Omission Impossible (Penultimate draft; final version in Philosophical Studies, 2016) Sara Bernstein Duke University

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Abstract: This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements
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Abstract: This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events, such as If the mathematician had not failed to prove that 2+2=5, the math textbooks would not have remained intact. After providing an account of impossible omissions, the paper argues for three claims: (i) impossible omissions play a causal role in the actual world, (ii) causal counterpossibles have broad applications in philosophy, and (iii) the truth of causal counterpossibles provides evidence for the nonvacuity of counterpossibles more generally. Omission Impossible (Penultimate draft; final version in Philosophical Studies, 2016) Sara Bernstein Duke University Right now, you omit to do to many things: clean your office, write that overdue referee report, and throw the winning pitch in the World Series, to name a few. Omissions (roughly, events that do not occur) are causally relevant: because of them, your office is messy, an author waits in anticipation, and your dreams of being a professional baseball player remain unrealized. In addition to the everyday things you omit to do, you also fail to do impossible things, such as prove that 2+2=5, and disprove that 5 is a prime number. Because of these omissions, mathematical laws remain intact, children s mathematics textbooks remain unchanged, and your bank account contains exactly what it does. Impossible omissions raise important and deep metaphysical questions that span ontology, causation, and semantics: what are impossible omissions? Are metaphysically impossible events causally relevant to the actual world in the way that possible events are? Can counterfactual causal claims involving impossibilia be true or false nonvacuously? This paper lays the groundwork for answering such questions. I provide a framework for understanding metaphysically impossible omissions and omissive causal statements, and argue that they are causally relevant to actual-world events. In Section 1, I provide some preliminary definitions and clarifications. In Section 2, I motivate and endorse the view that omissions are possibilities. I then extend my framework to account for metaphysically impossible omissions (Section 3.1). In Section 3.2 I argue that causal 1 counterpossibles are non vacuously true and provide evidence for the non vacuity of counterpossibles more generally. In Section 3.3, I suggest that impossible omissions play a causal role in the actual world. I then suggest that causal counterpossibles are philosophically helpful to a variety of debates. 1. Preliminaries Counterfactuals are conditional subjunctive statements of the form If c hadn t occurred, e wouldn t have occurred. Causal counterfactuals are such statements imbued with causal content; for example, If I hadn t dropped the glass, it wouldn t have shattered. Counterpossibles are counterfactuals whose antecedents appeal to impossible worlds; for example, If Hobbes had squared the circle, small children in rural Afghanistan would not have cared. The topic of my discussion will be causal counterpossibles: statements that are counterfactual, causal, and whose antecedents run contrary to metaphysical possibility. Causal counterpossibles are generated by omissive causal statements, or statements of the form If x hadn t failed to y, z wouldn t have occurred. All causal counterpossibles are omissive, since impossibilities are never actualized. 1 On the surface, such statements seem to be irredeemably abstract, or of no broader interest. But causal counterpossibles are of interest for two reasons. First, there has been a surge of interest in general counterpossibles in recent years; in particular, with respect to whether they can be true or false non-trivially. Second, causal counterpossibles generate intuitively true causal claims. Consider the mathematician who is scrambling to prove a prestigious theorem in order to win the Fields medal. After she fails, she begins talking about what would have happened if she hadn't failed to prove that 2+2=5: If only I hadn t failed to prove that 2+2=5, that medal wouldn t have gone to my rival!, she exclaims. Intuitively, this statement and others like it seem true, and they deserve an account that can make sense of them. Thus far, however, no one has analyzed these sorts of statements, for it seems 1 For example, the counterfactual If Billy hadn t squared the circle, the mathematicians wouldn t have been surprised is causally infelicitous, since there is no metaphysically possible world in which he does square the circle. 2 unlikely that impossibilia can enter into causal relations. But given some simple assumptions about causation and causation by omission, impossible events play a causal role in the actual world. Or so I will argue. Counterfactuals interact with problems about causation insofar as many take causal dependence to involve counterfactual dependence. 2 According to the standard Lewisian model, the counterfactual If c hadn t occurred, e wouldn t have occurred is true if the worlds closest to ours in which c occurs are worlds in which e also occurs. For example: If Billy had not thrown the rock, the window would not have shattered, is true if the possible worlds closest to ours in which Billy throws his rock are also ones in which the window shatters. The literature on the counterfactual theory of causation is vast, and I will not recap it here. But I will assume that counterfactual dependence plays a central role in causation. Finally, following Nolan (1997), Berto (2009), Yagisawa (1987), Van der Laan (2004) and Jago (2015), I will assume the existence and philosophical intelligibility of impossible worlds. I take no stand on what they are, but will assume that they can be ordered by similarity and ground the truth of statements with metaphysically impossible referents. 2. Omissions as Possibilities causal claim: To get a grip on impossible omissions, let us first begin with an ordinary omissive (Plant) If I hadn t failed to water your plant, the plant wouldn t have died. There are several puzzles concerning such a claim. First: what, exactly, is the referent of the failure to water the plant? Second: is the omission causal? Third: what are the semantics for such a claim? I will briefly treat these questions in turn. What is an omission? Omissions are not actual things, for there is no single event to which to reduce the omission. For example, suppose that the plant-watering takes 2 See Lewis (1973, 1999), and more modern interventionist theories such as Woodward (2003). 