1. Counterfactual Sentences and Context
One reason to think counterfactuals are closely bound up with the laws of nature is that the laws seem to hold ‘no matter what’ or ‘come what may’.Footnote 1 Lange takes this to be an essential feature of the laws and relies on it to ground the laws of nature. Lange's central principle, Nomic Preservation, is as follows:
(NP) m is a law if and only if in any conversational context, and for any p is relevant as a counterfactual antecedent in that context and logically consistent with all of the laws (taken together), the proposition expressed by “
” is true. (Lange Reference Lange2009, 15)Footnote 2
Lange takes this principle to determine what the laws are at a world w. Thus, consider a candidate collection of laws, 
, at w. The basic idea of NP is that each member deserves to be in the collection if and only if every counterfactual is true that has a nomically contingent antecedent (relative to the candidate laws) and a nomically necessary consequent (again, relative to n) in every context of w. If so, then the collection n has earned its status of lawhood, and statements m 1, m 2, … are each laws of w. Lange's view is particularly striking because these counterfactuals are not merely epistemically or heuristically useful for identifying the laws of nature; they ontologically ground the laws of nature. And, according to Lange, the counterfactuals are, in turn, ontologically grounded in primitive counterfacts.
1.1. Semantics and Context
According to a traditional semantic picture, sentence types in contexts express propositions. For example, the sentence “You are wearing an orange shirt,” in a context in which Lee is the addressee, expresses the proposition that Lee is wearing an orange shirt. The very same sentence can express different propositions in different contexts. For example, the same sentence would express a proposition about Jones in a context in which Jones is the addressee. A sentence in a context is true relative to a world, just in case the proposition expressed by the sentence in the context is true relative to that world.Footnote 3
When we apply this standard picture to counterfactuals, we do not just need to interpret standard contextually sensitive terms, such as indexicals (“I,” “you,” “here,” etc.); we also need to interpret “if” and “would have,” which require additional context sensitivity. Recall the famous counterfactuals about what Caesar would have done in Korea. Depending on the context, either Caesar would have used the atom bomb or Caesar would have used catapults. There is a great deal of debate about how this added layer of counterfactual context sensitivity affects the propositions expressed by counterfactual sentences.Footnote 4 For Robert Stalnaker and David Lewis, the counterfactual sentence “If you had worn an orange shirt, gravity would have held,” in a context in which Jones is the addressee, expresses (very roughly) the proposition that the closest worlds in which Jones wears an orange shirt are worlds in which gravity holds.Footnote 5 Whether such a proposition is true or false depends on what the closest orange-shirt worlds are like, as well as which worlds are closest for that context.Footnote 6 This is how they can accommodate our changing intuitions about what Caesar would have done in Korea. The context changes which worlds are closest: in one context, the catapult world is closer than the atom bomb; in others, vice versa.
Lange does not want to commit himself to a specific view of counterfactual semantics, but he does want to accommodate the fact that context can change the truth-values of some counterfactual sentences. For reference, we have the counterfactual sentence:
(1) “If you had worn an orange shirt, gravity would have held.”
In a context in which Jones is the addressee, this expresses the counterfactual proposition that:
(2) If Jones had worn an orange shirt, gravity would have held.
Since 1 has the form of NP, Lange insists that it is true in every context, even if that context varies due to counterfactual considerations.Footnote 7 For instance, the truth-value of sentence 1 should remain the same, even as the context shifts from the context of a physics classroom, to the context of an offhand conversation, to the context of a legal trial. But, sentences in different contexts can pick out different propositions, so we must proceed carefully. For instance, it is only because we have chosen a context in which Jones is the addressee of sentence 1 that it expresses 2. In a different context, in which Lee is the addressee, 1 expresses the different counterfactual proposition that:
(3) If Lee had worn an orange shirt, gravity would have held.
So far, Lange is right: sentence 1 is true in the few contexts we have tested. It does not matter who the addressee of sentence 1 is. The sentence, in that context (as well as the corresponding proposition) is true. Surely, if Jones, Lee, Lopez, Cohen, or anyone else had worn an orange shirt, gravity would have held. Of course, there are many ways to vary the context, and below I argue that not all of them yield such favorable results.
