In their response to Kearns, Turner and Capes use ‘\(\alpha \)’ to designate the actual world, and consider the world-indexed truth that Stephen murders someone in \(\alpha \) instead of that Stephen actually murders someone. They say the following:
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We deny that Stephen makes it the case that he murders someone in \(\alpha \), for the following reason. Possible worlds are maximally consistent states of affairs. \(\alpha \) is thus a maximally consistent state of affairs a defining feature of which is that it has the state of affairs ‘Stephen murders someone’ as a component. We contend that what makes world-indexed truths of the form ‘X happens in world w’ true is the fact that the state of affairs ‘X happens’ is compossible with the conjunction of all the other states of affairs that make up w. What makes ‘Stephen murders someone in \(\alpha \)’ true on this account is the fact that the state of affairs ‘Stephen murders someone’ is compossible with the conjunction of the other states of affairs of which the maximally consistent state of affairs \(\alpha \) is composed. Notice, though, that Stephen doesn’t make it the case that ‘Stephen murders someone’ is compossible with the other states of affairs of which \(\alpha \) is composed. Which states of affairs are consistent with which is not determined, even in part, by human behavior. Hence, Stephen doesn’t make it the case that he murders someone in \(\alpha \) (2018: p. 585).
Turner and Capes say that the sentence ‘Stephen murders someone’ is a state of affairs, which it is not. We believe what they mean is that the sentence ‘Stephen murders someone’ expresses a state of affairs or, better, a proposition, which is what is typically taken to be a truth-bearer. States of affairs, by contrast, are usually said to obtain or fail to obtain.Footnote 14 We should note too that Turner and Capes do not use the gerund form for states of affairs, as it is commonly done, and so it is not clear whether, for them, states of affairs are really distinct from propositions. Either way, the arguments presented here, in particular, the arguments in the next section, still seem to be applicable.Footnote 15
Now the proposition (or state of affairs) that Stephen murders someone in \(\alpha \) is apparently taken to be the same as, or at least equivalent in some sense to, the proposition that Stephen actually murders someone. In fact, the whole argument developed by Turner and Capes is intended as a defense of the claim that Stephen is not even partly morally responsible for the truth of the former proposition. (It is worth pointing out that Kearns (2011: p. 310) himself thinks the propositions in question are equivalent.) But whether these propositions are the same or, in some sense, equivalent, is not entirely obvious, since the latter proposition would be formalized as (3) above, in a first-order modal language with operators, whereas the former proposition would seem to require a richer language supplemented with a binary ‘truth-at-a-world’ predicate relating formulas to worlds according to which, roughly, T(p, w) would state that p is true at w. But even if we could derive the biconditional \(T(p,\alpha )\equiv @p\) or its necessitation in this richer language, this would not mean that \(T(p,\alpha )\) and @p are the same proposition, although they would be materially or maybe necessarily equivalent relative to the structure(s) in question. Indeed, since both propositions would presumably be necessarily true if true at all, and so true at every possible world, the interesting question here is, we think, whether they are identical, and not just true at the same worlds.Footnote 16 And depending on how fine-grained one takes propositions to be, these propositions could be distinguished, for example, simply on the basis of the different syntactic constructions of the sentences expressing them. For example, King (2007) provides an account of structured propositions according to which, roughly, the syntactic structure of the sentence expressing the proposition constitutes the structure of the proposition, and so difference in syntactic construction is sufficient for difference in proposition expressed. According to this account, ‘\(T(p,\alpha )\)’ and ‘@p’ would express distinct propositions. But, of course, Turner and Capes could reject this very fine-grained view of propositions. They could hold instead that propositions are coarse-grained in the sense of being identified with the sets of possible worlds at which they are true, or with functions from possible worlds to truth-values. Proponents of this view, for example, include Stalnaker (1976: pp. 79–80) and Lewis (1986: p. 53). According to this view, there is only one necessary truth, i.e. the set of all possible worlds. So the proposition expressed by, say, ‘\(2+2=4\)’, is the same as that which is expressed by ‘@p’, provided that the latter is true. But this view of the nature of propositions, combined with Turner and Capes’ claim about what makes a world-indexed proposition true, would result in the claim that what makes the proposition expressed by ‘\(2+2=4\)’ true is the fact that the state of affairs Stephen’s murdering someone is compossible with the conjunction of the other states of affairs composing \(\alpha \), which seems to be false. Indeed, it does not seem to us that Turner and Capes presuppose