Epistemic Possibilities
A Thesis submitted to the faculty of San Francisco State University In partial fulfillment of /\ -5 the requirements for -p r the Degree ^Oil- Master of Arts -K5IW In Philosophy
by David Anthony King San Francisco, California May 2017 Copyright by David Anthony King 2017 CERTIFICATION OF APPROVAL
I certify that I have read Epistemic Possibilities by David Anthony King, and that in my opinion this work meets the criteria for approving a thesis submitted in partial fulfillment of the requirement for the degree Master of Arts in Philosophy at San Francisco State University.
Asta, Ph.D. Associate Professor
David Landy, Ph.D. Associate Professor Epistemic Possibilities
David Anthony King San Francisco, California 2017
In this essay, I examine the nature of epistemic possibility. I argue that we have strong philosophical motivations to leave possible worlds semantics out of epistemic space. I argue that Lloyd Humberstone's possibility semantics better explain the domain of possibility that epistemic possibility talk quantifies over, and show how modeling epistemic possibilities in possibility semantics can explain and predict interesting features of epistemic possibility talk.
I certify that the Abstract is a correct representation of the content of this thesis.
Chair, Thesis Committee Date TABLE OF CONTENTS
Introduction...... 1 Section 1: Worlds Contra Possibilities...... 2 1.1 The Explananda...... 3 1.2 Possible Worlds Accounts of Epistemic Possibilities...... 4 1.3 Argument from the Unpalatability of Impossible Worlds...... 5 1.4 Argument from Parsimony ...... 6 1.5 Argument from Infertility...... 6 1.6 In Summary...... 7 Section 2: Modelling Epistemic Possibilities in Possibility Semantics...... 8 2.1 Possibility Semantics...... 8 2.2 Epistemic Possibilities in Possibility Semantics...... 11 Section 3: Explaining the Epistemic Might with Possibility Semantics...... 13 3.1 An Introduction to the Epistemic Might ...... 13 3.2 Epistemic Contradictions...... 16 3.3 Semantics for the Epistemic Might...... 17 Conclusion...... 19 Reference...... 20 1
Introduction Epistemic possibilities are known to have some unique features. Epistemic possibilities may be impossibilities according to all other forms of modality. While other modalities are defined by objective standards about what is and is not possible, what is epistemically possible is plausibly defined relative to an agent. Typical explanations of modality have a possibility as a possible world—a maximally specified way that a world can be. But epistemic possibilities, being relativized to an agent do not need to be ways that a world can be in any robust sense. They may well be ways that a world cannot be, according to all other forms of modality. Rather, they are ways that an agent is capable of believing the actual world to be. Where reasoning with other forms of modality tends to widen the sphere of an agent’s consideration, by allowing the agent to see what possible choices exist, reasoning according to epistemic modality is aimed at narrowing the agent’s sphere of consideration, in order to locate the contents of the actual world. When we quantify over a domain of epistemic possibilities, it is tempting to think we are quantifying over a domain of possible worlds that are not ruled out as candidates for the actual world. This is typically how epistemic possibility is cashed out. But what is epistemically possible for a given agent may not map onto a set of possible worlds. If the space of what is epistemically possible for an agent is given by what her ignorance permits, then, if she is ignorant of the right things, she may well have epistemic possibilities that are not physically, metaphysically, or even logically possible. Our options then seem to be to add impossible worlds' to the domain of quantification for epistemic possibility, or to reject that quantification over epistemic possibilities is quantification over a set of possible worlds. This essay takes the latter tack, and argues that possible worlds semantics are not adequate for explaining epistemic possibilities. I will argue that epistemic possibility talk is better explained by Lloyd Humberstone’spossibility semantics, wherein a possibility is not seen as an entity that is maximally determined. While Humberstone may not have had epistemic modality in mind when creating possibility semantics, I will argue that the considerations he levels in their favor are exactly the sort of considerations we need to have in mind when modeling epistemic possibility. In section 1 of the paper, I will explain what reasons we have for preferring
1 See Berto 2013 for a survey of impossible worlds 2
Humberstone’s possibilities to possible worlds. In section 2,1 will introduce the reader to the basics of the model theory of possibility semantics. I will then explain its philosophical motivations and offer some critiques of Humberstone’s program. I will then offer a definition of an epistemic possibility in terms of possibility semantics. In section 3,1 will argue that modelling the epistemic modal might in possibility semantics successfully explains and predicts some of the most interesting features of the epistemic might. Readers unfamiliar with the themes of this paper may find it useful to read section 3.1 before engaging with the rest of the paper.