3 thirty minutes. To which thirty-minute period does the plant-watering reduce?: 10-10:30am? 11:07-11:37pm? There is no single obvious candidate for the reduction base. Omissions are not non-things, for then they cannot play the explanatory, causal, and predictive roles that they do. 3 Omissions play central roles in our scientific, metaphysical, and moral theories; thus a desideratum for a theory of omissions is that we model their existence accordingly. The concept of an omission in a causal context is counterfactual: an omission is an event such that, had it occurred, another event would not have occurred. Thus I endorse an analysis according to which omissions are possibilities: specifically, an omission is a tripartite metaphysical entity composed of an actual event, a possible event, and a contextually specified counterpart relation between them. 4 For example: suppose that while I should have been watering your plant, I was instead singing karaoke. The omission is composed of my singing karaoke (the actual event), my watering your plant (the possible event), and a contextually specified counterpart relation between them. I will assume this account here in order to build on it. A few clarifications will help make its details clearer. First: the account makes use of de re predication for events. Roughly, an event has the de re property P if it is possibly the event P. De re predication for events works much the same way it does for objects: just as a lump is possibly a statue, a particular event is possibly another event. For example, my karaoke-singing is possibly a plant-watering; this paper-writing is possibly a sun-bathing. Taking omissions to be possibilities requires the use of two major modal notions: counterpart theory, and distance from actuality. I ll describe both briefly. I accept a counterpart relation between events, similar to the one Lewis holds for objects. Events are worldbound, but have counterparts at other possible worlds. Counterparthood is a matter of contextually specified similarity between events. For example, the omissive claim Sara failed to water the plant contextually identifies a salient similarity between the karaoke-singing and the plant-watering events (namely, 3 Varzi (2006) suggests that omissions can provide causal explanations without referring to actual things. 4 For an extended argument for such an analysis, see Bernstein (2014). 4 Sara s involvement.) Omissive claims by nature specify this relationship. Even omissive claims that fail to make explicit reference to an actual event (for example, There was no karaokesinging ) implicitly implicate an actual-world event ( There was no karaoke-singing at the time and place it should have occurred and by the person that should have performed it. ) Omissive claims differ from absences insofar as the latter are straightforward negative existential quantifications over events. For example, There was no karaoke singing has an absential reading according to which no actual-world event is implicated. The same statement can have an absential or an omissive reading. Like Lewis 5, I take distance from actuality to be a matter of similarity between worlds. A possible world in which everything is exactly the same as this one except that I have blue hair is more similar, and thus closer, to this one than a world entirely made of onions. Distance from actuality distinguishes between omissions and mere absences. Omissions, on my view, occur close to actuality; absences occur far from actuality. Absences are the entire class of things that don t occur. The threshold between an omission and an absence is vague. Consider the distinction at work in the following claims: (a) I failed to water the plant. (b) Barack Obama failed to water the plant. (c) Abraham Lincoln failed to water the plant. Intuitively, the reason that (b) and (c) seem strange is that the worlds in which Obama and Lincoln water the plants are much farther from actuality than the world in which I water the plant. My watering the plant is an omission, but Barack Obama s and Abraham Lincoln s failures are absences. There are strange contexts according to which Barack Obama s failure to water the plant counts as an omission (for example, he secretly promised to water it, but failed); but most contexts do not specify the relevant contextual 5 See Lewis (1973a). 5 similarity between the event in which he is involved at the actual world (say, a speech to the UN), and the plant-watering. The locution x failed to y most often indicates an omissive, rather than an absential, claim. While it is true that no one watered the plant, it seems strange to say that Barack Obama and Abraham Lincoln failed to water the plant. This is because the worlds closest to actuality are the ones in which I watered it. Closeness grounds truth conditions for omissive claims. 6 Whether or not omissions are causes (as opposed to causal explanations or something merely cause-like ) is controversial. Those who hold oomph or process theories of causation cannot accommodate causation by omission, since there is no thing or event from which energy can by transferred. Counterfactual theorists, on the other hand, generally endorse causation by omission, for omissions easily fit into counterfactuals of the form If I hadn t failed to water the plant, the plant wouldn t have died. My view occupies a middle ground between denying causation by omission and granting omissions full efficacy: omissions are causally relevant. Relevance is a property an event has in virtue of being a counterpart of an actualized event and being located at a world reasonably close to actuality. Causal relevance is a kind of causal relationship that does not require oomph or transfer of energy but nonetheless grounds causal claims via counterfactual dependence. 7 I will not argue for this view in detail, but I will motivate it briefly. Causally relevant omissions often play predictive, explanatory, and moral roles of causes simpliciter. By way of illustration, consider the following two cases: (Button) Pressing a button at time t will cause a weapon to detonate and kill innocent civilians. 6 One might be worried that norms are doing the work in ordering worlds; for example, my promise to water the plant places the world where I do order it closer to actuality. But I do not take norms to order worlds. Anyone in close proximity to the plant could have watered it, and thus omissively causes its death. And there are true omissive claims involving no agents at all; for example, The drought caused the famine specifies the nearby world in which the rain does, in fact, fall. 7 See my (2014) and Possible Causation (MS) for a view that possible and actual causation are determinates of a common determinable. 