this coarse-grained view of the nature of propositions. Perhaps they assume a broadly Fregean view of propositions according to which they are composed of Fregean senses, or something in the vicinity. This is a much more fine-grained account of propositions in comparison to the sets of possible worlds view. For example, ‘Hesperus is Phosphorus’ and ‘Hesperus is Hesperus’ would express different propositions according to this view, even though both propositions are necessarily true. Yet, Fregean propositions are not as fine-grained as propositions construed according to King’s account, for instance. While ‘Hesperus is Phosphorus’ and ‘Phosphorus is Hesperus’ presumably express the same Fregean proposition, these sentences do not express the same proposition according to King’s view, since the constituents at the terminal nodes in these propositions will differ. However, ‘\(T(p,\alpha )\)’ and ‘@p’ may plausibly fail to express the same Fregean proposition. If one overhears a conversation in which a reliable source says that Stephen has actually murdered someone, one will have good reasons to believe that Stephen is actually a murderer. But if all one hears is that Stephen has murdered someone in \(\alpha \), one might need further information to believe that Stephen has actually committed a murder. One might need to know that ‘\(\alpha \)’ is being used as a name for the actual world. More generally, a rational agent could believe that @p without also believing that \(T(p,\alpha )\), provided the agent fails to believe that \(\alpha \) is the actual world, and so the sentences ‘\(T(p,\alpha )\)’ and ‘@p’ can differ in their cognitive significance, in which case the thoughts or propositions expressed by them can also be different.Footnote 17
It should be noted, however, that there are views according to which ‘@p’ would express the proposition that p is true at the actual world \(\alpha \). Soames (2007) defends a view according to which ‘@p’ expresses the Russellian proposition that p is true at \(\alpha \), where \(\alpha \) is the actual world-state. This would raise questions about the commitment of Turner and Capes (and Kearns, for that matter) to Russellian propositions, although it could provide enough motivation for their claim. Notwithstanding, this account may not be necessary for the argument presented by Turner and Capes. The identification of \(T(p,\alpha )\) and @p might turn out to be inessential for their purposes, as Turner and Capes could have said instead that, more generally, what makes the proposition expressed by ‘@p’ true is the fact that the state of affairs corresponding to the proposition expressed by ‘p’ is compossible with the conjunction of the other states of affairs of which the actual world is composed, where a state of affairs corresponds to a proposition if it is described by that proposition. We are not sure if Turner and Capes would accept this revised proposal, although it seems more natural to us in the context of a response to the ‘actually’ counterexample to (A). Still, there would need to be a plausible account of the relation posited here between propositions and states of affairs. This relation might not be one-to-one, for example. If Stephen is also named ‘Bill’, then the propositions that Stephen is a murderer and that Bill is a murderer seem to describe a unique state of affairs, namely, Stephen’s being a murderer. On the other hand, if propositions are Russellian, and names directly refer, these propositions will presumably be identical. Regardless, let us just assume for the sake of argument that \(T(p,\alpha )\) and @p are the same proposition, if only to keep changes relative to Turner and Capes’ argument to a minimum.
Following our previous remarks, the counterexample involving ‘actually’ depends on the claim that Stephen makes it the case that the proposition that he actually murders someone, or murders someone in \(\alpha \), is true. If so, then it will follow that he is indeed (at least partly) morally responsible for the truth that he murders someone in \(\alpha \), since this proposition will be true (at least partly) because of what he did. Turner and Capes do not seem to deny this. What they deny is that Stephen makes it the case that he murders someone in \(\alpha \). Why? One crucial premise is their account of what makes world-indexed truths true, that is:
- (P):
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What makes [the proposition or state of affairs expressed by] ‘Stephen murders someone in \(\alpha \)’ true is the fact that the state of affairs Stephen’s murdering someone is compossible with the conjunction of the other states of affairs of which the maximally consistent state of affairs \(\alpha \) is composed.
And underlying (P) is a certain notion of possible worlds, to wit:
This premise concerning the nature of possible worlds motivates a more general account of truth-at-a-world: The proposition expressed by ‘Snow is white’ is true at a world w if and only if the state of affairs snow’s being white is compossible with the conjunction of the other states of affairs of which the maximally consistent state of affairs w is composed. Now the claim is that if one accepts (PW) and (P), thereby agreeing with Turner and Capes on what makes world-indexed truths true, one should also agree that Stephen will not make it the case that he murders someone in \(\alpha \).