Section 1: Worlds Contra Possibilities In this section, I will offer some philosophical motivation for abandoning Possible World Semantics for epistemic space. I will argue that these philosophical motivations should instead point us to adopting Lloyd Humberstone’s possibility semantics for epistemic space. Possible worlds are typically cashed out as maximally specified ways that a world can be.2 Humberstone’s possibility semantics model possibilities as entities that are not maximally specified.31 will use the italicized possibilities or possibility whenever I am talking about possibilities as conceived by Humberstone. I will use the same word without italics when I do not wish to make any commitment to the kind of possibility in question being either a possibility or a possible world. I will offer further details on the model theory of possibility semantics in section 2 of the paper. I will proceed in this section by first explaining some of the features a theory of epistemic possibility needs to be able to explain and how accounts employing possible worlds seek to explain these features. I will then make my case that we have reason to think that possible worlds do not have much of an explanatory role to play in accounting for epistemic possibility. I will give three arguments against possible worlds in epistemic space. The argument from the unpalatability of impossible worlds will argue that the route possible worlds theorists need to take in accounting for epistemic possibilities that are impossibilities according to non-epistemic forms of modality involves committing themselves to the existence of entities that we have good philosophical motivation to be leery of. The argument from parsimony will make the case that we reduce the size of our ontology by opting for possibilities
2 See, for example, Cappelen and Dever 2016 3 Humberstone 1981 3
instead of impossible worlds. Lastly, the argument from infertility will make the case that while possible worlds play an explanatory role in accounting for what a possibility is in the root modalities, they do not actually play an explanatory role in accounting for what an epistemic possibility is. Removing possible worlds from epistemic space does not rob us of any explanatory power.
1.1 The Explananda Talk of a strictly epistemic sense of possibility in contemporary thinking on modality goes back at least to Kripke’s Naming and Necessity. The basic idea that Kripke hit upon was that sometimes we use possibility talk when we are not talking about what is metaphysically possible, but because we don’t know what is the case. So, for example, we might take a mathematical theorem ®, whose truth or falsity is not known. We might say that
description of the possibility this student invoked. This student failed to see that the information he already possessed should be able to eliminate this possibility. This may have resulted from a poor understanding of logic or from a failure to consider the scenario in enough detail to be able to see the contradictions in the possibility he invoked. Impossibilities that are epistemic possibilities also come in many varieties that are more common and mundane. A man may hear his neighbors voice through the wall and come to recognize that voice, but not recognize the neighbor when the two meet in person. In this case, he will associate two different modal profiles with the same person, and be able to invoke possibilities with inconsistent information, where the man he saw in person and the man whose voice he hears through the wall are different people, doing different things. In all of these cases, agents are capable of forming beliefs whose informational content cannot be represented as a set of possible worlds. In each of them, we have descriptions which do not pick out a world, yet manage to be perfectly meaningful.
1.2 Possible Worlds Accounts of Epistemic Possibilities Accounts of epistemic possibility typically take possible worlds as their explanatory tool of choice.4 The basic intuition guiding such accounts is to take an agent’s information state and treat it like a Stalnekerian common ground. The idea is that we represent the information state of an agent as a set of worlds. Each new belief or item of knowledge divides the possibilities. So, if an agent comes to believe , this divides the information state according to O and ~
4 See, for example, Stalnaker 2016 5
then the question of epistemic possibilities which are impossible according to the root modalities needs to be addressed. One option would be to try to define a notion of an impossible world, and say that epistemic possibility talk quantifies over a domain of possible and impossible worlds. To be ignorant then could be defined as the inability to distinguish the possible worlds from the impossible worlds.
