One of the reasons for which some counterpossibles are considered false is due to the non-vacuous consequences of necessarily false theories. Thus, some propositions of the form ‘According to F, P’ or ‘If F were correct, P’ (where F stands for an implicit or explicit impossibility) are false. While (7) is true, the negation of this, (7*) ‘If there were an impossible world, there would be no true contradiction in the actual world’ is false.Footnote 8 This leads to the question of how to reconcile the intuition that (7*) is false and the ORT’s thesis that it—as any other counterpossible—is actually true.
David Lewis on counterpossibles
One way of explaining this is to move the burden of the problem from semantics to pragmatics and claim that the mentioned intuition has its roots in a conflation of a counterpossible’s truth-value and its assertion. Consequently, the mere fact that we do not assert (7*) does not entail its falseness. While this seems to be the case, one might raise the question of why (7*)—contrary to (7)—has not been asserted. To this, David Lewis responded:
We have to explain why things we do want to assert are true (or at least why we take them to be true, or at least why we take them to approximate to truth), but we do not have to explain why things we do not want to assert are false. We have plenty of cases in which we do not want to assert counterfactuals with impossible antecedents, but so far as I know we do not want to assert their negations either. Therefore they do not have to be made false by a correct account of truth conditions; they can be truths which (for good conversional reason) it would always be pointless to assert. (Lewis, 1973: p. 25)
The above could act as an explanation only if neither (7) nor (7*) had been asserted. That, however, is not the case. The first one expresses the problematic consequence of conjoining modal realism’s understanding of ‘p is true in world w’ and the notion of impossible worlds. As Lewis later argued, a belief in an impossible world w1, such that in w1 p& ~ p, would entail the truth of ‘at w1 p, and it is not the case that at w1 p’ at the actual world (Lewis, 1986: p. 7). This was meant to show that since a belief in w1 entails the truth of a contradiction in the actual world, one should not believe in impossible worlds. Counterfactual (7) adequately describes the consequence of extending modal realism by introducing spatiotemporal impossible worlds, and it has indeed been asserted. Hence, we do assert counterfactuals with impossible antecedents. Importantly, we do not assert all of them, but only some. Just as in the case of other counterfactuals.
Lewis’ response leaves open one more option. This is to claim that the reason for which one does not assert those counterpossibles, which advocates of UNORT recognizes as false, is that—considering conversational reasons—asserting such counterpossibles is pointless. While this could apply to cases such as (13CF) or (14CF), where it is not easy to find any relevance between the antecedent and a consequent, many examples seem to be worth asserting. Since there are conversations in which (7) is asserted, and since (7) and (7*) have the same subject matter and (according to ORT) both are true, it is difficult to find a reason for which (7*) would be pointless to assert. As a matter of fact, asserting (7) and (7*) would allow one to indicate some highly implausible consequences of extending modal realism by introducing impossible worlds. In virtue of the commonly accepted rule of conjunction of counterfactual consequences, conjunction of (7) and (7*) results in (7**)Footnote 9: ‘If there were an impossible world, some contradictions would be true in the actual world and no contradiction would be true in the actual world.’ Counterpossible (7**) shows that the extension of modal realism would result not only in true contradictions, but also in the apparent inconsistency of such an extension of modal realism. There is an important difference between those two outcomes. The first one makes the extension unacceptable for those who do not believe in a true contradiction. The last one makes it unacceptable even for those who believe in the truth of some contradiction, but who do not want to believe in a theory that is self-contradictory. For it is one thing to believe in true contradictions, and it is another to believe in an inconsistent theory.Footnote 10
(7) and (7*) are by no means special cases. If every counterpossible ‘A > C’ is vacuously true, any assertion of ‘A > (C& ~ C)’ allows one to prove the inconsistency of ‘A.’ Thus, if ‘A > C’ (as in (7)) is meant to indicate the disturbing consequences of ‘A’ being the case, so is ‘A > (C& ~ C)’ (as in (7**)). Accordingly, if both ‘A > C’ and ‘A > ~ C’ are true, and it is not pointless to assert the first one, then the assertion of the second is also motivated. Therefore, if conversational irrelevance is supposed to be the only difference between (7) and (7*) (i.e., a counterpossible that UNORT considers to be false), the question of why the latter is not asserted remains unaddressed.