1.2. The Problem
I argue that not all counterfactual sentences with law-statement consequents are true in every context, which is what Lange's NP requires. Lange (Reference Lange2009, 197) offers an example in which a patient is accidentally injected with a syringe that a doctor mistakenly believes to contain arsenic. Assume, for the sake of the example, that there are “arsenic laws,” which have as a consequence that if a normal human being takes arsenic, that person dies. Since the syringe does not, in fact, contain arsenic, the patient lives. The doctor, still believing the patient was injected with arsenic, is thrilled when the patient survives and prepares to write up this surprising result for a journal. The nurse later discovers that the patient was not actually injected with arsenic, and says,
(4) “If the doctor had given the patient arsenic, the doctor would be famous for discovering that arsenic does not always kill human beings.”
Prima facie, the counterfactual sentence 4 is a counterexample to NP since the sentence, in this context, is true, but the antecedent is logically consistent with all of the laws (of physiology, etc.) taken together, while the consequent is a violation of the laws. More technically, this counterexample has the form 
, where p is the contingent fact that the doctor injects the patient with arsenic, and m is entailed by the arsenic laws. Lange's principle NP requires that 
is true in any context. But, if we posit that p is contingent—not a vacuous antecedent, such as ‘if squares were circles’—then 
follows from NP, and 4 is indeed a counterexample. Lange (Reference Lange2009, 24) agrees with the formal point “we can demand not only that 
, but also that 
,” but Lange argues that sentence 4 is not a counterexample because, “in this conversational context, the counterfactual's antecedent is implicitly ‘Had the syringe used to inject the patient been filled with arsenic and the patient lived,’ which is logically inconsistent with the laws, so the truth of this counterfactual is no threat to NP” (197; italics added).
Thus, properly understood, 4 is really, or implicitly,
(5) “If the doctor had given the patient arsenic and the patient had lived, then the doctor would be famous for discovering that arsenic does not always kill human beings.”
But, it is difficult to see what Lange could mean by this. Lange cannot have thought that sentence 4 is really a different sentence, such as 5. While context can disambiguate lexical or structural features of sentences, as in “visiting relatives can be annoying,” it cannot change one clause such as “if the doctor had given the patient arsenic” into a radically different one that conjoins another clause, such as “if the doctor had given the patient arsenic and the patient had lived.” And recall that the context sensitivity specific to counterfactuals, as in “If Caesar had fought in Korea,” allows a single sentence to designate different propositions, depending on the context of utterance. It does not allow one sentence to somehow be a different sentence. But what, then, are we to make of Lange's claim?
One option that suggests itself is that 4 expresses the proposition that:
(5*) If the doctor had given the patient arsenic and the patient had lived, then the doctor would be famous for discovering that arsenic does not always kill human beings.
Indeed, this seems plausible. Semantic theories can be quite complicated, and propositions need not mirror the surface structure of the sentences that express them.Footnote 8 For instance, Lewis would argue that 5* is a proposition involving possible worlds and their relations in modal space. Kratzer would argue that 5* is a proposition involving a set of worlds restricted by the antecedent and other contextual factors. But these theories can be of no help to Lange since, if 4 expresses the proposition 5*, then Lange has successfully explained why 4 is true in that context, which is just what his theory needs him to deny. Recall that it is a consequence of NP that any sentence of the form “
” is false. Therefore, if Lange is correct, 4 must be false. But, if 4 expresses the proposition 5*, then we have just shown it is true. After all, sentences that express true propositions are likewise true. Thus, Lange has not only given us a counterexample to his own theory, but he has also motivated the very interpretation of the counterexample that makes it a counterexample to his account.Footnote 9
1.3. Two Possible Responses
In the face of these considerations, Lange could develop an error theory for this kind of problematic counterfactual. Rather than arguing that sentence 4 is implicitly 5, Lange could bite the bullet and say that strictly speaking, 4 is false. We mistakenly believe it to be true because we have in mind a different counterfactual, namely, 5. Indeed, I find this solution most promising. However, Lange (personal communication) thinks this response has too high a cost and prefers to take our intuitions about the truth or falsity of such sentences at face value. But because a standard semantics does not include any notion of “implicitly,” according to which 4 is implicitly 5, appealing to such a notion will not help unless Lange can say more about it. Thus, this article could be read as an invitation for Lange to motivate an account of “implicitly” that is able do the work he envisions.Footnote 10
Another way of responding to the above objection is to give up on sentences altogether. Indeed, finicky linguistic items are an odd choice for grounding the laws of nature. John Carroll (Reference Carroll2011, 14) agrees: “On the face of it, [Lange's account] is troubling. What regularities are laws is tied to whether certain sentences are true in all contexts. This is startling; I find myself imagining Kip Thorne phoning Robert Stalnaker for a consult on the laws of quantum gravity!”