1.3 Argument from the Unpalatability of Impossible Worlds However, if we are to do such a thing, we have to be able to say just what an impossible world is and why it is needed to explain the explananda. I will here give my argument from the unpalatability of impossible worlds, and make the case that we have good philosophical motivation to be leery of accepting impossible worlds. Accounting for an impossible world requires saying at what point an inconsistent state of information is maximally described. Any logic where explosion is possible will have to be omitted from the closure conditions for such a world. Any explosive logic will result in all impossible worlds being the same entity, because every description and its negation will be provable. So opting for impossible worlds plausibly amounts to a rejection of classical logic. The notion of maximal description at work in possible worlds seems to be grounded by facts about ways that a world can be according to a fixed set of rules—according to some form of modality. Maximal descriptions of ways a world cannot be do not seem to have any such restrictions. What’s more, there is somethingprima facie puzzling about the fact that impossible worlds may contain contradictions, and that they are being eliminated from an agent’s information state because they contradict an agent’s information. By the fact that they contain contradictions, they should already be eliminable from an agent’s information state. The reason that an agent cannot do so seems to be that she does not know that there is a contradiction in such a world. But if the agent does not know there is such a contradiction, this seems like reason in itself to deny that such entities explain what information is in the agent’s information state. Using possibilities, we can represent the agent’s information state as not having that information at all. Information which the agent does not have or is incapable of modelling does not play into explaining the agent’s information state. 6
1.4 Argument from Parsimony My argument from parsimony is essentially an appeal to Occam’s Razor. Preferring possibility semantics in epistemic space to possible worlds reduces our metaphysical commitments significantly. Possibilities are merely possible sets of information. All the possibilities that exist are all of the sets of information that could possibly be regarded as true at the same time. Such entities need to exist, even if we appeal to impossible worlds to explain the epistemic possibilities that are not possible according to any other form of modality. Whether we call such sets of information possibilities or something else, their existence plays an explanatory role in any account of how an agent reasons about what is epistemically possible. So, for example, in the case of a mathematical theorem O, whose truth (or falsity) is not known, even if we say that the explanation for it being epistemically possible that $ is true (or false) is that there is an impossible world wherein the O is true (or false), any agent regarding O as epistemically possible still needs to be able to hold a set of beliefs that is less informationally determinate than a maximal description of a way that the world can (or cannot) be. So invoking impossible worlds commits us to the existence of a new class of entities that need to exist to explain our epistemically modal reasoning. Possibility semantics on the other hand only commits us to the belief that it is possible to hold true a set of descriptions that are less informationally determinate than a possible world. Such a belief is, I imagine, relatively uncontroversial.
1.5 Argument from Infertility I will here give my argument from infertility, making the case that neither possible worlds nor impossible worlds add anything to our explanations about what is epistemically possible. When reasoning about what is possible using the root modalities, ways a world could be factor prominently in explaining why modal reasoning is successful. This is true for at least what is physically possible. When I am making a decision about what to do, I invoke different possible actions I could take. The action I choose will be one of the possibilities invoked. Let’s call the action (I>. So, assuming that I have correctly modelled the way the world works and have a good handle on what is possible, one of those possible worlds picked out in my reasoning about what is 7
possible will become actual when I perform ®. There will be some possible world where d> is true that becomes the actual world. The reason why I can make such a choice is because there exist ways the world could be that include me performing O. While I certainly do not represent a maximal description of a way that the world can be, being able to choose to do (I) gives us justification that O is possible (since it became actual), and that justification delivers a justification that there are ways that a world could be. Because physical modality is plausibly seen as a subset of metaphysical and logical possibilities, this justification seems to extend to all of the root modalities. But there is no parallel reasoning for epistemic modality. While we may use the phrase ways a world could be when talking about what is epistemically possible, the sense of what is possible that is picked out by the could is an epistemic one. So what we have are only ways that an agent cannot rule out as being the actual world. And since many epistemic possibilities cannot become actual, we do not get a similar justification for the existence of any possible or impossible worlds. The existence of ways that an agent cannot rule out the actual world to be do not seem to require maximal descriptions of ways a world can be. Presumably, the agent has epistemic possibilities because she lacks information. This does not seem to justify the existence of entities which contain information that she lacks. Impossible worlds may also contain contradictions. If the agent’s information state results in epistemic possibilities that are impossible according to the root modalities, but the information that she possesses contains no contradictions, this does not seem to offer a justification for the existence of impossible worlds that contain contradictions that are not in the agent’s information state. Without such a justification, it is not clear that worlds of any kind play an explanatory role in explaining epistemic possibility talk. The most fruitful parts of explanations of epistemic possibility talk using possible worlds come from employing conversational dynamics. But nothing about these dynamics requires that the entities being quantified over be worlds. If this is right, advocates of possible worlds need to be able to offer an account of what explanatory work worlds are actually doing, and why that work cannot be done by another entity.
