Presupposing counterfactuality *

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Introduction
There is by now long standing agreement both among philosophers and linguists that the term 'counterfactual conditional', though often used and well entrenched, is misleading if not a misnomer. Speakers felicitously using the conditionals in question may commonly convey that the antecedent is false, but contrary to what the label 'counterfactual' suggests, they by no means need to. 1 The relationship between these conditionals and the counterfactuality of their antecedents is thus not one of presupposing. It is one of conversationally implicating.
This agreement enfolds two types of the conditionals in question, typically individuated by tense: 2 so-called 'would' or 'non-past subjunctive conditionals' (NPSCs for short), such as (1) If Jones took cocaine, he would be dancing all night.
and so-called 'would have' or 'past subjunctive conditionals' (PSCs for short), such as (2) If Jones had taken cocaine, he would have been dancing all night. 3 Neither NPSCs nor PSCs presuppose the falsity of their antecedents, it is held. If the speaker of either conditional conveys the falsity of the antecedent at all, she conversationally implicates it. 4 There are two prominent arguments against the presupposition and in favor of the conversational implicature view. The first goes back to Alan Anderson and provides cases in which speakers use conditionals of the relevant form without committing to the falsity of the antecedent. The second is due 1 Here and in the following, I am using 'to convey that p' in a broad sense similar to Grice's 'to (speaker) mean that p'. 2 I will confine myself to English counterfactual conditionals. For crosslinguistic investigations, see, e.g., Iatridou 2000, Nevins 2002, and Karawani 2014. 3 I am borrowing the labels 'non-past subjunctive conditional' and 'past subjunctive conditionals' from Ippolito 2003. Further common labels are 'present counterfactuals' and 'past counterfactuals'. 4 The conversational implicature view is defended in, e.g., Stalnaker 1975, Karttunen & Peters 1979: 4ff. Comrie 1986: p. 89, von Fintel 1998, von Fintel 2012: p. 467, Iatridou 2000: p. 232, Nevins 2002, Ippolito 2003: p. 147, Edgington 2008, Leahy 2011a: 285f. Leahy 2011b, Leahy 2018, and Arregui & Biezma 2015. See, similarly, Starr 2014: p. 1024and Mackay 2019. The only more recent proponents of the presupposition view are Portner 1992 andKarawani 2014. For the claim that the falsity of the antecedent is 'implied', see Will 1947, Hampshire 1948, and Pears 1950 to Bob Stalnaker and offers a reductio against the presupposition view: if NPSCs and PSCs were to presuppose the falsity of their antecedents, modus tollens arguments containing them as premises would come out as question begging.
Though widely endorsed, neither of these arguments has been discussed in detail. In fact, most researchers these days almost exclusively talk about the various aspects of the alleged conversational implicature, such as how it is calculated and under which conditions it arises. The claim that the counterfactuality assumption actually is a conversational implicature is often simply taken for granted. 5 This is surprising because the conversational implicature view is not without problems. Not only has developing an account of the calculation of the alleged conversational implicature proven to be more complicated than one might have hoped, 6 we also seem to be forced to accept that some of the proclaimed conversational implicatures are not cancellable. 7 This paper is a first step towards filling this gap in the debate on the semantics and pragmatics of what are still called 'counterfactual conditionals'. It provides a thorough examination of the arguments against the presupposition view as applied to PSCs -the second type of conditionals listed above -and finds none of them conclusive. All the relevant linguistic data, it is shown, are compatible with the assumption that PSCs presuppose the falsity of their antecedents. The paper does not assess analogous arguments against the presupposition view as applied to NPSCs -the first type of conditionals from above. Here, the presupposition view seems less plausible to me, and so I am inclined to think that one major difference between PSCs and NPSCs is that while the former presuppose, the latter merely conversationally implicate antecedent falsity, but I will have to leave this as well as the question of how this difference is encoded in tense and how it relates to the question of whether there is a deep difference between indicative and subjunctive conditionals to future research. 8 5 See, for instance, Iatridou 2000, Ippolito 2003, Leahy 2011a, Leahy 2011b, Leahy 2018 Arregui & Biezma 2015. One exception is von Fintel (1998), who discusses in detail whether (past-)subjunctive conditionals could be true counterfactuals. 6 For the most recent discussion, see Leahy 2018. For criticism of (an early version of) Leahy's approach, see Starr 2014: p. 1025. 7 See, e.g., Arregui & Biezma 2015. See also conditionals like my example (24) below, which have gone unnoticed in the literature so far. 8 For the claim that there is a 'profound semantic difference', see Gibbard 1981: p. 211, andalso Bennett 2003: p. 256. For the opposite claim, see, e.g., Edgington 2008 andStarr 2014. For discussion, see, e.g., von Fintel 2012.