Assertions and counterpossibles
Another orthodox approach to counterpossibles has been proposed by Nina Emery and Christopher Hill (2017). The main difference between theirs and Lewis’ approach to counterpossibles is that they do admit that some counterpossibles are asserted. Their explanation of which counterpossibles are asserted and which are not is based on reference to the well-known views of Paul Grice (1975) concerning the maxims and implicatures of conversation. Among the maxims that are supposed to govern conversations, the Maxim of Quantity advises you to make your contribution as informative as is required for the current purposes of the exchange. Accordingly, Emery and Hill claim that.
if a speaker asserts a proposition that is trivially true, and therefore uninformative, the audience will assume that the speaker intends to communicate a more substantial proposition that is related to the asserted proposition in subject matter and will look around for salient propositions that have these properties. (Emery & Hill, 2017: p. 139)
Thus, assuming that a speaker and his or her audience obey Gricean maxims, the aim of asserting (1) is to communicate (1*): ‘Every fish has gills.’ The fact that (1*) is a true and substantial proposition, which is related to (1), and which cannot be communicated by asserting (2), explains why we tend to assert (1) and not (2). The mere assertion of (1), however, does not have to entail the falseness of (2) (Emery & Hill, 2017: p. 139). Accordingly, one does not have to change the semantic analysis or introduce impossible worlds in order to address the intuitions that underpin the problem of counterpossibles. These intuitions may be explained away by indicating that the reason for which some counterpossibles are asserted is that such assertions allow for an indirect expression of a true and substantial (i.e., non-vacuous) proposition.
There are two problematic aspects of this approach. The first one is directly related to examples such as (10CF)–(14CF), the other concerns a more general question concerning the debate over counterpossibles. Following Emery and Hill’s analysis, one would have to admit that the reason for which we tend to assert (11CF) and not (10CF) is that it allows for expressing ‘a more substantial proposition that is related to the asserted proposition in subject matter.’ It seems that what one might communicate by asserting (11CF) (as opposed to asserting (10CF)) is precisely a consequence of paraconsistent logic. Considering that, (11SP): ‘According to paraconsistent logic, some contradictions are true’ is one of the natural candidates of a proposition that could be indirectly expressed by asserting (11CF). Proposition (11SP), however—in virtue of the paraphrase of the story prefix to subjunctive conditional, and the thesis of ORT—is vacuously true. Assuming that by ‘more substantial proposition’ Emery and Hill mean a proposition that is not vacuously true, their analysis does not explain why (11CF) is asserted and (10CF) is not. In order to change this, one would have to provide either an alternative paraphrase of expressions that contain a story prefix or reasons for which (11SP) should not be considered a proposition that is indirectly expressed by asserting (11CF).
The second problem is that this approach allows to put into a question the standard possible world semantics. Emery and Hill use a line of argumentation which is meant to support the orthodox view against the charge outlined by advocates of UNORT. This means that it purports to reveal that one can explain away pre-theoretical intuitions about counterpossibles with the view that while some counterfactuals with merely possible antecedents are false, each and every counterfactual with an impossible antecedent is true. However, if—as Emery and Hill claim—an assertion of (1) does not affect the truth-value of (2), one may adopt the very same strategy to claim that every counterfactual is vacuously true. After all, just as in the case of counterpossibles, we can indicate propositions that are indirectly expressed by asserting counterfactuals with merely possible antecedents. Thus assuming—for the sake of argument—that every counterfactual is vacuously true, the assertion of ‘If Christopher Columbus had reached the place he was planning to reach in 1492, he would have arrived in India’ can be explained by the fact that this allows one to indirectly express a more substantial proposition that is related to the asserted proposition in subject matter, e.g., ‘Christopher Columbus was planning to reach India.’ As a result, this pragmatic approach equally undermines believing in non-vacuous counterpossibles as it does believing in the non-vacuous truth of counterfactuals with merely possible antecedents. This consequence, however, goes against the primary motivation for the orthodox analysis of counterfactuals.Footnote 11
Epistemically irresponsible utterances
From ORT’s point of view, the problem of counterpossibles is not the only one where the assertion of a true counterfactual is infelicitous. The other one is known as the problem of reverse Sobel sequences (RSS). Consider a conversation about Sophie, who is a fan of a baseball player, Pedro:
(Sa) If Sophie had gone to the parade, she would have seen Pedro.
(Sb) But if Sophie had gone to the parade and been stuck behind a tall person, she would not have seen Pedro.
Both counterfactuals are true, and both can be asserted in the same conversation. The above is an example of a Sobel sequence, and it finds an elegant explanation in terms of the standard possible worlds semantics (e.g., Lewis, 1973: p. 10). The sequence, however, becomes more problematic to explain if one changes the order of assertions, i.e., in the case of a reverse Sobel sequence:
(S*a) If Sophie had gone to the parade and been stuck behind a tall person, she would not have seen Pedro.