1.6 In Summary 8
Possible worlds accounts of epistemic modality tend to be the standard for explaining epistemic possibilities and epistemic possibility talk. If my arguments have been successful here, then they have undermined the case for taking possible worlds to be the obvious choice for explaining epistemic possibility talk. Possibility semantics are at least as fruitful of an explanation, and they can account for epistemic possibilities with less ontological commitments and less unpalatable consequences. While this may not amount to a falsification of possible worlds accounts of epistemic possibility, it does serve to undermine the obviousness of importing this semantic machinery into epistemic space.
Section 2: Modelling Epistemic Possibilities in Possibility Semantics In this section, I will give an outline for Lloyd Humbersone’s possibility semantics and offer some thoughts about the philosophical motivations Humberstone gives for his project. While some considerations of why possibility semantics may be a better model for epistemic possibility may come into play, I will not primarily be concerned here with defending the choice to model epistemic possibilities in possibility semantics. The case for doing so is made in sections 1 and 3 of the paper. In section 2.1,1 will start by outlining the philosophical motivations that Humberstone levels in favor of possibility semantics. While the examples and explanations I offer there will be my own, the ideas at work are Humberstone’s. Any reservations I have about Humberstone’s project are kept until 2.2.1 will then proceed to give some details about the model theory of possibility semantics. In 2.2,1 offer some reservations about how far Humberstone’s project can extend and argue that what he has in mind is more appropriate for epistemic space than for the root modalities. I will then define an epistemic possibility in possibility semantics.
2.1 Possibility Semantics Humberstone’s Posssibility Semantics are concerned with modelling possibilities as less determinate entities than possible worlds.5 A common view of possible worlds is to think of them as maximal descriptions of a way that the world could be. In other words, a possible world contains a description of every single thing
5 Humberstone 1981 9
that is occurring, has occurred and will occur in that world. Invoking such entities to explain our common every day possibility talk may seem to be overkill. When we talk of possibilities, we never come close to needing a fully specified description of how the world could be. So it is not obvious that such entities are required to explain our possibility talk. For every possibility we invoke, there is a potentially infinite number of possible worlds6 that match the description we give of the possibility. At best, our possibility talk gives us a region of logical space7 (or, if we are leery of spatial metaphors for logical space, we can say that it makes certain worlds salient). Humberstone is worried that there may be something incoherent about the very idea of a possible world. Invoking a maximal description of a way that the world could be, he argues, is like invoking the infinitieth number in an infinite sequence.8 There is no point in an infinite sequence that is picked out by such a description. There is always another number in the sequence. Any description we can give of a way the world might be can always be further specified.9 In order to see just what he is after, take the following sentences: (1) (a) Michael walked to class. (b) Michael walked to his English class. (c) Michael walked to his English class, in the late afternoon. (d) Michael walked to his English class, at 3:45 pm, on April 30th. (e) Michael walked to his Philosophy class, at 7:00 pm.
