caesar case provide more challenges to it). But I'm not pessimistic as yet, given the range of resources described above.

20. Hi Brit,

I take the point about (A) and (B) not being backtrackers. My initial reaction, on behalf of the Lewisian, is that (A) should be true on a standard metric, and (B) should be true on whatever metric is appropriate to backtrackers (notice that the priming you mention for (B) does seem easily and best put as a backtracker: if you were to jump out, there would have to have been a net there).

So I think if the Lewisian can deal with backtrackers, they've got a good chance of dealing with this case. But I don't know what they do and should say about backtrackers, so it's kinda difficult to evaluate.

21. This is an independently interesting issue. I agree that "If I had jumped, then I would have been alive and well", on it's true reading, is a backtracker (primer: if I had jumped, there would have been a net there). But I wonder if the same holds for "if I were to jump, then I would be alive and well" or "should I jump, then I would be alive and well" (primer: should I jump in the future, then there would be a net"). I wonder if future subjunctives can be backtrackers. They don't seem to require any backtracking.

Here is a different case: suppose the set-up is one where there are nets outside on Mondays, Wednesdays and Fridays only. Now consider:

(A) If I were to jump, I probably would die
(b) If I were to jump, I probably wouldn't die.

If we keep the background fact fixed that I am most likely to be in the building on a Monday, then (A) is true.

If we keep the background fact fixed that I am a prudent person who would be unlikely to jump unless there is a net, then (B) is true.

No backtracking it seems.

Anyhow, I would like to know how Lewisians propose to deal with backtrackers.

22. I meant to say "if we keep the background fact fixed that I am most likely to be in the building on a Tuesday, then (A) is true"

23. Lee (and Robbie): I have now had a chance to read the paper you (Lee) linked to above. I see where you are coming from but I also think you're misinterpreting us. Given one common conception of context, we are right. Let me explain. Consider:

(1) If the speed of light hadn't been constant, then the physics books would have been mistaken.

(1) has two readings. On the true reading, the physics books would have been the way they actually are. So, the closest worlds are worlds where the speed of light is not constant but where the physics books are just the way they actually are, and hence wrong. On the other reading, even if the speed of light hadn't been constant, the physicists would have been as intelligent as they actually are. So they wouldn't have had the evidence they actually have, and they wouldn't write books that are the way the actual books are. So, (1) is false.

The problem, of course, is that a similarity metric that just prioritizes facts about the intelligence of physicists is compatible with the closest worlds being those where the speed of light isn't constant but where everything else is as close as possible to the way it actually is. So physicists have the same intelligence and the same evidence as they actually do, and the books are the way they actually are, and so on. To get the false reading of (1), we need to specify both which facts are prioritized and which facts are not prioritized in the similarity metric. In other words, it seems that to evaluate counterfactuals the context needs to specify a whole bunch of facts about how the worlds are ordered.

But now consider (2). To evaluate it non-vacuously, we have to give up on a whole bunch of prioritized facts in order for the antecedent to be true.

(2) If the speed of light hadn't been constant but the world had been just the way it actually is in nearly all other respects, then the physics books would not have been mistaken.

Since we have to give up on a whole bunch of prioritized fact to evaluate (2) non-vacuously, we are in some sense changing the context. A context in the Stalnakerian sense is most naturally taken to be defined partially in terms of the set of facts that the conversationalists take for granted. You can, of course, insist that we are not changing the context. But the dispute then is a dispute about whether moving further away in the the space of ordered worlds and hence giving up on prioritized facts is kind of context change. Why isn't giving up on prioritized facts (i.e. moving further away in the space of ordered worlds) just a way of changing the context? After all, to evaluate (2) non-vacuously we have to suppose (for the sake of evaluation) that these prioritized facts do not obtain. That seems to be the same as changing the context.

Also, your reading of our proposal is uncharitable, in particular the following claims:

"Brogaard and Salerno (2008) argue that once context is held fixed, Stalnaker-Lewis semantics for counterfactuals validates contraposition, strengthening the antecedent and hypothetical syllogism, rests on a contextual fallacy"

"Brogaard and Salerno’s reading of Lewis is extremely uncharitable, as on it Lewis
misapplies his own theory"

"Brogaard and Salerno’s mistake then, is to move from the fact that “the set of contextually determined background facts must remain fixed” (42) to the thought that on Lewis’s semantics these facts must hold at all the worlds relevant to assessing
counterfactuals within that context."

The claims you make about us are uncharitable and in some cases mistaken. We do not claim that Lewis interprets or misinterprets his own semantics. We are saying that Lewis and others should take *giving up prioritized facts for the sake of evaluating a counterfactual non-vacuously* to be a way of changing the context. We are saying that moving further away in the space of ordered worlds amounts to giving up prioritized facts and hence amounts to changing the context. We are not saying that Lewis misinterprets his own stuff.

Later in the paper you say: "We could, however, consider Brogaard and Salerno not as drawing out a consequence of holding context fixed within Lewis’s semantics, but rather as rejecting Stalnaker-Lewis semantics."

This is a charitable (and somewhat correct) reading of our paper, at least if you take us to be rejecting the idea that one can give up prioritized facts in order to evaluate counterfactuals non-vacuously without changing the context at least temporarily.

You also say:

"the conclusion of (Wet Match) concerns what would have been the case, if, contrary to fact, the match had been soaked overnight. To hold fixed the fact
that it has not been soaked overnight, is to miss what it is that we are concerned with."

Not true. We allow for context-shifts in our semantics. So, we don't miss "what it is we are concerned with". The conclusion obviously triggers a shift of context.

You also say:

"the following argument is valid for Brogaard and Salerno since one of the background
facts held fixed when considering the premiss, is that the coin landed heads.