(S*b) But if she had gone to the parade, she would have seen Pedro.
While the truth-values of the above counterfactuals did not change, it seems that there are good reasons to consider such a sequence of assertions infelicitous. This observation led some to argue against the standard possible worlds semantics for counterfactuals and to propose alternative dynamic approaches towards RSS (Gillies, 2007; von Fintel, 2001). Others seek to explain the infelicity of reverse Sobel sequences without giving up the standard view. One such explanation has been proposed by Sarah Moss, and it is based on the notion of epistemically irresponsible utterances (EI):
It is epistemically irresponsible to utter sentence S in context C if there is some proposition φ and possibility µ such that when the speaker utters S:
(i) S expresses φ in C
(ii) φ is incompatible with µ
(iii) µ is a salient possibility
(iv) The speaker of S cannot rule out µ. (Moss, 2012: p. 568)Footnote 12
In virtue of EI, since the assertion of (S*a) raises the salient possibility of Sophie being stuck behind a tall person, assertion of (S*b) is epistemically irresponsible. As Moss explains:
Someone who utters (S*b) generally will not be able to rule out the possibility that if Sophie had gone to the parade, she might have been stuck behind a tall person. Hence EI entails that it is epistemically irresponsible to utter (S*b), since:
(i) (S*b) expresses the proposition that Sophie would have seen Pedro if she had gone to the parade.
(ii) The proposition that Sophie would have seen Pedro if she had gone to the parade is incompatible with the possibility that Sophie might have been stuck behind a tall person if she had gone to the parade.
(iii) The possibility that Sophie might have been stuck behind a tall person if she had gone to the parade is a salient possibility.
(iv) The speaker of (S*b), at the time at which she utters (S*b), cannot rule out the possibility that Sophie might have been stuck behind a tall person if she had gone to the parade. (Moss, 2012: p. 569)
Thus, even though both (S*a) and (S*b) are true, there is a pragmatic explanation for why the utterance of one of them is infelicitous. The explanation has it that the assertion of (S*b) is an example of an epistemically irresponsible assertion.
As mentioned, the problem of RSS is in some sense similar to the problem of counterpossibles. In both cases, an advocate of the standard possible worlds analysis (or ORT) faces the question of why an utterance of some true counterfactuals is infelicitous. Moreover—as Sarah Moss claims—EI does not just explain RSS but is meant to be a general principle governing assertability (Moss, 2012: p. 568). That suggests that EI might be a helpful tool for orthodoxy in the debate over counterpossibles, for it may explain why—regardless of their vacuous truth—the utterance of some counterpossibles is felicitous and the utterance of others is infelicitous. It seems, however, that the notion of epistemically irresponsible assertion fails to provide support for ORT against UNORT. The reason for this is that as far as counterpossibles go, it is impossible to satisfy one of the essential conditions of EI. Consider two counterpossibles:
(MCF) If Meinongianism were correct, some objects would not exist.
(MRCF) If Meinongianism were correct, every object would be red.
An advocate of UNORT believes that, of the two, the first one is true and the second is false. This difference makes it felicitous to assert (MCF) and infelicitous to assert (MRCF). An advocate of ORT may try to explain the infelicity of an utterance of (MRCF) by showing that such an utterance is epistemically irresponsible. This, however, requires (MRCF) to express a proposition that is incompatible with a possibility raised by (MCF). Meanwhile, there is no such possibility. After all, if it is impossible for Meinongianism to be correct, it is also impossible for Meinongianism to be correct and for some objects to not exist.
Alternatively, one may combine Moss’s view with the proposal of Emery and Hill. This will result in considering µ correlated not with a possible world but with an indirectly expressed, true proposition. Thus, in the case of (MCF), µ has it that (MSP) ‘According to Meinongianism, some objects do not exist,’ and the proposition φ expressed by (MRCF) is (MRSP) ‘According to Meinongianism, every object is red.’ While this may help overcome the problem of µ not being possible, it still does not explain the infelicity of the assertion of (MRCF). This is due to the failure to satisfy condition (ii) of EI, which has it that (MRSP) has to be inconsistent with (MSP). Since, in virtue of ORT, both are vacuously true, there is no inconsistency between them. As Moss claims, the question of whether there is any inconsistency between µ and φ is meant to be determined by conversational common ground (Stalnaker, 2002; Moss, 2012: p. 560). Thus, unless ORT is not part of the common ground, there is no inconsistency between (MRSP) and (MSP). Accordingly, since there is no possible µ raised by (MCF), there is no reason for which an utterance of (MRCF) should be considered epistemically irresponsible.Footnote 13
The assumption about µ being possible not only makes EI difficult to apply to the problem of counterpossibles but also raises a worry about whether the notion of epistemically irresponsible utterances provides a complete explanation of RSS. This worry relates to those case of RSS that are sequences of counterpossibles, e.g., (K) and (K*):
(Ka) If Kate had squared the circle, she would have become a famous mathematician.
