Impossible worlds and logical omniscience: an impossibility result

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents.     

The space of possibilities of dispositional essentialism

How we define the space of possibilities of dispositional essentialism (DE)—that is, the set of possible worlds that are genuinely possible from the point of view of DE—has important consequences for central modal debates such as how to understand the concept of essence or the relation between DE and the necessity of laws of nature. In order to define DE’s space of possibilities we need to explore DE’s consequences regarding both necessity and possibility. Unfortunately, the notion of possibility has not received much attention within the DE literature. In this paper, I attempt to fill this gap. I argue that the standard way of understanding possibility found in the literature—a proposition is possible iff it expresses the manifestation of some actual disposition—needlessly restricts the space of possibilities by not accepting global and absolute possibilities, including some alien properties, as genuinely possible. I propose instead to accept a more permissive understanding of possibility: a proposition is possible iff it does not contradict any of the necessities that follow from the core commitments of DE. This allows dispositionalists to expand their modal space and to account for modal intuitions that may otherwise undermine the tenability of DE.     

Possible disagreements and defeat

Conciliatory views about disagreement with one’s epistemic peers lead to a somewhat troubling skeptical conclusion: that often, when we know others disagree, we ought to be (perhaps much) less sure of our beliefs than we typically are. One might attempt to extend this skeptical conclusion by arguing that disagreement with merely possible epistemic agents should be epistemically significant to the same degree as disagreement with actual agents, and that, since for any belief we have, it is possible that someone should disagree in the appropriate way, we ought to be much less sure of all of our beliefs than we typically are. In this paper, I identify what I take to be the main motivation for thinking that actual disagreement is epistemically significant and argue that it does not also motivate the epistemic significance of merely possible disagreement.     

Brown on Mackie: Echoes of the Lottery Paradox

In “The possibility of morality,” Phil Brown considers whether moral error theory is best understood as a necessary or contingent thesis. Among other things, Brown contends that the argument from relativity, offered by John Mackie—error theory’s progenitor—supports a stronger modal reading of error theory. His argument is as follows: Mackie’s is an abductive argument that error theory is the best explanation for divergence in moral practices. Since error theory will likewise be the best explanation for similar divergences in possible worlds similar to our own, we may conclude that error theory is true at all such worlds, just as it is in the actual world. I contend that Brown’s argument must fail, as abductive arguments cannot support the modal conclusions he suggests. I then consider why this is the case, concluding that Brown has stumbled upon new and interesting evidence that agglomerating one’s beliefs can be epistemically problematic—an issue associated most famously with Henry Kyburg’s lottery paradox.     

Critical Thinking is Epistemically Responsible

Michael Huemer ( 2005 ) argues that following the epistemic strategy of Critical Thinking—that is, thinking things through for oneself—leaves the agent epistemically either worse off or no better off than an alternative strategy of Credulity—that is, trusting the authorities. Therefore, Critical Thinking is not epistemically responsible. This article argues that Reasonable Credulity entails Critical Thinking, and since Reasonable Credulity is epistemically responsible, the Critical Thinking that it entails is epistemically responsible too.     

One standard to rule them all?

It has been argued that an epistemically rational agent's evidence is subjectively mediated through some rational epistemic standards, and that there are incompatible but equally rational epistemic standards available to agents. This supports Permissiveness, the view according to which one or multiple fully rational agents are permitted to take distinct incompatible doxastic attitudes towards P (relative to a body of evidence). In this paper, I argue that the above claims entail the existence of a unique and more reliable epistemic standard. My strategy relies on Condorcet's Jury Theorem. This gives rise to an important problem for those who argue that epistemic standards are permissive, since the reliability criterion is incompatible with such a type of Permissiveness.     

Relies to our critics

We respond to the central concerns raised by our commentators to our book, The Epistemological Spectrum. Casullo believes that our account of what we term “low-grade a priori” justification provides important clarification of a kind of philosophical reflection. However he objects to calling such reflection a priori. We explain what we think is at stake. Along the way, we comment on his idea of that there may be an epistemic payoff to making a distinction between assumptions and presumptions. In the book, we argued that an epistemically important form of nonaccidental reliability can be understood as a matter of processes being “transglobally reliable under modulational control.” Graham recommends another form of nonaccidental reliability, one rooted in evolutionary etiology. We explain why we think that the reliability of perceptual processes is best understood as turning of the kinds of modulational control that we highlight. We clarify how this approach represents a kind of reasonable epistemic patience—modulational control takes time, as it must turn on agents generating information about their own capacities and foibles. Lyons raises interesting questions regarding how (what we term) morphological content possessed by the agent can do the work that we set for it. We argue that it is necessary in order for agents to accommodate the background information that is relevant to many central problems of belief formation. We clarify how it can be expected to work.     