To keep the spirit of Lange's account, if not the letter, we could reformulate NP in terms of propositions rather than sentences:
(NPP) A proposition m is a law if and only if for any proposition p that is logically consistent with all of the laws (taken together), the counterfactual proposition 
is true.
Lange can avoid the counterexample raised above by maintaining that sentence 4 is true because it expresses the counterfactual proposition 5*, which has an antecedent proposition that is incompatible with the laws. Therefore, 5* is no threat to NPP. By characterizing laws of nature in terms of propositions, Lange would avoid the objection raised above, but he would not escape a second objection that I raise for his view below.
2. Nested Counterfactuals
In this section, I will argue that another feature of Lange's account, namely, his theory of nested counterfactuals, admits of counterexamples as well. Recall that Lange maintains that if p is compatible with all of the laws taken together, and m is a law, then 
. While this guarantees that m is counterfactually true, it does not guarantee that m is counterfactually a law, which is a further requirement of Lange's. Since all laws obey the principle 
, then if m is counterfactually a law, it must be the case that 
. For instance, if Jones had worn an orange shirt, gravity would have held. Additionally, Lange requires that if Jones had worn an orange shirt, then gravity would still have been a law and would not have held merely accidentally.
In order to secure this result by applying Lange's theory of counterfactually grounded laws, it must be true that if Jones had worn an orange shirt, then if any other contingent thing had happened, the law would still have held.Footnote 11 For that, Lange needs m to counterfactually satisfy NP as well. This Lange achieves by nesting counterfactuals.
Thus, if p and q are each individually compatible with all of the laws taken together, and m is a law, then 
must be true. In other words, if it were that p, then if it were that q, it would be that m. As discussed above where p and q are each possibly true (i.e., the antecedents are not vacuous), Lange's principle entails 
. It is this second formulation that I will argue against below.
Lange is at pains to emphasize that p and q need not be jointly compatible with the laws or even logically consistent with one another. “For example, consider the nested counterfactual ‘Had the object been entirely made of rubber, then here's a counterfactual conditional that would have been true: had it been entirely made of copper, it would have been electrically conductive’” (Lange Reference Lange2009, 23). While this example may be favorable to Lange's theory, there are many other examples that are not. For example, recall
(5) If the doctor had given the patient arsenic and the patient had lived, then the doctor would be famous for discovering that arsenic does not always kill human beings.
Lange is happy to concede that 5 is true. Since it has an antecedent that contradicts the ‘arsenic laws’, it is no threat to his theory. But, suppose we modify it by turning it into the following nested counterfactual:Footnote 12
(5′) If the doctor had given the patient arsenic, then if the patient had lived, then the doctor would be famous for discovering that arsenic does not always kill human beings.
Counterfactual 5′ also seems true, and if so, it is a counterexample to NP. To see this, note that it is compatible with the laws that the doctor gives the patient arsenic, it is compatible with the laws that the patient lives, and yet the consequent is contradicted by the arsenic laws. It is easy to design a formula for producing such counterexamples. Take p and q to be jointly although not individually incompatible with some law of nature (m). Then, in general, 
will be true and a counterexample to Lange's theory. Consider another example:
(6) If the earth were twice as massive, then if the moon's orbit were the same as it is now, gravity (as it is now) would not hold.
The above nested counterfactual seems true, but Lange's theory requires it to be false. To defend his theory, Lange must argue that despite appearances, 6 and all other nested counterfactuals of the form 
are false.