(Kb) But if Kate had squared the circle and it had never been revealed, she would not have become a famous mathematician.
Regardless of whether one favors ORT or UNORT, both (Ka) and (Kb) are considered true. Moreover, the above sequence is a felicitous one. As opposite to this, it seems that advocates of ORT and UNORT will consider the sequence below infelicitous:
(K*a) If Kate had squared the circle and it had never been revealed, she would not have become a famous mathematician.
(K*b) But if Kate had squared the circle, she would have become a famous mathematician.
In order to justify the irresponsibility of an utterance of (K*b), there would have to be a possibility raised by (K*a) that would be incompatible with a proposition expressed by (K*b). Since it is impossible to square the circle, it is also impossible to square the circle and to never reveal doing so. Likewise, if µ is meant to be a true proposition and not a possible world, in the case of (K*b) it ought to be ‘If Kate had squared the circle, it might never have been revealed that she did.’ Due to the necessary truth ‘If Kate had squared the circle, it would have been revealed that she did,’ the mentioned µ is necessarily false. Hence it is not a salient possibility. That means that there is no µ raised by (K*a). Thus, there is no reason for considering an assertion of (K*b) epistemically irresponsible.
Sequences (K) and (K*) provide motivation for an alternative explanation of the pragmatics of counterfactuals—one which takes into consideration utterances of counterpossibles. Importantly, such an explanation ought to be of interest to both ORT and UNORT. While in the case of UNORT it would aim to explain the infelicity of sequences such as (K*), in the case of ORT it ought to go beyond that and explain why it is infelicitous to assert the vast majority of (vacuously) true counterpossibles. The question of whether it is possible to provide an explanation of RSS without rejecting ORT is an important and open one, but I do not intend to answer it here.
Arguments and counterpossibles
Another way of addressing the question of the reasons for which we tend to assert (7) and not (7*) is to recognize an important difference in the epistemic aspects of these counterpossibles. This difference is related to reductio ad absurdum arguments.Footnote 14 As a matter of fact, many of such arguments are counterfactuals. In some cases, their antecedents express impossibilities, which—in virtue of ORT—makes them vacuously true. One should not, however, consider every counterpossible to be a reductio ad absurdum argument. Compare (7) and (13CF). As already pointed out, the first one expresses the problematic consequence of conjoining modal realism’s understanding of ‘p is true in world w’ and the notion of impossible worlds. It is difficult to find a similar argument that could be expressed as (13CF). Nevertheless, both of them are vacuously true.
The above shows that there is a difference between a proof or an argument for the necessary falseness of ‘A’ (e.g., (7)) and a conditional of which ‘A’ is an antecedent, and of which we know (or assume) that it is impossible for ‘A’ to be the case (e.g., (7*), (13CF)). As Timothy Williamson noticed:
the mere truth of a claim does not permit one to rely on it in a proof. For that, the claim must have some epistemically appropriate property: it must be an axiom, or have been already proved, or the like […] More generally, assertibility requires some epistemically appropriate status, such as being known by the asserter, for which truth is insufficient. (Williamson, 2016a: pp. 5–6)
Thus, neither Andrew Wiles could simplify his proof of Fermat’s Last Theorem by saying, ‘If Fermat’s Last Theorem were false, 2 + 2 would be 5′ (Williamson, 2016a: p. 5) nor David Lewis could simplify his argument by saying ‘If there were an impossible world, every object would be red.’ This shows that for a claim to be a proof, the claim has to be not only true, but it also has to be known to be true. Because of this the orthodoxy’s explanation of unorthodoxy’s intuitions about the falseness of counterpossibles such as (13CF) or (14CF) could be that, while these are actually true, due to a lack of the above-mentioned ‘epistemically appropriate property,’ they are not asserted.