Let us attempt to spell out the above argument in a bit more detail, while hoping that our reconstruction remains faithful to what Turner and Capes originally had in mind. Say that states of affairs s and t are compossible if and only if there exists a possible world relative to which both s and t obtain, whereas propositions p and q are compossible if and only if there exists a possible world where both p and q are true. (Similarly for any (possibly infinite) number of states of affairs and propositions.) Premise (P) seems to require, additionally, that there be a conjunction of all the states of affairs composing a world minus a single state of affairs—in this case, Stephen’s murdering someone. This in turn seems to call for a certain ‘subtraction’ operation on worlds according to which, for every possible world w and for every state of affairs s, there is a state of affairs \(\bigwedge w^{-s}\) which is the conjunction of all the states of affairs composing w with the exception of s. Turner and Capes provide no argument in favor of this subtraction principle. And, indeed, this principle brings to light a further possible difficulty for this defense of rule (A). For even though they say that a possible world is just a maximally consistent state of affairs, the principle of subtraction just stated seems to suggest that possible worlds are composed of states of affairs as conjuncts.Footnote 18 And even if possible worlds are maximally consistent states of affairs, it is not obvious why one should take them to be composed in this way. Notwithstanding, the principle of subtraction can be modified to avoid this worry, by saying only that those conjunctions are included in the corresponding possible worlds, that is:Footnote 19
- (Sub.):
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For every possible world w and for every state of affairs s, there is a conjunctive state of affairs \(\bigwedge w^{-s}\) which is the conjunction of all the states of affairs included in w with the exception of s.
Let m stand for the state of affairs Stephen’s murdering someone. Then, by (Sub.), the state of affairs \(\bigwedge \alpha ^{-m}\) exists. (Note that if m were not included in \(\alpha \), \(\bigwedge \alpha ^{-m}\) would just be \(\alpha \).) Now Turner and Capes’ principle (P) can be reformulated as follows:
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(9)
The compossibility of m and \(\bigwedge \alpha ^{-m}\) is what makes it the case that \(T(\exists x Msx,\alpha )\),
from which they seem to suggest we can draw the following consequence:
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(10)
Stephen does not make it the case that m and \(\bigwedge \alpha ^{-m}\) are compossible,
and so:
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(11)
Stephen is not even partly morally responsible for the fact that \(T(\exists x Msx,\alpha )\).
Given the identification of propositions \(T(\exists x Msx,\alpha )\) and \(@\exists xMsx\), Turner and Capes conclude that Stephen is not even partly morally responsible for the fact (or truth) that \(@\exists xMsx\). In fact, they claim that no one is responsible for this fact, and so (4), from the argument given by Kearns, is false.
That seems to be the main argument from Turner and Capes in defense of rule (A). Now, is it sound? We do not think so. At the very least, we believe that this defense of rule (A) is not persuasive, and in the rest of this article we will lay out our reasons for why we believe so.
First, this defense of rule (A) relies on a certain conception of possible worlds, namely, (PW). But whether the direct argument is valid is a question which is in principle independent of idiosyncratic conceptions concerning the nature of possible worlds. In Sect. §4 we discuss a more detailed view according to which possible worlds are maximally consistent states of affairs. But it must be pointed out that there are multiple views concerning the nature of possible worlds or, more generally, of what type of entity is involved in what makes a proposition true. For instance, one could hold, as Lewis (1986) did, that possible worlds are concrete entities instead of abstract states of affairs, and this view does not seem to require principles such as (P). By contrast, one could hold that propositions are true (false) relative to possibilities (Humberstone 1981), situations (Barwise and Perry 1983), or states (Fine 2017a, b), for example. That is, entities which might sometimes be taken to ‘make up’ a world but which are not themselves full possible worlds. There is nothing in those views that seem to require an explanation of world-indexed truths along the lines of (P). Of course, whether the ‘actually’ counterexample to rules (A) and (Alpha) holds in alternative frameworks is also a further issue that will depend on the various semantic entries for the actuality operator. Still, there is also nothing in the traditional semantics for modal logics built upon a set of ‘possible worlds’ requiring these to be identified intuitively with maximally consistent states of affairs. It would be surprising if the direct argument (or the consequence argument) demanded this, and it would be desirable that it did not.