Counterfactual epistemic scenarios

In two-dimensional semantics in the tradition of Davies and Humberstone, whether a singular term receives an epistemically shifted reading in the scope of a modal operator depends on whether the world considered as actual is shifted. This means that epistemically shifted readings should be available only in environments where an explicit contrast between the actual world and some counterfactual worlds cannot be made. In this paper, I argue that this is incorrect. Whether a singular term receives an epistemically shifted reading is independent of whether the world treated as actual is shifted. This, I argue, undermines the two-dimensionalist account of epistemic shift. I then turn to the question how a positive view should handle these two phenomena separately. I argue for treating singular terms with a version of counterpart theory in which the difference between epistemically shifted and other readings is determined in the context of utterance.     

Propositions, Sets, and Worlds

If we agree with Michael Jubien that propositions do not exist, while accepting the existence of abstract sets in a realist mathematical ontology, then the combined effect of these ontological commitments has surprising implications for the metaphysics of modal logic, the ontology of logically possible worlds, and the controversy over modal realism versus actualism. Logically possible worlds as maximally consistent proposition sets exist if sets generally exist, but are equivalently expressed as maximally consistent conjunctions of the same propositions in corresponding sets. A conjunction of propositions, even if infinite in extent, is nevertheless itself a proposition. If sets and hence proposition sets exist but propositions do not exist, then whether or not modal realism is true depends on which of two apparently equivalent methods of identifying, representing, or characterizing logically possible worlds we choose to adopt. I consider a number of reactions to the problem, concluding that the best solution may be to reject the conventional model set theoretical concept of logically possible worlds as maximally consistent proposition sets, and distinguishing between the actual world alone as maximally consistent and interpreting all nonactual merely logically possible worlds as submaximal. I am grateful to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Royal Netherlands Academy of Arts and Sciences (KNAW), for supporting this among related research projects in philosophical logic and philosophy of mathematics during my Resident Research Fellowship in 2005-2006.     

Explaining in conversation: Towards an argument model

We examine the proposition that, in ordinary conversation, people are concerned to argue — to justify their claims and to counter potential and actual counter claims. We test out the proposition by analysing explanations in one particular conversation. We attend to the validity claims of what the speakers say, and to the authority with which they say it. Viewed in that light, we find that the majority of what might look like causal attributions turn out to look like argumentative claim-backings. We then go on to flesh out the quasi-pragmatic rules which might help to decide formally whether any given utterance is be er understood as an argument or a causal explanation. These rules revolve around the speaker's apparent intention and the projected relationship between the clauses in what she or he says. All of this takes us a fair way from attribution theory's model of explanation as the reporting of a cause, and we end up with an argumentative model of ordinary explanation.     

What are impossible worlds?

In this paper, I argue for a particular conception of impossible worlds. Possible worlds, as traditionally understood, can be used in the analysis of propositions, the content of belief, the truth of counterfactuals, and so on. Yet possible worlds are not capable of differentiating propositions that are necessarily equivalent, making sense of the beliefs of agents who are not ideally rational, or giving truth values to counterfactuals with necessarily false antecedents. The addition of impossible worlds addresses these issues. The kinds of impossible worlds capable of performing this task are not mysterious sui generis entities, but sets of structured propositions that are themselves constructed out of possible worlds and relations. I also respond to a worry that these impossible worlds are unable to represent claims about the shape of modal space itself.     

