(Partial cross-posting from the comment section of a post over at Matters of Substance)
Lee Walters has an interesting paper responding to a paper I co-wrote with Joe Salerno on counterfactuals and context last year. One of Lee's objections is that "once the role of context for Lewis is properly understood, strengthening and the rest [of the argument forms normally claimed to be invalid for counterfactuals] are invalid as Lewis himself claimed". This is exactly what we argue is not the case. Once the role of context is properly understood, this is not the result we get. Consider:
(1) If the speed of light hadn't been constant, then the physics books would not have been mistaken.
(1) has two readings. On the false 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 have written the books they actually wrote. So, (1) is true.
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 ones 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, the books are the way they actually are, and so on. To get the true reading of (1), the similarity metric must specify a large number of facts, including facts about the production of physics books.
But now consider (2) below. To evaluate it non-vacuously, we must bracket a number of these prioritized facts.
(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 bracket prioritized facts in order to evaluate (2) non-vacuously, we are in some sense changing the context when we evaluate it. A context in a Stalnakerian sense is most naturally defined partially in terms of the set of facts that the conversationalists hold fixed. One can, of course, insist that this is the wrong notion of context. But the dispute then is a dispute about what the correct notion of a context is. Why isn't moving in the space of ordered worlds and hence bracketing prioritized background facts 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 is just a way of changing the context, given our preferred notion of context. But now, when we keep the context fixed, then strengthening etc turn out valid.
Lee claims that "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."
However, this is not a mistake. Bracketing prioritized facts for the sake of evaluating a counterfactual non-vacuously just is a way of changing the context. Moving in the space of ordered worlds amounts to bracketing prioritized facts and hence amounts to changing the context, given our preferred notion of context. Note that we are not suggesting that there can't be an overall similarity metric. We are simply suggesting that when we move in the space of ordered worlds, the context may shift. So, our approach is not simply a strict conditionals approach.
Later in the paper Lee claims: "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 he takes us to be rejecting the idea that one can bracket prioritized facts in order to evaluate counterfactuals non-vacuously without changing the context at least temporarily.
Lee also says:
"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.
Lee further claims:
"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.
If you had bet heads you would have won
Therefore, if the coin had come up tails, it would have come up heads and
you would have won
We do not reason like this and have no interest in counterfactuals assessed in this way."
Exactly. We do not reason in this way. But what this shows is that we don't keep the background fact that the coin landed heads fixed when we evaluate the conclusion. Of course, we don't. We allow context to shift. Lee's case is not a counterexample to our proposal.
Lee also holds that we mis-evaluate the following counterexample to MP:
If a Republican were to win, then if Reagan were not to win, Anderson would win.
A Republican will win.
So, if Reagan were not to win, Anderson would win.
He thinks that we mistakenly have Lewis assign the truth-value true to the first premise. But this is not a mistake. At the closest worlds at which a Republican wins and Reagan does not win, Anderson wins. So (1) is true. Of course, Lee might insist that we have to evaluate the first premise differently. He might insist that we have to go to the closest world where a Republican wins (the actual) and then to a world where Reagan doesn't win. Carter wins there (as he was second in polls though not republican). But that would defeat the purpose of a contextual semantics that is claimed to capture intuitive truth-values. Our semantics has the advantage over the standard one that it does not entail a rejection of MP.
In conclusion Lee says: "we have no interest in counterfactuals assessed a la Brogaard and Salerno".
As we explain in the paper and in an earlier comment over at Matters of Substance, epistemic contextualists seem to assume it. Moreover, a Stalnakerian notion of a context seems to push us in this direction, as I explained earlier in this post.
Saturday, February 28, 2009
Lee Walters on Counterfactuals and Context
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3 comments:
Thanks Brit. My reply is below. Sometime I write as if addressing you and sometimes as if addressing others about you - apologies.