21:3 Julia Zakkou
The paper is divided into four sections. In Section 2, I examine different versions of Anderson's argument. In Section 3, I investigate Stalnaker's argument. In Section 4, I consider two further arguments against the presupposition view for PSCs due to Dorothy Edgington and Kai von Fintel. In Section 5, I briefly sum up.
Before I start, let me clarify two things. First, I will stay neutral on the controversy of whether PSCs have truth values. 9 I take the conclusion of this paper to be compatible with and relevant to both sides of the divide, but I will not dwell on the various ways to incorporate it here. Second, while I will not start from a specific view of presuppositions, I will make the following assumption: (Ass) If PSCs presuppose the falsity of their antecedents, then speakers using PSCs presuppose the falsity of the respective antecedents at every context of felicitous use. By way of (Ass) I will mostly talk of speakers of PSCs presupposing things, while I will ultimately counter objections that are commonly directed against PSCs themselves presupposing things. Support for (Ass) comes from two different directions. (i) (Ass) plausibly entails that presuppositions, unlike conversational implicatures, are not contextually cancellable (neither are they explicitly cancellable) in the sense specified by Grice 1989: ch. 2: they are present at every context at which the sentences triggering them are felicitously used. (ii) (Ass) is plausible as a claim about the connection between what are often called semantic or sentence presuppositions (left hand side of (Ass)) and what are often called pragmatic or speaker presuppositions (right hand side of (Ass)). In any case, (Ass) seems to be shared among my opponents, that is opponents of the presupposition view for PSCs. For often enough they object to the claim that PSCs presuppose the falsity of their antecedents by arguing that speakers using PSCs do not presuppose the falsity of the respective antecedents at every context of felicitous use (i.e., they deny the left hand side of (Ass) by arguing against the right hand side of it). Note that (Ass) is compatible with both semantic characterizations of presuppositions, according to which false presuppositions make the sentences triggering them gappy, and conversational characterizations, according to which presuppositions are secondary, non-at-isse, non-proffered, or backgrounded contents. (Ass) is thus impartial to different views of presuppositions and can be taken on board by scholars from different backgrounds.

Anderson's argument
Consider the following PSC, which will be called Anderson Conditional: (3) If Jones had taken arsenic, he would have shown the same symptoms he actually shows.
Assume that this sentence is used by a doctor, call her A, at the autopsy of Jones's body. Anderson holds that in [the autopsy] context the doctor's statement [of (3)] would probably be taken as lending support to the view that Jones took arsenic -it would certainly not be held to imply that Jones did not take arsenic. (Anderson 1951: p. 37) We can give the thought expressed here a more linguistic spin by looking at the following two utterances by our doctor A: (4) A: If Jones had taken arsenic, he would have shown the same symptoms he actually shows. So he did not take arsenic.
(5) A: If Jones had taken arsenic, he would have shown the same symptoms he actually shows. So he took arsenic.
Anderson seems to assume that, given the presupposition view, (4) should sound fine and (5) should sound bad. Intuitively, though, it is the other way around: (4) is bad and (5) is fine. The presupposition view should thus be rejected. In the autopsy context, A does not presuppose that the antecedent of the Anderson Conditional is false. 10 But why exactly would one think that the presupposition view makes these counterintuitive predictions? Let's start with (4). The presupposition view seems to predict that A is not contradicting herself. She is presupposing that Jones did not take arsenic and she is stating precisely the same: that Jones did not take arsenic. Her contribution should thus come out as fine. Consider furthermore the following utterance: 10 Various authors make use of this argument. See, e.g., Stalnaker (1975: p. 277 According to the presupposition view, this utterance is similar to the one in case (4): A first presupposes and then explicitly states that someone is drinking martini. This utterance sounds perfectly fine. By analogy, (4) should thus come out fine as well.
Let's next consider (5). The presupposition view seems to predict that A is contradicting herself. She is presupposing that Jones did not take arsenic and she is stating that Jones did take arsenic. Her contribution should thus come out as bad. Consider also the following utterance: (7) A: The man with the martini is wearing pink shorts. So there is nobody drinking martini.
According to the presupposition view, this utterance is similar to the one in case (5): A first presupposes that somebody is drinking martini and then explicitly denies that this is the case. This utterance sounds bad. So by analogy, (5) should come out bad as well.