Additionally, since 
, the only way for Lange to deny that these are counterexamples is to say that if p were to hold, then if q were to hold, then something about p would not hold (otherwise, if p held, we would have a consequent that violated m). In general, when p and q are jointly incompatible with m, Lange has to say 
, a very counterintuitive result indeed. Thus, the following counterfactuals, although they seem false, according to Lange's account, must be true:
(7) If the doctor had given the patient arsenic, then if the patient had lived, then the doctor would not have given the patient arsenic.
(8) If the earth were twice as massive, then if the moon's orbit were the same as it is now, the earth would not be twice as massive.
And, Lange says just that, arguing that when you say, or think about, counterfactuals such as 5′ or 6 with the right emphasis, they do sound false. Similarly, when you say, or think about, counterfactuals such as 8, they do sound true.Footnote 13 Thus, he asks us to consider the following alternative but arguably equivalent formulations of 5′ and 6:
(5″) Suppose the doctor gave the patient arsenic, then here is a counterfactual that would be true: if the patient had lived, then the doctor would be famous for discovering that arsenic does not always kill human beings.
(6″) Suppose the earth were twice as massive, then here is a counterfactual that would be true: if the moon's orbit were the same, gravity would not hold.
Lange (personal communication) claims that when we think carefully about these nested counterfactuals, they sound false. But what counts as ‘thinking carefully’? One tempting option is to use the theoretical structure of the Stalnaker/Lewis semantics for counterfactuals, supplemented with an ordering on worlds, such as a closeness metric. On such an account, evaluating counterfactuals requires a kind of world-hopping tour. We begin at the actual world, then go to the closest first-antecedent world, for instance, the closest world where the doctor gives the patient arsenic. Next, we go to the closest second-antecedent world from the first-antecedent world, namely, the closest world where the patient lives. Finally, we check whether the consequent is true or false in the final world, that is, to see whether the doctor is famous for discovering that arsenic does not always kill human beings. It is arguable that, with the right closeness metric, a world where the doctor is mistaken about injecting arsenic is closer to the world where the doctor injects arsenic than a world where arsenic does not always kill human beings. Therefore, the whole nested counterfactual is false, and Lange's prediction is borne out.
But, there are two problems with this option. First, Lange (Reference Lange2009, 198) says that he does not want to commit himself to this picture. He claims that such talk is merely a “metaphor” and uses scare quotes when he says, “the ‘metric’ determining the ‘closest possible world’ where that antecedent obtains.” And it would be a mistake to lean too heavily on a metaphor when evaluating the metaphysical plausibility of Lange's theory.
The second problem is that, although it is tempting to use the theoretical structure of a semantic theory to inform our intuitions about which counterfactual sentences are true, such a use misunderstands the point of a semantic theory, which is merely to capture common usage. A semantic theory should not be in the business of determining usage. Semantic theories are evaluated by how well they predict linguistic data; they should not generate linguistic data. Therefore, taking our pretheoretic intuitions about such sentences seriously, and unless Lange can say more about what ‘thinking carefully’ amounts to in such cases, we have every reason to think that 5′, 6, 7, and 8 are counterexamples to NP.
3. Counterfacts
If I am right and Lange's account cannot answer these objections, there is one final retreat available. We could give up on counterfactual sentences and counterfactual propositions in favor of ontologically primitive counterfacts. While Lange posits these entities as truth-makers for counterfactual propositions, the above counterexamples show that he must make a choice: either the counterfacts ground the counterfactuals or they ground the laws, but not both. To see this, recall the true counterfactual:
(5′) If the doctor had given the patient arsenic, then if the patient had lived, then the doctor would be famous for discovering that arsenic does not always kill human beings.
Now, if counterfacts are truth-makers for counterfactuals, then the following counterfact obtains:
(9) [If the doctor had given the patient arsenic, then if the patient had lived, then the doctor would be famous for discovering that arsenic does not always kill human beings.]Footnote 14
But, if the counterfacts are also grounding the laws, then the following counterfact obtains as well:
(10) [If the doctor had given the patient arsenic, then if the patient had lived, then the doctor would NOT be famous for discovering that arsenic does not always kill human beings.]