Charity
Brit, you are right that my reading of your and Joe Salerno’s paper is *very* uncharitable, but that is because I find it hard to provide a charitable reading. In my note I consider two readings
1) That you misunderstand the role of context for Lewis
2) That you are considering an alternative view of context to Lewis’s, which you do not signal as an alternative, (rather it reads as you are simply discussing the standard account), and for which you provide no argument
You have disputed my first reading and suggested my second reading is closer the mark, although you would not put it that way yourself! So if the second reading is correct, I take it your paper says roughly the following
Context determines some set of background facts, F
A>C is true iff C holds in the closest A-worlds where F obtains
When assessing a further counterfactual, B>D, in the same context, B>D is true iff D holds in the closest B-worlds where F obtains
Now you keep referring to the standard account but nowhere signal that the view above is not it, but rather a suggested correction. Indeed you present the first two parts in a paragraph explicitly discussing the standard account. In any case, there is no argument for this account. So on this *very* uncharitable reading, you outline a view which you do not clearly distinguish from the standard view you are discussing and for which you do not argue for.
So I would like to know what the charitable reading of your paper is.
Also, as I note in my paper
Brogaard and Salerno’s reading of Lewis is extremely uncharitable, as on it Lewis misapplies his own theory. Further, once we admit the validity of the argument forms under consideration, Lewis’s account is unmotivated: it was the failure of antecedent strengthening and the rest that led Lewis to see the counterfactual as a variably strict conditional (1973a: 4-19). Indeed Lewis thought counterfactuals must be variably strict conditionals since (Wet Match) highlights not “a conflict between counterfactuals in different contexts, but rather between counterfactuals in a single context” (1973a: 13).
Your Paper
“The standard account of subjunctives – it is alleged – explains why these classical inference rules [antecedent strengthening, contraposition and hypothetical syllogism] fail” and that “The standard account explains our pre-theoretical intuitions about the cited classical inferences”
The standard account is, of course, the Stalnaker-Lewis account. You signal this in footnote 2 “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.”
For your discussion you highlight two salient features of the standard account: 1) counterfactuals with impossible antecedents are vacuously true, 2) closeness is contextually determined.
1 and 2 are true of the standard account but do nothing on their own to show that strengthening and the rest are valid. This comes with your interpretation of how context interacts with closeness. What you say is
“We will talk about the respects in which the A-worlds are relevantly similar to w as the ‘background facts’. Then whether, in w, A counterfactually implies B is a matter of whether B holds in the A-worlds that share (with w) the relevant background facts.”
“On the standard treatment, context determines a set of background facts. But if context must remain fixed when evaluating an argument for validity, the set of contextually determined background facts must remain fixed when evaluating an argument involving subjunctives for validity. And once we fix the background facts when evaluating arguments involving subjunctives for validity, contraposition, antecedent strengthening and hypothetical syllogism come out valid.”
You demonstrate this as follows. Consider the alleged failure of antecedent strengthening
(Wet Match)
If this match had been struck, it would have lit.
Therefore, if this match had been soaked in water overnight and struck, it would have lit.
You think this is fallacious because
If the context for evaluating the true premiss of (Wet Match) requires us to consider only worlds where a typical dry match is struck, then it will be precisely those worlds that figure in our evaluation of the conclusion.
Now all of the above seems to be a discussion of the standard account. Nowhere do you signal any change in focus. As a result I took you to be talking about the standard account. If I was wrong to do so, I would be interested to learn what it was that I missed in your paper that showed you were now considering an alternative to the standard account.
But as a summary of the standard account your paper simply gets it wrong. Talk of “background facts” is not Stalnaker and Lewis’s; their semantics is not predicated on considering worlds that share contextually-determined background facts. For them, context determines a function from the world of evaluation and a proposition (the antecedent) to a set of worlds. The counterfactual being true if the consequent holds in all worlds in this set. So in order not to be guilty of contextual fallacy this function must be held constant. But that is quite consistent variation in the background facts shared with the closest antecedent world, since as the antecedents of the counterfactuals we are considering vary, so too can the output of the selection function
Your argument for the validity of antecedent strengthening is based on the following claim
If the context for evaluating the true premiss of (Wet Match) requires us to consider only worlds where a typical dry match is struck, then it will be precisely those worlds that figure in our evaluation of the conclusion
But the antecedent of this conditional is false in Lewis’s framework. If you think Lewis is mistaken about this, then I would have expected some argument to show this, but you provide none. We can accept that context needs to be held fixed. Lewis has a way of doing it which is not the way you outline in the paper, but if you think yours is the correct way, then what is the argument for it? But you were, I thought, discussing the role of context in the standard account – that is why you highlight that closeness is contextually determined, no?