6 (Modified Button) Failing to press a button at time t will cause a weapon to detonate and kill innocent civilians. Whether or not the weapon is detonated because I press the button or fail to press it, there are not important asymmetries between such causes. Either the button-pushing or the failing-to-push-the-button predicts whether the weapon will be detonated, and explains why it is. And I am morally responsible for the killing of the civilians in either scenario. For theoretical purposes, there is no principled reason to distinguish between causally relevant events and actual causes. Causation theorists have struggled, in recent years, to generate a theory of causation that both vindicates productive intuitions roughly, causation as a transfer of conserved quantity from one thing to another with dependence intuitions roughly, causation as counterfactual dependence between one event and another. 8 Productive intuitions track energy transfer and spatiotemporally local causal chains; for example, one domino knocking over another. Counterfactual intuitions largely track dependence without direct energy transfer: for example, my call to a friend in Tokyo causing her to pick up the phone. Omissions do not participate in energy transfer or production. But if we are to account for the causal status of omissions, then we must accept that their participation in true causal counterfactuals generally suffices for some sort of causal relationship. I call this relationship relevance so as not to confuse it with oomph causation, and also to suggest that which omissions turn out to be causally important is partly a matter of context. More on this below. Recap: I ve endorsed the view that omissions are possibilities; specifically, that an omission is a tripartite entity composed of an actual event, a possible event, and a contextually specified counterpart relation between them. Omissions are causally relevant to the actual world and ground true causal claims in virtue of participating in true counterfactuals. They are truth evaluable using a framework based on counterpart theory 8 See Ned Hall s (2004) for more on this distinction. 7 and closeness of worlds. 3. Impossible Omissions With this framework in hand, we can now move on to impossible omissions. Consider the following omissive claim: The mathematician failed to prove that 2+2=5. Several questions arise. First: what is the referent of the impossible omission? Second: does the mathematician s failure to prove that 2+2=5 count as an omission in any informative sense? After all, none of us proved that 2+2=5. Does singling out the mathematician s failure communicate additional informative content? Further, there are countless things we are not doing at every moment; for example, none of us are dissolving into a horde of conscious dust particles. In what sense can we be said to be failing to do those things? Third: is the impossible omission causally relevant to the actual world? 3.1 Impossible Omissions Have Components at Impossible Worlds Extending the preceding account of omissions yields the result that an impossible omission is one whose nonactual component occurs at a metaphysically impossible world. For example, suppose that the mathematician proved that 2+2=4 when she aimed to prove that 2+2=5. The omission is a tripartite entity composed of the actual event (proving that 2+2=4), the impossible event (proving that 2+2=5), and a contextually specified counterpart relation between them. Impossible omissions differ from normal omissions in that context predicates of the actual event that its counterpart is located at an impossible world. An immediate problem arises: how can a counterpart relation obtain between an impossible event and a possible one? It is natural to think that all possible events are more similar to each other than any impossible one. If the counterpart relation is a matter of contextually specified similarity, then an impossible event must be more similar to an actual world event than a 8 possible one in order for the impossible event to count as its counterpart. This idea violates Nolan s Strangeness of Impossibility Condition (hereafter: SIC). SIC holds that any possible world is closer to actuality than any impossible one. The idea is that any possible world, no matter how weird, is less weird than a world in which, for example, logical or mathematical laws don t hold. A possible world made entirely of onions is still less strange than the world exactly like ours in every respect except in which a mathematician secretly proves that 2+2=5. The friend of impossible omissions should not abide by SIC. Context orders worlds by specifying relevant dimensions of similarity between events. For the purposes of omissive claims, the dimensions of similarity often involve a particular person (for example, the mathematician) or a particular activity (for example, working on mathematical proofs). Context naturally prioritizes these features over, for example, sameness of mathematical laws. This picture isn t as counterintuitive as one might think. Consider the event of the mathematician proving that 2+2=4 and the impossible event of the mathematician proving that 2+2=5. Intuitively, these events are more similar to each other than is the former to a random basketball game in which the mathematician does not participate: we imagine the mathematician hunched over her desk in both cases, scribbling proofs and reveling in the joy of mathematical discovery. There is more similarity between the two proving events than there is between the mathematician s proof that 2+2=5 and the metaphysically possible event of the game. 9 (I will discuss this idea more in section 3.) The account also allows for differential closeness of impossibilia. Such differences ground variance in the informativeness of impossible omissive claims. For on the surface, it seems that no impossible omission claim is truly illuminating: no one proved that 2+2=5, so what content is asserted by The mathematician failed to prove that 2+2=5? The answer is that context specifies a particular dimension of similarity between 9 Similar arguments have been made with respect to the comparative closeness of impossible worlds. Advocates for this view argue that there can be impossible worlds closer to the actual world than some possible ones. See Nolan (1997) for more on this point. 9 the actual event and the counterpart. To get a handle on t
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