There is a sense in which the information contained in (a) is also contained in (b-e). But (a) underspecifies the details of what is happening. We can see the sequence of (a) through (d) as each specifying the details of what is happening a little 6 Portner 2009 contains a proof that there are an infinite number of possible worlds satisfying any description. The basic idea is that we can conceive of any way the world is and then imagine that there is one more thing in the world. We can do this an infinite number of times. Thus there are infinite possible worlds. However, this proof seems to require that conceivability entail possibility—something 1 am not eager to endorse. As such, 1 have remained non-committal here about whether or not there are an infinite number of worlds satisfying every possible description. That there are generally more worlds than we could ever hope to count satisfying most descriptions of possibilities is, 1 think, most likely true. 7 Humberstone 1981 8 Humberstone 1981 9 Humberstone 1981 10
further. This process could continue long past our interest in entertaining what is happening. Were we to view the sentences as something like sets of information, we could say that the following relations hold: (2)a£b £c Qd But notice that the following also holds: (3) a £e (4) d <£e; c (£e; b (te,(l Not only is (a) able to be further specified, it is able to be specified in different ways. We can take this as our basic model for how the entities we are interested in function. The entities which Humberstone has in mind, he calls possibilities.1' Possibilities are entities which are informationally indeterminate,12 in the sense that we may say that (la) is indeterminate. This seems to capture something about the indeterminate nature of much of our possibility talk. If I say, “Maybe we can grab lunch.” The possibility invoked does not seem to contain the information about where we grab lunch, what the waiter is wearing, how good the food tastes, etc. It can be further specified in a number of different ways. The only thing that these different possibilities have to have in common is that in each of them, we grab lunch. So our possibilities will need to be governed by two things: persistence and refmabilityP Persistence tells us that in all possibilities under consideration, us grabbing lunch evaluates to true, no matter what details we may add to our description. Refinability tells us that we can always refine our possibility further, by adding in additional information. Our model for the semantics will be a quadruple {W, >,R, V}. W is our set of possibilities. R is our accessibility relations. V is our usual valuation function. And > gives us our refinement relation. When a possibility Y is refined to X, we will use the
10 Note: if we were viewing the sentences in (1) as Stalnakerian propositions (sets of worlds), then the relations described in (2-4) would all need to be reversed. But that is not what we are trying to describe in (2-4). The relations described here are just a first pass at trying to capture a loose notion of informational content. 11 Humberstone 1981 12 Humberstone 1981 13 Humberstone 1981 11
notation X > Y. This can be read as “X is a refinement of Y.” If X is a refinement of Y, then X and Y are different entities, but X contains all of the information that Y does and includes more information than Y does.14 Humberstone defines persistence and refinability more formally as follows: Persistence: For any propositional variable, n and any X, YEW, if V(n, X) is defined and Y> X, then V(n, Y) = V(jt, X) Refinability: For any n, and any X, if V(n, X) is undefined, then there exist Tand Zin Wsuch that Y> X with V(n, Y) = T and Z > X with V(n, Z) = F.15 Readers interested in further details of the model theory can consult (Humberstone 1981). For our purposes this should be sufficient. So the picture this gives us of (1) is of having (b-d) as further refinements on (a). The truth of (a) persists through each further specification. The truth of both (a) and (b) persist in (c). And the truth of (a), (b), and (c) all persist in (d). (e) is an alternative refinement of (a). The truth of (a) persists in (e), but the information contained in (b-d) does not persist in (e).
2.2 Epistemic Possibilities in Possibility Semantics I think there is likely some confusion in Humberstone’s discussion of the possible. In my example of invoking a possibility where we go to lunch, while my description of the possibility did not contain a full description of everything that would occur in that possibility, it does not seem to follow that the entity invoked is a less determinate one than a possible world. When we are making decisions, it makes sense to think that in any of our choices, there will be a fully determined world in which whatever we choose occurs. We may not know all that occurs in that world, nor all that will determine it, but in possibilities where we go to lunch, it seems reasonable to think that whatever happens in that possibility, there will be more that occurs than the fact that we go to lunch. The fact that we can further refine our description of the possibility does not seem to be a fact about what is possible, but about how we relate to the possible. If we can successfully mind a conceptual gap
14 This account of the model theory is from Humberstone 1981 15 These definitions of persistence and refinability are copied directly from Humberstone 1981 .The preceding paragraph summarizes the basics of the model theory, as outlined in the same essay. 12
between what is possible, and how we successfully reason about what is possible, then I do not think that any of the arguments that Humberstone levels against possible world semantics go through. Possibility semantics seems to be an inherently relational notion of possibility. It requires facts about what is possible to be reducible to facts about how an agent refines a possibility. So when we are talking about what is actually possible, independent of what agents know or reason about, I am skeptical of the viability of possibility semantics to do the job. However, epistemic possibilities do seem to be inherently relational, in much the same way that possibility semantics conceives possibilities to be. It does seem plausible to think that facts about what is epistemically possible reduce to facts about how we relate to the world and to a domain of facts about what beliefs we can have about the world. And modelling epistemic possibility talk with possibilities does a good job of providing a story of how we reason about possibility. The basic idea here will be to regard an agent’s information state as a possibility, consisting of all of the information that the agent holds true. Let’s call the information state K. We can then define an epistemic possibility as follows: Epistemic Possibility. For any n, and any X, such that V(n ,X) is defined and V(k ,K) is not false, and X> K, n is epistemically possible. To put that in plain English, an epistemic possibility can be defined as an admissible refinement of an agent’s information state, when that information itself is regarded as a possibility. When an agent regards a piece of information as true, we will say that it is true in K. This does not mean that it is actually true in the real world, but rather that the model the agent has of the world includes that element. This allows us to define what is epistemically possible relative to an agent.