Further, I don’t see how your blog post helps either. You write
(1) If the speed of light hadn't been constant, then the physics books would not have been mistaken.
“To get the true reading of (1), the similarity metric must specify a large number of facts, including facts about the production of physics books.”
What is true is that, for Lewis to get the true reading of (1), the similarity ordering must be such that the closest A-worlds are worlds where the consequent is true. This might be done via a similarity metric that says something like, ‘the closest worlds are those that do not match actual world in facts about the production of physics books’.
You then say
“But now consider (2) below. To evaluate it non-vacuously, we must bracket a number of these prioritized facts.
(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 bracket prioritized facts in order to evaluate (2) non-vacuously, we are in some sense changing the context when we evaluate it.”
But what has bracketing facts got to do with it? Our toy similarity metric says that the closest worlds share the facts about the production of physics books, not that all worlds do. Some worlds do not share these facts but they are not as close. Now by Lewis’s semantics the closest worlds where the speed of light hadn't been constant but the world had been just the way it actually is in nearly all other respects, will not be worlds that do not match actual world in facts about the production of physics books. But so what? The contextually determined similarity ordering hasn’t changed and this ordering does not require that these facts be shared by all A-Worlds considered in a context.
Of course you can take account of context in the way you suggest, but this has nothing to do Lewisean similarity orderings. If this is your preferred way of doing things where is the argument? (To be fair you do say something over at Matters of Substance about epistemic contextualism, which I have not read as I am an invariantist. But there is no argument in your paper).
I’m not sure how appealing to Stalnaker’s notion of a context is supposed to help either. For Stalnaker, the conversational participants share a common ground or set of presuppositions which narrow down the class of possible worlds that could be actual. Now in considering the series of counterfactuals A>C and (A&B)>C, if we are to hold context fixed we must hold this set of presuppositions fixed. (This isn’t quite right as by making utterances, perceiving new events, learning new information and accepting assertions we change these presuppositions, but we don’t want to say that contexts, in the relevant sense, are so fragile as to be replaced by new contexts every time some such thing happens. As Stalnaker writes “A conversation is a process taking part in an ever-changing context.” (86) So contexts can evolve. I shall ignore this in what follows.) Let us say that amongst these presuppositions is the fact that this match is dry. The actual world, if we are right, is one where the match is dry. Now how are we to assess
(Wet Match)
If this match had been struck, it would have lit.
Therefore, if this match had been soaked in water overnight and struck, it would have lit.
Well we must continue to think that the actual world is one where the match is dry. Ok let’s do that. Now given this fact, the premise of (Wet Match) is true. How about the conclusion? Well given the match is actually dry what would have been the case if it had not been dry and had been struck? Plausibly it would not have lit – the closest worlds where the match is wet and struck are ones where the match does not light.
But wait surely I have not held fixed the fact that the match is dry? Well I have I considered the conclusion of Wet Match the light of this fact. What I didn’t do is insist that in this context any counterfactual world must be one at which this fact obtains. But there is nothing in Stalnaker’s notion of a context that requires I do this as far as I can see. Indeed, being charitable to Stalnaker, given this is not the way he assesses counterfactuals, there is nothing in his notion of a context that requires this. That we take for granted that the match is dry is one thing, that all our counterfactual suppositions must hold this fact fixed is another. If I am wrong, Brogaard and Salerno have not shown why.
Modus Ponens
Brogaard and Salerno consider the following argument
(Election)
(1) If a Republican were to win, then if Reagan were not to win, Anderson would win.
(2) A Republican will win.
(3) So, if Reagan were not to win, Anderson would win.
Brit in her post writes “At the closest worlds at which a Republican wins and Reagan does not win, Anderson wins. So (1) is true.” (2) is true and, in this context, Brit would argue (3) is true also so no problem for modus ponens.