Second, and apart from this issue, it is not clear how exactly is (10) supposed to follow from (9), if at all. The only thing said in favor of this inference is that “Which states of affairs are consistent with which is not determined, even in part, by human behavior”. (2018: p. 585) And this seems to be considered an a priori truth for Turner and Capes. We confess, however, that whether agents can be responsible for the consistency or compossibility of certain states of affairs is not the kind of thing we have any robust intuitions about. Perhaps the claim is motivated by the assumption that it is a necessary truth whether a certain state of affairs is consistent with another, and therefore no one could be even partly morally responsible for such things, since no one could be even partly morally responsible for necessary truths. But if this is the reason, then it seems to be question-begging, for the claim that no one could be even partly morally responsible for necessary truths is precisely what is at stake here. It might be that there is some such principle in the vicinity that is warranted a priori, and it might be that this principle would justify the inference in question. But we are not sure what principle would serve this purpose, much less if it is warranted or even plausible.Footnote 20
Third, even if the inference from (9) to (10) is warranted a priori and the argument is valid, why should one accept (P) and so (9)? We are persuaded by Murder! simply because we think the proposition expressed by ‘Stephen murders someone in \(\alpha \)’ is made true at \(\alpha \) (at least partly) because Stephen murders someone in \(\alpha \). The truth of that proposition is said to depend on the world. It is because Stephen murders someone in \(\alpha \) that the proposition expressed by ‘Stephen murders someone in \(\alpha \)’ comes out true. This seems to be in agreement with the traditional Aristotelian idea that propositions are true or false (at a world w) because of the way the world (w) is:
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This is clear, in the first place, if we define what the true and the false are. To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true; so that he who says of anything that it is, or that it is not, will either say what is true or what is false (Metaphysics 1011b, pp. 24–29)
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If there is a man, the statement whereby we say that there is a man is true, and reciprocally—since if the statement whereby we say that there is a man is true, there is a man. And whereas the true statement is in no way the cause of the actual thing’s existence, the actual thing does seem in some way the cause of the statement’s being true: It is because the actual thing exists or does not that the statement is called true or false. (Categories 14b, pp. 15–22)
The addition we make to this Aristotelian idea is the relativization to worlds. We say:
And since whether Stephen murders someone in \(\alpha \) is, presumably, a matter of his own choice, we think the proposition made true because of this is too a matter of his own choice: By (freely) doing something one (freely) makes a proposition true.Footnote 21
So, why should we reject this explanation in favor of the Turner and Capes account? Unfortunately, the authors provide no argument for (P). What we have here seems to be a conflict between two answers to the question of what makes the world-indexed proposition that Stephen murders someone in \(\alpha \) true. And the answer to this question is crucial to determine whether or not Stephen is (at least partly) morally responsible for the truth of that world-indexed proposition. The first, the Aristotelian answer, says that what makes the proposition expressed by ‘Stephen murders someone in \(\alpha \)’ true is Stephen murdering someone in \(\alpha \), which is something that is at least partly up to Stephen. According to this view, truth depends on the world. The truth of a proposition at a world depends on how that world turns out. The second, Turner and Capes’ answer, appeals to the compossibility of states of affairs. The truth of a proposition at a world depends on whether a corresponding state of affairs is compossible with the conjunction of every other state of affairs which make up or compose (or are included in) that world, which is in turn motivated by (PW). Which one should we accept?
We think one should favor the Aristotelian view. It is uncommitted with respect to a particular conception of the nature of possible worlds. It is weaker than some versions of the correspondence theory, to wit, those requiring that for every truth there is something corresponding in the world in question. And it is also weaker than some versions of truthmaker theory, to wit, those requiring that for every truth there is a truthmaker in the world in question. But it motivates such views (although they are not necessary for our point), and it does so precisely because it amounts to a trivial fact about truth, namely, that it is contingent upon how the world turns out—at the very least, in a great number of cases. We claim that this is true of certain world-indexed propositions as well: They are true because of the way the world in question turns out; and they are up to someone if their truth depends on what someone freely does.
In Lampert and Merlussi (2021) we suggest that the claim that truth depends on the world can be understood via a truthmaker relation, or the positing of some sort of grounding relation. But it is clearly unnecessary to endorse either of these views in order to hold on to the more basic and ecumenical Aristotelian view described here. We aim to be neutral with respect to such views, for we think the idea that the truth of propositions expressed by sentences such as ‘@p’ depends on how the actual world turns out is compatible with many developments of truthmaker theory, correspondence theory, and different understandings of ground.
It might be objected that while the direct argument should not rely on one specific account of the nature of possible worlds, it should not rule one out either. However, while the Aristotelian answer seems unproblematic, we believe things are different with respect to (P). Apart from the issues we have raised here concerning some of the principles and inferences in Turner and Capes’ defense of rule (A), and the fact that there is an orthodox Aristotelian account of what makes a proposition true that combines very well with our claim, namely, that one can be (at least partly) responsible for the truth of certain world-indexed propositions, we shall argue in the next section that the Turner and Capes answer is, given plausible assumptions, subject to more serious difficulties. It deserves mention that our critique is not intended in the spirit of hostility. Rather, our point is that the Turner and Capes response (which is the most up-to-date incompatibilist reply to the objection) appeals to a framework that lacks detail in terms of the specific theory of the nature of possible worlds that is assumed. And when we attempt to fill in the gaps, by introducing some principles about states of affairs which seem to us at least as plausible as principles such as (Sub.), we can show that there are no possible worlds in the sense envisaged by (PW), i.e. the theory of possible worlds motivating (P).