Section 3: Explaining the Epistemic Might with Possibility Semantics In section 1,1 offered the philosophical motivations for preferring possibilities to possible worlds in epistemic space. In section 2 of this paper, I introduced the reader to possibility semantics and offered a definition of epistemic possibility, employing possibility semantics. In this section, I will further the aims of section 1 by putting possibility semantics to work, and showing that they can account for some of the most puzzling features of epistemic possibility talk. 13
In section 3.1,1 will start by introducing readers to the epistemic might. This will involve a brief introduction to modals and some of the work that has been done to explain how modals function. In section 3.2,1 will introduce readers to one of the more puzzling features of the epistemic might: epistemic contradictions. In section 3.3,1 will show how modelling the epistemic might in possibility semantics offers an intuitive and satisfying explanation for epistemic contradictions. Giving an account of all of the interesting features of the epistemic might is a project that is much bigger than what I can hope to engage in here. But if my arguments are successful, then they will lend credibility to the claim that possibilities are a viable candidate for explaining the domain over which epistemic possibility talk quantifies.
3.1 An Introduction to the Epistemic Might Modals are auxiliary verbs that express necessity or possibility. Words like can, could, should, must, and might are examples of modals. The proper taxonomy of modals is a contentious issue,16 and it is one that I will not try to wade into here. For our purposes, a somewhat reductive, but useful first pass will be to divide modals into root modals and epistemic modals.17 When we embed a descriptive sentence in a modal, the sentence becomes a claim about what is possible or necessary, relative to some standard of evaluation. If the relevant standard of evaluation is one of the root modalities, then it is a claim about what is possible or necessary relative to the rules of an objective standard, such as logic, metaphysics, or physical law. If the standard of evaluation is an agent’s beliefs or knowledge, then the claim is about what is possible or necessary for an agent to believe about the world. Spelling out just what that amounts to is the goal of this paper. The same modal can be used with different flavorings. One way we might try to make this notion clearer, is by invoking Kratzer’s notion of a modal restrictor.18 Consider the following sentences: (5) Given what is moral, you should not kill anyone. (6) Given what I know, the keys should be in the hall drawer.