Rebuttal: Part I
I will postpone the discussion of the arguments by analogy to Section 2.2 and for now concentrate on the first type of the challenge. My objection to both parts of this challenge will rely on the claim that for contributions of the form (4) and (5) to be fine not one but two conditions have to be met: (i) A is not contradicting herself.
(ii) A is providing a good reason for the claim made by the second sentence.
The second condition is motivated by the fact that by introducing the second sentence of (4) and (5) with 'so', A triggers the expectation that this second sentence is the conclusion of some kind of argument and that what she said before provides a good reason for the conclusion. I will argue in the following that Anderson-style arguments overlook that (4) violates the second condition and that they are wrong to assume that, on the presupposition view, (5) violates the first.

21:6
The argument regarding (4) is straightforward. It is clear that condition (i) (the no contradiction condition) is fulfilled: by presupposing that Jones did not take arsenic and then asserting precisely the same, A is not contradicting herself. It is anything but clear, however, that condition (ii) (the good reasons condition) is fulfilled as well. With her utterance of the Anderson Conditional, A is conveying that a certain relevant, necessary condition for Jones's having taken arsenic is met. This, though, only provides a good reason for the claim that Jones did take arsenic. It does not provide a good reason for the claim that Jones did not take arsenic. This shows that proponents of the presupposition view can explain why (4) sounds bad after all: it sounds bad because A does not provide a good reason for what she presents as a conclusion.
The argument regarding (5) is a bit more complex. To begin with, let us rehearse a well-known and widely-shared picture according to which presuppositions and assertions, though different in several respects, share an important feature: with them, speakers take a stand on the common ground. More precisely, by presupposing that p and asserting that p alike, speakers either suggest to put p in the common ground or they endorse the fact that p is already in the common ground (Stalnaker 1973 andStalnaker 1978). 11 Does this picture entail that by presupposing that not-p and then asserting that p the speaker takes jointly inconsistent stands and thus contradicts herself?
Let us call to mind some more details of the above picture. The common ground is conceived as the set of propositions that the participants of the conversation mutually accept. Acceptance of p is taken to be a weak positive attitude towards p that is compatible with a range of different more specific attitudes towards p. Most often, one will accept that p because one believes that p, but one can also accept that p because one, for instance, assumes it for certain purposes, for instance, as a helpful simplification, to reduce p to absurdity, etc. (Stalnaker 1974: p. 5151 andStalnaker 2002: p. 716716). Importantly, these more specific attitudes are not only independent (one can believe that p without assuming that p and vice versa). They can also be consistently held towards incompatible propositions. For instance, one can consistently believe that p and assume that not-p. Given the notion of acceptance in play, participants of a conversation can thus (individually or mu-tually) accept incompatible propositions: if they accept that p because they believe p to be the case and accept that not-p because they assume that for a given purpose, no inconsistency arises.
This shows that by presupposing that not-p and then asserting that p the speaker need not take jointly inconsistent stands on the common ground. If she presupposes that not-p in order for not-p to be mutually accepted as an assumption for a given purpose and then asserts that p in order for p to be mutually accepted as something that is actually the case, no inconsistency arises. She is thus not contradicting herself.
But isn't the speaker still aiming for a common ground that contains incompatible propositions? And aren't such cases commonly taken to result in a break down of the conversation? If one thinks that (a) there is exactly one common ground which is (b) a homogenous whole to which (c) propositions can only be added as the conversation proceeds, it seems indeed natural to expect a break down of the conversation. After all, if both speech acts are successful the common ground will be inconsistent in an obvious way and so allow for all kinds of mad inferences. However, each of these three assumptions is controversial, and they should at best be accepted as simplifications or idealizations. To adequately model the complexity of our conversational reality, we should either -in contrast to (a) -acknowledge that there are at least two common grounds, an official and an unofficial one (Stokke 2013a: 55ff.), or -opposed to (b) -think of the one common ground as being compartmentalized so that propositions associated with different attitudes are stored in different compartments, e.g., there is one for propositions that are merely assumed and one for propositions that are actually believed (Yalcin 2018), or we should -in contrast to (c) -think of the common ground as something to and from which propositions can be added and subtracted as the conversation proceeds (Karttunen &Peters 1979: p. 8, n.5 andLeahy 2018: p. 61). 12 Each modification would be sufficient to prevent a break down of the conversation in the cases in question. According to the first and second, successfully presupposing that not-p and then asserting that p will lead to not-p and p being stored in two kinds of common ground or two parts of just one common ground. According to the third, successfully presupposing that not-p and then asserting that p will result in a common ground which, 12 Interestingly, these latter two papers use the possibility of a temporary revision of the common ground to defend the view that indicative conditionals presuppose the epistemic possibility of their antecedents. Using the same idea to defend the presupposition view of PSCs is therefore not ad hoc.
21:8 at a first stage, contains not-p, but, at a second stage, does not contain not-p anymore. 13 But wouldn't it follow that speakers can always unproblematically string together speech acts that suggest or endorse jointly incompatible propositions? More specifically, wouldn't it follow that there is nothing strange about conjoining a presupposition of p with a presupposition of not-p, and likewise, an assertion of p with an assertion of not-p? This is a general challenge for all of the accounts of the common ground outlined. Let me point to two plausible addenda to avoid such consequences. First, it may well be that with presuppositions and assertions alike, speakers take a stand on what the participants of the conversation should mutually accept, but this is compatible with presuppositions and assertions being governed by different norms. While the norm of assertion seems to be belief or something even stronger, the norm of presupposition seems to be weaker than belief. That is, for a speaker's assertion that p to be proper, she has to at least believe that p, but for a respective presupposition to be proper, she only has to assume that p for certain purposes (for norms of assertion, see, e.g., Williamson 1996, Lackey 2007, and Turri 2017. To corroborate, note that (a) the talk of 'asserting something for the purposes of the conversation' is far stranger than that of 'presupposing something for the purposes of the conversation', and that (b) we are far less happy to explicitly assert the existence of fictional characters than to presuppose it. This should give the assumption of different norms at the very least some initial plausibility. Being governed by different norms would help to explain why it is easier to felicitously concatenate a presupposition and an assertion of jointly incompatible propositions than it is to felicitously concatenate two presuppositions or two assertions of jointly incompatible propositions. Second, inconsistent concatenations may be allowed only if the speaker clarifies her attitudes towards the relevant propositions to her audience. One option is to tell her audience outright about her 13 Immediate support for this claim comes from the following cases known from the debate on protagonist projection (see Holton 1997, but also Stokke 2013b and Buckwalter 2014): (i) A: Tim knew that Tom would never let him down, but, like all the others, he in the end did.
(ii) A: Jill saw a shooting star last night. She wished on it, but it was just a satellite.
According to one prominent construal at least, A is here presupposing something which, as she immediately afterwards reveals, she does not take to be the case. Both cases sound fine, though.