But, 10, as a counterfact, makes true the following counterfactual:
(11) If the doctor had given the patient arsenic, then if the patient had lived, then the doctor would NOT be famous for discovering that arsenic does not always kill human beings.
So 9 and 10 cannot both obtain, or they would make true two contradictory counterfactuals, 5′ and 11. Thus, if we are positing counterfacts to ground the laws of nature, they cannot also be truth-makers for counterfactual propositions. To avoid confusion, I will reserve the term “counterfact” and square brackets for the truth-makers of counterfactual propositions and use the term “Lange-fact” and angle brackets for the ontological ground of the laws.
Once we have disconnected the Lange-facts from counterfactual sentences and propositions, we see that there can be no objections to the view on the basis of our intuitions about counterfactual sentences or propositions. Thus, it does not matter that the following statement is true: “If the doctor had given the patient arsenic, then if the patient had lived, then the doctor would be famous for discovering that arsenic does not always kill human beings,” because the following Lange-fact can still obtain: 〈If the doctor had given the patient arsenic, then if the patient had lived, then the doctor would NOT be famous for discovering that arsenic does not always kill human beings〉.
We can formulate a revised nomic preservation for the Lange-facts, according to which the laws are states of affairs that obtain in the world 
, rather than law statements or law propositions.
(NPC) 
is a law if and only if for any 
that is possibly coinstantiated with all of the laws (taken together), the Lange-fact 
obtains.
As far as I can tell, such an account is clear and consistent. Nevertheless, we should strive for more than clarity and consistency when grounding the laws of nature. I have argued that Lange-facts bear no relation to counterfactual sentences or propositions, so we cannot use our “great confidence” in counterfactual facts to help us determine the Lange-facts, which makes them awfully mysterious. And, since the Lange-facts are primitive, there is no further story to tell about them. In the end, such a theory would be plausible only if the Lange-facts were simpler or more explanatory than the laws they were postulated to ground.
But, this does not seem to be the case. There are many unanswered questions about them.Footnote 15 For instance, is there a distinct Lange-fact for every possible coinstantiated state of affairs? Do the Lange-facts bear any logical relations to one another, and if so, what are they? Lange gestures toward answers to these questions. But much more needs to be said in order to make the Lange-facts stand on their own since, on this particular formulation, they are independent of the counterfactuals. Consequently, our only access to which Lange-facts obtain and which do not is via the laws of nature.
Lange rightly points out, “That we figure out which counterfactuals are true by consulting what we already know about the laws (among other things) does not at all support the idea that the truths about the laws are ontologically prior to the subjunctive truths” (Reference Lange2009, 136). But, as I have argued, on this final view, the only access we could have to primitive Lange-facts is through the laws of nature making them an ontological extravagance. If the Lange-facts have no theoretical virtues, but add a significant ontological cost, we should not accept them.
4. Conclusion
In this article, I have argued that, because of context sensitivity, Lange cannot characterize his view of lawhood in terms of stable sets of counterfactual sentences. I have also argued that his account predicts the wrong results for many nested counterfactuals. I conclude that the laws of nature cannot depend on stable sets of counterfactuals, whether construed as sentences, the option he endorses, or alternatively, as propositions or primitive facts. While I agree with Lange that there are some important connections between laws and counterfactuals, I think he is wrong about what those connections are.
” is true. But, on the standard picture, the proposition is true if and only if the sentence, in context, is true. Lange gives us no reason to reject the standard picture, so asking about the truth of sentences in contexts is equivalent to asking about the truth of the propositions they pick out. Of course, there is an entirely different view according to which it is the counterfactual proposition that we should care about—a view I will come to in the next section. But that is not Lange's view.
is true because q, then q is implicitly in the antecedent if and only if 
is false. For example, It is because the patient survived that the doctor would have been famous had the injection contained arsenic. But, this counterfactual is false: “If the patient had been injected with arsenic, the patient would have survived,” so the survival clause is implicit in the original counterfactual. While this test tells us which clause is implicit, crucially, it does not tell us what “implicit” means.
is logically equivalent to 
.