Of course, I agree with the first sentence of the quote. If the logical form of (1) is that of a counterfactual with a conjunctive antecedent, then (1) is true and Lewis gets this right. But then we do not have an instance of modus ponens as (2) is not the antecedent of (1), so no problem.
If, however, (1) wears its logical form on its sleeve, and is a counterfactual with a further counterfactual as its consequent, then (1) is false for Lewis. Brit anticipates this response: “Of course, Lee might insist that we have to evaluate the first premise differently. He might insist that we have to go to the closest world where a Republican wins (the actual) and then to a world where Reagan doesn't win. Carter wins there (as he was second in polls though not republican).” This is, I think, what Lewis would do (in his book Marc Lange talks about iterated counterfactuals, and this is precisely what he does). As such (1) is false, so again no problem with modus ponens.
But Brit counters that this approach “would defeat the purpose of a contextual semantics that is claimed to capture intuitive truth-values”. I agree that there is an intuition that (1) is in fact true and this is a problem for Lewis. But Brit has things no better as she endorses the validity of the inference from (1) and (2) to (3), but no one thinks that (3) is true. Moreover, Lewis does a better job of capturing the intuitive truth values and intuitively valid inferences in a wide range of cases.
(Election) does present a test case for theories of counterfactuals but it is one that challenges all accounts. Brit writes that “Our semantics has the advantage over the standard one that it does not entail a rejection of MP.” But as I have explained, MP does not fail for Lewis. Indeed it cannot since A & A>C is true iff C is true. Both Lewis and Brogaard and Salerno have to explain away our intuitive verdicts on one of (1) to (3) but both validate MP. More generally, there are 3 options here for everyone: deny (1) wears its logical form on its sleeve, reject one of the intuitive truth values or deny MP.
One more thing.
When I note that you count the following argument as valid
If you had bet heads you would have won
Therefore, if the coin had come up tails, it would have come up heads and you would have won
I am not suggesting that this is a counterexample to your proposal. Rather I am pointing out that the way you take account of context, renders intuitively invalid arguments valid, whereas Lewis's does not. Absent any argument that yours is the correct way, this seems to be reason to favour Lewis.
As you note in your paper, you can explain away these intutions. But Lewis does not have to do any explaining away here, so preserves more of what we take to be the pre-theoretical data. So Lewis's approach seems preferable ceteris paribus. You will deny that the ceteris paribus clause holds, but again where is the argument? If there is an argument for your view in your paper, I cannot find it.
Hi Lee, Thank you for these comments. I reply below.
"Brit, you are right that my reading of your and Joe Salerno’s paper is *very* uncharitable, but that is because I find it hard to provide a charitable reading."
Lee, what about the one I just offered you in my post? That's also explicitly in the paper.
"Now you keep referring to the standard account but nowhere signal that the view above is not it, but rather a suggested correction."
I am not sure what else it could be? A restatement of the standard account?
"Indeed you present the first two parts in a paragraph explicitly discussing the standard account. In any case, there is no argument for this account. So on this *very* uncharitable reading, you outline a view which you do not clearly distinguish from the standard view you are discussing and for which you do not argue for."
The point is that certain ways of changing the background facts held fixed by the conversationalists, which on Lewis's account does *not* constitute a context change, does constitute a context change if we are right. And should constitute a context change. Not to take it to be a context change is a contextual fallacy. We say that explicitly in the paper.
"Also, as I note in my paper
Brogaard and Salerno’s reading of Lewis is extremely uncharitable, as on it Lewis misapplies his own theory."
Our paper is not an interpretation of Lewis, ergo, it's not a reading of Lewis, and so it does not make claims about how Lewis applies his own theory. However, we do think that Lewis should consider radical changes of background facts contextual changes.