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attitudes; another is to provide more indirect evidence, for instance, by giving reasons which undermine the one proposition (and so make clear that it was merely assumed) and support the other (and by that make clear that it is supposed to be believed). If the speaker does not clarify her attitudes, her contribution comes out odd. This too would forestall the overgeneralization worry. Both addenda need to be worked out in more detail, but I take them to be plausible enough to shift the burden of proof to those who press the overgeneralization worry.
We can thus conclude that the presupposition view as applied to contribution (5) does not predict a violation of condition (i) (the no contradiction condition). If the proposition that Jones did not take arsenic is meant to be accepted only as an assumption for certain purposes and the proposition that Jones took arsenic is meant to be accepted as something to be believed, no inconsistency arises. What about condition (ii) (the good reasons condition)? With her utterance of the Anderson Conditional, A is conveying that a certain necessary and also clearly relevant condition for Jones's having taken arsenic is met: there is no doubt that Jones is showing the symptoms he is actually showing. This, recall, does not provide a good reason for the claim that Jones did not take arsenic. But it does provide a good reason for the claim that Jones did take arsenic. Admittedly, it does not provide a full, but only a partial reason. But still, given certain background assumptions, even a partial reason can be a good enough reason for a claim. This shows that proponents of the presupposition view can explain why (5) sounds fine after all: it sounds fine since A is not contradicting herself and provides a good reason for what she presents as a conclusion.

Rebuttal: Part II
So far we have only addressed the first challenge presented at the beginning of Section 2. As for the argument by analogy, recall the relevant two utterances (6) and (7): (6) A: The man with the martini is wearing pink shorts. So there is someone drinking martini.
(7) A: The man with the martini is wearing pink shorts. So there is nobody drinking martini.