Although increasing the standards for a true claim to be a proof is reasonable, this does not help to justify the claim that (13CF) or (14CF) does not satisfy a proper condition of assertion. Assuming that ‘A’ is impossible, the mere acceptance of ORT’s thesis justifies the assertion of any counterfactual of which ‘A’ is an antecedent. Thus both (13CF) and (14CF) (and any other, of which it is known that its antecedent is impossible) have the mentioned epistemic property after all. This property is guaranteed by the acceptance of ORT’s thesis. Just as the disjunction introduction and the knowledge of the truth of A proves the truth of A \(\bigvee\) B.
Hence, in virtue of ORT, if it is known that ‘A’ is impossible, every ‘A > C’ is known to be true, and one is justified in considering every one of them to be a proof. What differentiates (7) and (7*) is what they are proofs of. The first one proves (by reductio ad absurdum) the falseness of the hypothesis of the extension of modal realism. The second assumes what (7) proved, and along with ORT’s thesis, proves one of the consequences of the hypothesis of the extension of modal realism. Consequently, the truth of every counterpossible of the form ‘A > C,’ where ‘A’ expresses (implicitly or explicitly) a truth of a necessarily false theory, is a proof of any arbitrary consequence of this theory. Thus, ORT allows for proving that every necessarily false theory has exactly the same consequences, which makes debates over them either pointless or impossible. Once again, this is in conflict with the fact that there is more than one necessarily false theory, and that we can truly ascribe them different consequences.
A way of blocking that would be to say that the fact that we know the impossibility of ‘A’ being the case is not enough to prove the truth of every proposition being A’s consequent. This could be done by pointing out that when considering consequences of ‘A,’ one should abstract from its actual truth-value and modal status.Footnote 15 Accordingly, the procedure of proving that ‘C’ is a consequence of a given necessarily false theory T being correct should narrow the premises to only axioms and theorems of that theory. Since ORT’s thesis does not have to belong to those axioms or theorems, one should abstract from this thesis when proving the consequences of T being correct. This restriction would block the arbitrary consequences of necessarily false theories and at the same time allow one to indicate those consequences of T being correct that follow non-trivially (assuming that T is not trivialism). While these may sometimes differ from what the author(s) of T assumed, as long as they are consequences of T’s axioms and theorems, it would be appropriate to take them as a proof of ‘C’ being a consequence of T being true.
The above gives justice to differences between various necessarily false theories. At the same time, positing this restriction is not available to advocates of ORT. After all, that would entail considering counterpossibles in the same manner as counterfactuals with merely possible antecedents. While advocates of UNORT argue in favor of this approach, advocates of ORT are strongly against it. Further, if one could abstract from the modal status of antecedents when considering the consequences of necessarily false theories, it is not clear why the same could not be done in the cases of other counterpossibles, such as (1)–(4).Footnote 16 For this reason, UNORT appears to provide a more accurate analysis of counterpossibles and ultimately counterfactuals in general.
At the very end, it is worth to consider what may seem to be a problematic consequence of UNORT. It is commonly claimed that ‘any logical truth of the form A → B gives rise to the true conditional A > B’ (Priest, 2009: p. 331).Footnote 17 Assuming that the actual world is ruled by classical logic and ex contradictione sequitur quodlibet, every counterfactual with logically inconsistent antecedent would be true. Thus both (V): ‘If it had been raining and not raining at the same time, the Vatican would have won the World Cup’ and (V*): ‘If it had been raining and not raining at the same time, the Vatican would not have won the World Cup’ are true. This could put into a question the plausibility of unorthodoxy’s intuitions and tip the scale in favor of orthodoxy.
Nevertheless, it does not have to be so. The truth-value of a counterpossible—just as the truth-value of any other counterfactual—often depends upon the context (Vander Laan, 2004). Thus as long as we are interested in what in virtue of classical logic are consequences of contradiction being true, every counterpossible with logically impossible antecedent is vacuously true. This, however, does not depends on whether one believes in ORT or UNORT, but on what are theorems of classical logic. Accordingly, assuming this particular context of conversation, advocates of ORT and advocates of UNORT can agree on what are truth-values of (V) and (V*). However, as pointed above, this is not the only context in which we make use of counterpossibles. Thus one can find a context where (V*) is true and (V) is false, or perhaps even a context where none of them is true (Berto et al., 2018: 707). Since what is a logical truth of classical logic does not have to be a truth of a given non-classical logic, it is fair to assume that the mentioned relation between ‘A → B’ and ‘A > B’ is always restricted to a particular logic. Hence, just because ‘A → B’ is a logical truth of logic L1, this does not yet mean that ‘A > B’ is simply true, but rather that it is true in virtue of L1. Because of this, there is no tension between UNORT and the relation between logical truths and truth-value of counterfactuals.