One reason we talk about the *standard account* rather than Lewis's is that Lewis has already taken a stance on the issue of what counts as a context (i.e., the truth-values of counterfactuals are relative only to an overall ordering of the worlds). Another reason we talk about the standard account rather than Lewis's is that Lewis doesn't accept the limit assumption. But, as we argue in "Remarks on Counterpossibles", once you accept the limit assumption, which there are several good reasons to do, then we get the following account of counterfactuals:
A subjective, 'if it were the case that p, it would be the case that q', is true just when every closest p-world is a q-world, where 'closest' is read as 'most relevantly similar'
This is what we call the 'standard account'. The standard account is silent on the issue of what counts as a context. That is, it is consistent with treatment of the truth-values of counterfactuals as relative only to an overall ordering of worlds, and it is consistent with a treatment of the truth-values of counterfactuals as relative to background facts held fixed by the conversationalists.
However, the standard account, we argue, should treat the arguments valid for conditionals as valid for counterfactuals. In "Remarks on Counterpossible" we use the limit assumption to make this sort of argument. When you accept the limit assumption not every metaphysically possible world is accessible to the base world. So, the strict context-shifting view offered in the Analysis paper becomes natural, as it takes different sets of metaphysically possible worlds to be accessible to the base world in different contexts.
"Further, once we admit the validity of the argument forms under consideration, Lewis’s account is unmotivated: it was the failure of antecedent strengthening and the rest that led Lewis to see the counterfactual as a variably strict conditional (1973a: 4-19). Indeed Lewis thought counterfactuals must be variably strict conditionals since (Wet Match) highlights not “a conflict between counterfactuals in different contexts, but rather between counterfactuals in a single context” (1973a: 13)."
Yes, the proposed change turns Lewis's account into something like a variably strict conditionals account. The main difference between the account we propose and the variably strict conditionals account is that we allow for an overall similarity metric, just like Lewis, but consider changes of background facts changes in context (unlike Lewis). So we can take the determnation of the sphere of worlds relevant for the evaluation of counterfactuals to be a two-step procedure. (1) Fix an overall ordering of the worlds, and (2) Fix the background facts.
"The standard account is, of course, the Stalnaker-Lewis account."
What does "The Stalnaker-Lewis account" mean? There is no such thing as the Stalnaker-Lewis account. Their accounts are very different. The standard account often assumed in the general philosophical literature is this:
A subjective, 'if it were the case that p, it would be the case that q', is true just when every closest p-world is a q-world, where 'closest' is read as 'most relevantly similar'.
But this account is consistent with various different treatments of the notion of a context. We argue for one notion. Lewis argues for a second. Stalnaker argues for a third.
"Fo r your discussion you highlight two salient features of the standard account: 1) counterfactuals with impossible antecedents are vacuously true, 2) closeness is contextually determined.
1 and 2 are true of the standard account but do nothing on their own to show that strengthening and the rest are valid. This comes with your interpretation of how context interacts with closeness."
Yes that's exactly right.
" Now all of the above seems to be a discussion of the standard account. Nowhere do you signal any change in focus. As a result I took you to be talking about the standard account."
We are talking about the standard account but the standard account is not one that requires us to adopt a particular notion of a context.
"But as a summary of the standard account your paper simply gets it wrong. Talk of “background facts” is not Stalnaker and Lewis’s; their semantics is not predicated on considering worlds that share contextually-determined background facts."
It is not a summary of Lewis's account, and it is not a summary of Stalnaker's account. It's not a summary. It's an argument for a different notion of a context given the standard account (as characterized above). If you *assume* Lewis's notion of a context, then of course we "get it wrong". If p, then p.
"If the context for evaluating the true premiss of (Wet Match) requires us to consider only worlds where a typical dry match is struck, then it will be precisely those worlds that figure in our evaluation of the conclusion
But the antecedent of this conditional is false in Lewis’s framework. If you think Lewis is mistaken about this, then I would have expected some argument to show this, but you provide none."
We are not arguing that the arguments are valid in Lewis's framework. If we assume that counterfactuals have their truth-values only relative to an ordering of the worlds, then of course they have their truth-values only relative to an ordering of the worlds. If p, then p. We offer several arguments for thinking the context (understood partially in terms of the background facts held fixed) should be kept fixed when evaluating arguments for validity.