16 See Portner 2007 and Portner 2009 for explorations of these issues. 17 For more on this division beyond what is explained here, see Portner 2009—Chapter 4, in particular. 18 Kratzer 1977 and Kratzer2012 14
Both of these sentences make use of the modal should, but they are very different claims. The should in (5) is a claim about what the rules of morality require. (6) is perhaps best seen as a claim about what the speaker’s beliefs about the world require her to believe. Now consider these two similar sentences: (5a) You should not kill anyone (6a) The keys should be in the hall drawer. In (5) and (6), the relevant standard of evaluation at work in the modal claim is made explicit. But in (5a) and (6a) the standard of evaluation is not made explicit. In (5) and (6), each statement is prefaced with a statement of the form “given X,” where x is the relevant standard of evaluation. This “given x” statement is our modal restrictor. It tells us what kind of domain we are quantifying over in our modal claims. When we do not have a modal restrictor explicitly mentioned in the sentences, we have a bare modal. The sentences still require a modal restrictor in order to make sense, but the modal restrictor is given by context. In most contexts where (5a) is spoken, it is most reasonably interpreted to be equivalent to (5). But a different context may provide us with a very different reading. We can imagine two serial killers talking shop. One of them is worried that the police may be on her trail. The other may express (5a) in response, meaning something more like the following:
(5b) Given that you do not want to be caught, you should not kill anyone (for the time being). Thus the same sentence may take on vastly different meanings, depending on what modal restrictor is relevant to determining the relevant domain of quantification. While the modal restrictors do not tell us what kind of entities we are quantifying over or give us necessary and sufficient conditions for truth claims in that domain of quantification, they do give us some idea of what “flavor” of modality we are dealing with. What we are most interested in for this section of the paper is in uses of the modal might where the relevant modal restrictor is an epistemic one. Not all uses of the word might are epistemic. Consider the following passage, not so much for its content, but for its uses of the word might. 15
(6) I might not have been speaking now; Archbishop Tutu might have been speaking instead.19 This example is from Gillian Russell, in a context where she is clearly talking about metaphysical possibility, and it is operating like an existential quantifier over a domain of possible worlds. Further examples of world-class philosophers using might for metaphysical possibility are not hard to find. The practice is ubiquitous. But if we say the following: (7) The keys might be in the drawer.20 It seems a little odd to read this as a claim about what is possible according to logic, metaphysics, or physical law. While keys being in drawers is possible in each of those standards of evaluation, in most contexts where (7) would be spoken, it is plausibly read as a claim about what is epistemically possible—what cannot be ruled out by an agent’s beliefs or knowledge. This epistemic might has many puzzling features. Many of the explanations we would have to give in modeling the epistemic might with possibility semantics would be similar to other approaches to the epistemic might, so I will not attempt to address all of the interesting features of the epistemic might.2' Instead I will focus only on the areas where modelling epistemic possibilities in possibility semantics proves to be particularly interesting and rewarding.
3.2 Epistemic Contradictions One of the more puzzling features of the epistemic might is what Seth Yalcin has called epistemic contradictions.22 Consider the following sentence: (8) ?? It is raining and it might not be raining.23
19 Russell 2008 20 This example is oddly pervasive in the literature. Its influence seems to be a result of its inclusion in Egan, Hawthorne and Weatherson 2005. 21 For a helpful survey of such features, see Bach 2011. 22 Yalcin 2011 23 Yalcin 2011 16
Most English speakers will find this a puzzling thing to say. One way we might try to explain the puzzling features of this sentence is to try and argue that it is Moorean-paradoxical. We could thus count it as semantically equivalent to: (9) ??It is raining and I do not know that it is raining. This also sounds puzzling. But as Yalcin points out, explaining (8) as being Moorean-paradoxical in the same way that (9) is will not work. To see why, we only need to embed (8) and (9) into more complex sentences. (10) ?? Suppose it is raining and it might not be raining. (11) Suppose that it is raining and I don’t know that it is raining. (12) ?? If it is raining and it might not be raining, then I will get wet. (13) If it is raining and I don’t know that it is raining, then I will get wet.24 (11) and (13) sound just fine, but (10) and (12) are just as puzzling as (8). So epistemic contradictions can be projected into embedded contexts in a way that Moorean-paradoxicality cannot.25 Another puzzling feature of epistemic contradictions is the fact that the order of the conjuncts seems to matter—or at least it does in determining whether or not English speakers will find it an acceptable thing to say. Natural language speakers seem to find (8) unacceptable, but most find (14) to be acceptable.26 (14) It might not be raining and it is raining. To see why this is so puzzling, let’s consider another example of a conjunction where order matters. (15) Steve ran to the edge of the cliff and jumped. (16) Steve jumped and ran to the edge of the cliff.27 Both of these sentences seem to have the same conjuncts, yet are likely to be interpreted very differently by natural language speakers. (15) seems likely to be
24 These examples are all included in Yalcin 2011 25 Yalcin 2011 26Veltman 1996 27 For more on such examples, see Carston 1988 17 interpreted as a suicide, whereas (16) does not seem to admit such a reading. The reasons for this difference appear to be pragmatic, rather than semantic. Both of the conjuncts are events. It is natural for listeners to take the order in which the conjuncts stand to each other in the sentence to be the same as the order in which the events occurred. But in (8) and (14), there is no temporal sequence to explain the reason why order matters. What’s more, it seems as though there is no reason why the conjuncts cannot evaluate to true at the same time, or in any temporal sequence we might wish to place them in. So the ordering of the conjuncts problem in epistemic contradictions does not lend itself to similar explanations as the one employed to explain the differences between (15) an (16).