21:10
A's utterance in (6) sounds fine and her utterance in (7) sounds strange. So, shouldn't we expect the same pattern for (4) and (5), given the presupposition view?
In light of the discussion above, it should be clear that (6) and (7) are relevantly dissimilar from (4) and (5). Relevantly similar cases would have the speaker first presuppose a proposition and then present reasons for doubting this very proposition, such as in the following two cases: (8) A: The man with the martini is drinking something that looks, smells and tastes like water. So there is someone drinking martini.
(9) A: The man with the martini is drinking something that looks, smells and tastes like water. So there is nobody drinking martini.
By using the definite description, A is presupposing that somebody is drinking martini and by attributing 'is drinking something that looks, smells and tastes like water' she is providing reasons against this proposition. She is providing reasons for thinking that the man in question is not drinking martini. So (4) and (5) are much more like (8) and (9) than like (6) and (7). And with (8) and (9), we have the same intuitive pattern as with (4) and (5): concluding that the presupposition is true is strange and concluding that the presupposition is not true is fine. If you are suspicious of the examples because they contain definite descriptions that are used referentially (as opposed to attributively), take a look at the following cases: 14 (10) A: The round square has two properties that very rarely show up together. So there is a round square.
(11) A: The round square has two properties that very rarely show up together. So there is no round square.
Just like with the Anderson Conditional, A is presupposing something while providing reasons for doubting the presupposition in (10) and (11). Here, too, we have the same intuitive pattern as with (4) and (5) Kripke (1977), they are good cases in point: just as referentially used definite descriptions carry a presupposition that need not be believed by the speaker, Anderson-style PSCs (i.e., PSCs with a necessarily true consequent) carry presuppositions that need not be believed by the speaker.

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presupposition is true is strange and concluding that the presupposition is not true is fine. 15 To avoid misunderstandings, let me be clear that the presupposition view I suggest does not entail that presuppositions are cancellable in the sense that one can use a sentence without conveying that p (Grice 1989: ch. 2 andZakkou 2018). With PSCs, speakers always convey that the antecedent is contrary to the facts. They always suggest to add not-p to the common ground or endorse the fact that it is already in the common ground. It's just that the suggestion or endorsement can be merely temporary, or it can concern a specific compartment of the common ground or an unofficial common ground.

Further cases
Up until now, we have focused on (4) and (5) And what about cases in which she intersects the plain statements within the Anderson Conditional?
As for the first question, consider the following exchanges between A and her colleague B: A's response in (12) sounds strange while her response in (13) sounds fine. However, even though, compared to (4) and (5), the order of the sentences is reversed, (12) and (13) are similar to (4) and (5) in that we naturally take A to give the conditional as a reason for the affirmation of the claim that Jones did not take arsenic and that Jones did take arsenic, respectively. Proponents of the presupposition view can thus offer the very same account of the two data points they have given before for (4) and (5): A's response in (12) sounds strange because even though she is not contradicting herself with first stating that Jones did not take arsenic and then presupposing that he did not take it, the Anderson Conditional does not provide a good reason for what needs confirmation. A's response in (13), in contrast, sounds fine because, as spelled out above, she is neither contradicting herself with asserting that Jones took arsenic and then presupposing that he did not take it, nor does she fail to provide a good reason for what she is trying to show.
To corroborate this, note that the intuitions about (12) and (13)  A's response in (16) seems fine now and her response in (17) strange. Proponents of the presupposition view can account for this: A's response in (16) is fine because even though she commits to the view that Jones did not take arsenic by 'Right', she provides a reason against this claim with the Anderson Conditional. So her use of the contrast marker makes perfect sense. A's response in (17) is strange, however, because A does not only commit to the claim that Jones took arsenic by 'Right', she also provides a reason for this very claim. Hence her use of the contrast marker is odd.