"We can accept that context needs to be held fixed. Lewis has a way of doing it which is not the way you outline in the paper, but if you think yours is the correct way, then what is the argument for it? But you were, I thought, discussing the role of context in the standard account – that is why you highlight that closeness is contextually determined, no?"
The standard account (as formulated above) does not take a stand on what counts as a context. Lewis makes one suggestion. We make another.
" "(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 bracket prioritized facts in order to evaluate (2) non-vacuously, we are in some sense changing the context when we evaluate it.”
But what has bracketing facts got to do with it?"
As I say in the blog post, in order to evaluate (2) non-vacuously (on Lewis's account) we must move to a different sphere of worlds. So, the background facts we held fixed when we evaluated (1) can no longer be held fixed when we evaluate (2). This, and just this (i.e. no longer holding fixed the same background facts) amounts to a change of context. That is what we propose. Bracketing is highly relevant. Moving to a different sphere of worlds is to bracket background facts that were kept fixed earlier in the reasoning. And that, we argue, constitutes a change in context. Lewis, of course, would disagree. But we are not making a claim about what Lewis would or would not agree to. We don't offer textual exegesis.
"Our toy similarity metric says that the closest worlds share the facts about the production of physics books, not that all worlds do. Some worlds do not share these facts but they are not as close. Now by Lewis’s semantics the closest worlds where the speed of light hadn't been constant but the world had been just the way it actually is in nearly all other respects, will not be worlds that do not match actual world in facts about the production of physics books. But so what? The contextually determined similarity ordering hasn’t changed and this ordering does not require that these facts be shared by all A-Worlds considered in a context."
Of course, the overall similarity ordering hasn't changed. It hasn't changed on our account either. If you relativize truth-values only to the overall similarity ordering, then of course what we are saying will come out false. We are proposing that you do not relativize truth-values only to the overall similarty ordering but that you relativize to background facts kept fixed.
"Of course you can take account of context in the way you suggest, but this has nothing to do Lewisean similarity orderings. If this is your preferred way of doing things where is the argument? (To be fair you do say something over at Matters of Substance about epistemic contextualism, which I have not read as I am an invariantist. But there is no argument in your paper)."
The point about epistemic contextualism is in the Analysis paper too (albeit a shorter version of it). Why wouldn't you read about epistemic contextualism because you are an invariantist? You could still appreciate other positions in logical space even if you disagree with them. We offer a number of other arguments in the Analysis paper and a further argument in "Remarks on Counterpossibles".
"What I didn’t do is insist th at in this context any counterfactual world must be one at which this fact obtains. But there is nothing in Stalnaker’s notion of a context that requires I do this as far as I can see. Indeed, being charitable to Stalnaker, given this is not the way he assesses counterfactuals, there is nothing in his notion of a context that requires this. That we take for granted that the match is dry is one thing, that all our counterfactual suppositions must hold this fact fixed is another. If I am wrong, Brogaard and Salerno have not shown why."
I don't know which notion of context you are referring to. The Stalnakerian notion of a context I was referring to is one where certain changes in the background facts held fixed constitue a context change (ala Gillies/von Fintel).
"Of course, I agree with the first sentence of the quote. If the logical form of (1) is that of a counterfactual with a conjunctive antecedent, then (1) is true and Lewis gets this right. But then we do not have an instance of modus ponens as (2) is not the antecedent of (1), so no problem."
Sure there is still a problem if "if p, then if q, then r" is equivalent to "if p & q, then r". You can argue that it's not. But that has counterintuitive consequences, as you yourself admit. Of course, this may be the real problem for Lewis. That he has to reject this equivalence, given his framework. So, either he accepts the equivalence or he rejects it. Either way, there is trouble for his account. That's an independently interesting point. In fact, it is still interesting even if we don't get it 100% right either.
" But Brit counters that this approach “would defeat the purpose of a contextual semantics that is claimed to capture intuitive truth-values”. I agree that there is an intuition that (1) is in fact true and this is a problem for Lewis. But Brit has things no better as she endorses the validity of the inference from (1) and (2) to (3), but no one thinks that (3) is true."
But we do not claim that our semantics captures the intuitive truth-values. We get the intuitive truth-values when the context is changed by the conversationalists.
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