3.3 Semantics for the Epistemic Might In this section, I will show how we can make sense of epistemic contradictions using possibility semantics. I will proceed by first giving a definition of the epistemic might in possibility semantics. I will then explain how we can put it to work in explaining interesting features of might talk. While possibility semantics is not unique in being able to explain epistemic contradictions, it does have a satisfying explanation for why epistemic contradictions occur built into the semantics. If we define epistemic possibilities in possibility semantics, then we can define the epistemic might as a quantifier over a domain of epistemic possibilities. We can build this notion of epistemic possibility into the semantics for an epistemic might as follows: (17) Might: might be the case, iff there is some X such that V(0, X) = T, while the V(&, K) ± F, and X>K. Our next step is to see how well these semantics handle epistemic contradictions, like the one contained in (8). If we view (8) as a possibility, then it is easy to see why it does not sound right. We can view the second conjunct as making a claim about what refinements are possible on the first. But persistence, forbids the second conjunct from being part of an admissible refinement. However, in (14), the conjunct with the epistemic modal comes first. So at the time the epistemic modal claim is registered, it does not violate persistence. 18
Explaining it this way requires that we factor in some notion of dynamics. The reason why we need dynamics to factor in is because order does not matter for the semantics of a conjunction. Typical semantics for conjunctions are static. The order in which speakers and listeners give and receive information is irrelevant to what the conjunction means and the function it performs. Humberstone’s semantics for conjunctions are also static. He defines a conjunction as follows: (18)Xl= A&B iff Xt=A andXt=B28 The most straightforward way to explain the strangeness of (8) and the apparent acceptability of (14) is to model it with a Stalnakerian model of conversational dynamics, but without the possible worlds framework. We do this by saying that while the semantics for conjunctions are static, real world speech environments are not. Humans process information in a temporal order. Thus in (8), we can say that first conjunct refines K. This makes it is raining true in K. The second conjunct then makes a claim about it is not raining being an admissible refinement of the newly refined K, which violates persistence. In (14) the claim about what is an admissible refinement on K comes before the information which would make it inadmissible. Next we need to see how well this holds up when we project the epistemic contradictions into embedded contexts. (10) ?? Suppose it is raining and it might not be raining (12) ?? If it is raining and it might not be raining, then I will get wet.29 Again, our possibility semantics do the job. In each of these, we are having a counterfactual scenario specified. If we view each of these as possibilities, then the same explanation applies. In (10) and (12) we are being told to think of counterfactual scenarios where it is raining. The only thing we know about these scenarios is that it is raining, so persistence forbids any admissible refinement wherein it is not raining. So (10) and (12) come out infelicitous. But notice that each of these is just fine: (19) Suppose it is raining and Karen believes it might not be raining. (20) If is raining and I believe it might not be raining, then I might get wet.
28 Humberstone 1981 29 Yalcin 2011 19
When we specify a different context of evaluation for the might statements, we can embed them just fine. In (8), (10) and (12), there is no salient context of evaluation which would make the statements non-contradictory. We default to the context of evaluation that is necessary for counting the first conjunct true. And in all such contexts of evaluation we know that the first conjunct makes the second inadmissible. If this is right, then we have successfully demonstrated that possibility semantics is up to the task of explaining some of the more puzzling features of the epistemic might.
Conclusion I have argued here that epistemic possibilities are better explained without recourse to possible worlds. If my arguments here have been successful, then they have shown that we have good reason to prefer possibilities as our tool of choice in epistemic space. I have also demonstrated that possibility semantics is capable of explaining some of the most puzzling features of epistemic possibility talk. 20
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