21:13 Julia Zakkou
As for the second question raised at the beginning of this section, consider the following utterances: (18) A: If Jones had taken arsenic -which he didn't -he would have shown the same symptoms he actually shows.
(19) A: If Jones had taken arsenic -which he did -he would have shown the same symptoms he actually shows.
Intuitions might not be univocal but it seems that there are contexts in which (18) and (19) are fine. 16 Consider (18) first. One might think that, given the presupposition view, this utterance should strike us as redundant, because A is both presupposing and then stating that Jones did not take arsenic. In light of what I said before, however, it should be clear that this would be much too quick. According to the presupposition view, we can understand A as signaling that she accepts the proposition that Jones did not take arsenic for the time being and as going then on record that she actually believes this. 17 Of course, in conversations in which it is either entirely uncontroversial that Jones did not take arsenic or completely irrelevant whether he did, stressing her belief will sound somewhat strange. But in a conversation in which the question of whether Jones took arsenic is controversial and of great importance, revealing her belief that Jones did not take it can make perfect sense.
Consider next (19). One might think that, given the presupposition view, A's utterance should strike us as contradictory, because, on the presupposition view, A is here presupposing and asserting jointly incompatible propositions. But, again, in light of what I said before, it should be clear that things are more complicated. There surely are conversations in which everyone will be just fine with assuming a certain proposition, say, for simplicity's sake, and where the actual truth of the proposition is not of great importance. But there are other contexts in which one is happy to go along as far as a certain assumption is concerned but in which one still finds it important to go on record that one actually believes the opposite. In these latter cases, at least, (19) will sound fine.
So, to sum up, proponents of the presupposition view can counter Anderson's objection. The assumption that by using the Anderson Conditionalthe PSC (3) -one presupposes that the antecedent is contrary to the facts does not have counterintuitive consequences.

Stalnaker's argument
Consider the following PSC: If Jones had taken cocaine, he would have been dancing right now.
Assume that this sentence is used by a detective, call her C, as part of a drug investigation. More concretely, assume that C utters the following: (21) C: If Jones had taken cocaine, he would have been dancing right now. He is not dancing right now. So Jones did not take cocaine.
Stalnaker claims that the presupposition view falsely predicts that C's reasoning is bad. Not because C would be contradicting herself, nor because C would not be giving a good reason for what she presents as a conclusion. The problem rather seems to be that, by presupposing that Jones did not take cocaine, C would assume something in an argument that she only tries to establish in the course of her reasoning. Case (21) should thus come out as question begging -that is, as an argument that has its conclusion as a premise -even though, intuitively, it sounds perfectly fine. Or to use Stalnaker's own words: The subjunctive conditional premiss in [a] modus tollens argument cannot be counterfactual since if it were the speaker would be blatantly begging the question by presupposing, in giving his argument, that this conclusion was true. (Stalnaker 1975: 277) Stalnaker thus concludes that in a case like (21) C does not presuppose the falsity of the antecedent. I agree that, intuitively, (21) sounds fine and not question begging. But the assumption that the presupposition view predicts otherwise seems to rest on a confusion of two senses of the word 'presupposing'. There is not only the somewhat technical sense used before; there is also a perhaps more 21:15 intuitive sense according to which presupposing something in an argument roughly means to tacitly introduce it as a premise.
The proponent of the presupposition view will happily acknowledge that, given the first, technical sense, C presupposes the conclusion in (21). But it is not clear why she should accept that presupposing the conclusion in this sense would make (21) question begging. Compare the following utterance which does not feature a PSC: (22) C: If Jones took cocaine yesterday -which he didn't -he would be dancing right now. He is not dancing right now. So he did not take cocaine. 18 Even opponents of the presupposition view can agree that, in (22), C presupposes that Jones did not take cocaine yesterday by her use of the parenthesis. Yet the argument is not question begging, because C only anticipates the conclusion. She merely indicates the argumentative direction she is taking, she does not introduce it as a premise. Both (21) and (22) are thus analogous to the following: (23) C: Jones did not take cocaine yesterday. If Jones took cocaine yesterday, he would be dancing right now. He is not dancing right now. So he did not take cocaine.
Here, too, C merely anticipates the conclusion without introducing it as a question begging premise. 19 Moreover, ask yourself why the conversational implicature view would be any better off regarding (21) than the presupposition view and thus why presupposing the conclusion in the first, technical sense would lead to question-beggingness any more than conversationally implicating the conclusion would. You might think this has something to do with the fact that This argument is not question begging. Scholars from all sides will have to agree, however, that whether its a conversational implicature or a presupposition, the proposition that Jones did not take potassium cyanide as conveyed by C's use of PSC (24) is not cancellable. 'If Jones had taken potassium cyanide, he would have shown completely different symptoms than he actually shows. But I don't mean to suggest that Jones did not take potassium cyanide' sounds clearly off. Additionally, people from all sides will most likely grant that (24) entails the falsity of the antecedent. They will thus acknowledge that (24) depends for its truth on whether Jones took potassium cyanide. So if (21) poses a problem for the presupposition view, an analogous problem arises for everybody in the case of (25). In fact, however, there is no problem for anybody. In the case of both (21) and (25), C merely anticipates the conclusion of her argument while stating her first premise. The proponent of the presupposition view will also grant that, given the second, more ordinary sense of 'presupposing', presupposing the falsity of the antecedent should make (21) question begging. For presupposing that Jones did not take cocaine in this second sense would mean to introduce this proposition as a tacit premise. And this in turn would mean to introduce the conclusion as a premise. But she need not accept that C presupposes the conclusion in (21) in this second sense. As indicated, she has to accept that C presupposes the conclusion in the first and technical sense, but this does not mean that she introduces this presupposition as a premise. She may merely anticipate the conclusion to indicate the direction the argument is taking.

21:17 Julia Zakkou
We can thus conclude that the presupposition view does not predict that (21) sounds question begging. The view does entail that the conclusion of the argument in (21) is presupposed in the first, technical sense of 'presupposing the conclusion', but this does not imply question-beggingness. The view does not, however, entail (nor suggest otherwise) that the conclusion is presupposed in the second, more intuitive sense ('tacitly introducing the conclusion as a premise'). So even though this would imply question-beggingness, it is not a prediction of the presupposition view. Just like Anderson's argument, Stalnaker's objection to the presupposition view seems inconclusive. All the relevant linguistic data are compatible with the presupposition view.

Further arguments
Anderson's and Stalnaker's arguments are by far the most cited objections to the presupposition view. But they are not the only ones. In this section, I will briefly address two further reasons for abandoning the presupposition view.
The first can be attributed to Edgington (2008). She asks us to consider a case in which our detective C utters the following in an investigation to a drug crime: (26) C: If Jones had taken cocaine, he would have been dancing right now. So let's go to his place and see whether he is dancing right now.
Intuitively, this utterance sounds fine. One might think that this poses a challenge for the presupposition view. 20 If C already knew that Jones did not take cocaine, why would she go to his place to see whether he is dancing? To spell this out a bit: if C finds that he is dancing right now, she cannot infer anything regarding the question at hand, because Jones's dancing is compatible with both the assumption that he took cocaine and the assumption that he did not. Meanwhile, if she finds that he is not dancing right now, she can only infer what she already knew, namely that Jones did not take cocaine. Given what we said above, it should be clear where the argument goes wrong: presupposing that Jones did not take cocaine does not require knowing or even believing that Jones did not take cocaine. So C may very well feel the need to go to Jones's place to see whether he is still dancing. For if she finds that he is not, she will come to know what she previously only presupposed, namely that Jones did not take cocaine.
The second argument is due to von Fintel (1998). He asks us to consider a case in which our doctor A utters the following in response to B's question about how the dinner was with their colleagues Polly and Uli: A: If Polly had come to dinner tonight, we would have had a good time. If Uli had made the same amount of food that he in fact made, she would have eaten most of it.
Intuitively, this utterance sounds fine. Unlike the Anderson Conditional, though, which has a consequent that cannot be false, the second conditional here has an antecedent that cannot be false: necessarily, Uli made the same amount of food he in fact made. One might think that this rules out the presupposition view, because it does not make sense to presuppose something that is obviously necessarily false. 21 It seems to me, however, that (27) is naturally understood as a case of modal subordination in the sense of Roberts 1989: by evaluating the second conditional, we do not think of the actual situation in which Uli made the same amount of food he in fact made. We think of a counterfactual situation in which Uli made the same amount of food he in fact made and in which Polly came to the party. By presupposing that this situation does not obtain, A is not presupposing a necessary falsehood because Polly could have failed to come. It is thus not clear that (27) provides a counterexample to the presupposition view. To support this suggestion, note that PSCs with necessarily true antecedents cannot be discourse initials. They are fine when preceded by another PSC as in (27), but they are strange if they are the first sentence in a conversation. This is what one would expect given the modal subordination view.

Conclusion
I have argued that the most prominent and presumably strongest arguments against the claim that PSCs presuppose the falsity of their antecedents are inconclusive. All the relevant linguistic data involving PSCs are compatible with the assumption that speakers of such conditionals always presuppose the falsity of the respective antecedents. This means that the conversational