Varieties of Epistemic Freedom

When we deliberate about what to do, we appear to be free to decide on different options. Three accounts use ordinary beliefs to explain this apparent freedom—appealing to different types of ‘epistemic freedom’. When an agent has epistemic freedom, her evidence while deliberating does not determine what decision she makes. This ‘epistemic gap’ between her evidence and decision explains why her decision appears free. The varieties of epistemic freedom appealed to might look similar. But there is an important difference. Two rely on an agent's ability to justifiably form beliefs unconstrained by evidence, and identify decisions as beliefs—either beliefs about acts (Velleman) or about decisions (Joyce and Ismael). But, when used to explain apparent freedom, these accounts face serious problems: they imply that agents have epistemic freedom over evidence-based beliefs, and rely on a faulty notion of justification. Underlying these troubles, it turns out that these accounts presuppose an unexplained apparent ability to form different beliefs. A third variety of epistemic freedom uses ignorance conditions instead (Levi and Kapitan). We appear free partly because we're ignorant of what we'll decide. Ignorance-based accounts avoid the above problems, and remain a promising alternative.     

Testimony,epistemic egoism,and epistemic credit

It is generally acknowledged that testifiers can play a central role in the production of knowledge and other valuable epistemic states in others. But does such a role warrant any form of epistemic credit and is an agent more successful qua epistemic agent insofar as she is a successful testifier? I here propose an affirmative answer to both questions. The core of the current paper consists in a sustained defense of this proposal against a series of objections. I further argue that the proposal allows us to recognize an important additional epistemic harm that arises in cases of testimonial injustice beyond those described by Miranda Fricker. Finally, I conclude by distinguishing between four kinds of credit—distinctions that allow us to avoid inappropriately attributing epistemic credit in problematic cases. If the current proposal is correct, our understanding of successful epistemic agents needs to be significantly modified in order to take into account their role in producing epistemically valuable states in others.     

Functionalism about possible worlds

Various writers have proposed that the notion of a possible world is a functional concept, yet very little has been done to develop that proposal. This paper explores a particular functionalist account of possible worlds, according to which pluralities of possible worlds are the bases for structures which provide occupants for the roles which analyse our ordinary modal concepts. It argues that the resulting position meets some of the stringent constraints which philosophers have placed upon accounts of possible worlds, while also trivializing the question what possible worlds are. The paper then discusses a range of problems facing the functionalist position.     

On the factivity of implicit intersubjective knowledge

The concept of knowledge can be modelled in epistemic modal logic and, if modelled by using a standard modal operator, it is subject to the problem of logical omniscience. The classical solution to this problem is to distinguish between implicit and explicit knowledge and to construe the knowledge operator as capturing the concept of implicit knowledge. In addition, since a proposition is said to be implicitly known just in case it is derivable from the set of propositions that are explicitly known by using a certain set of logical rules, the concept of implicit knowledge is definable on the basis of the concept of explicit knowledge. In any case, both implicit and explicit knowledge are typically characterized as factive, i.e. such that it is always the case that what is known is also true. The aim of the present paper is twofold: first, we will develop a dynamic system of explicit intersubjective knowledge that allows us to introduce the operator of implicit knowledge by definition; secondly, we will show that it is not possible to hold together the following two theses: (1) the concept of implicit knowledge is definable along the lines indicated above and (2) the concept of implicit knowledge is factive.     

Proposition-valued random variables as information

The notion of a proposition as a set of possible worlds or states occupies central stage in probability theory, semantics and epistemology, where it serves as the fundamental unit both of information and meaning. But this fact should not blind us to the existence of prospects with a different structure. In the paper I examine the use of random variables—in particular, proposition-valued random variables—in these fields and argue that we need a general account of rational attitude formation with respect to them.     

Radical moral encroachment: The moral stakes of racist beliefs

Historical patterns of discrimination seem to present us with conflicts between what morality requires and what we epistemically ought to believe. I will argue that these cases lend support to the following nagging suspicion: that the epistemic standards governing belief are not independent of moral considerations. We can resolve these seeming conflicts by adopting a framework wherein standards of evidence for our beliefs to count as justified can shift according to the moral stakes. On this account, believing a paradigmatically racist belief reflects a failure to not only attend to the epistemic risk of being wrong, but also a failure to attend to the distinctively moral risk of wronging others given what we believe.     

Constructing worlds

You and I can differ in what we say, or believe, even though the things we say, or believe, are logically equivalent. Discussing what is said, or believed, requires notions of content which are finer-grained than sets of (metaphysically or logically) possible worlds. In this paper, I develop the approach to fine-grained content in terms of a space of possible and impossible worlds. I give a method for constructing ersatz worlds based on a theory of substantial facts. I show how this theory overcomes an objection to actualist constructions of ersatz worlds and argue that it naturally gives rise to useful notions of fine-grained content.     

Opaque Updates

Journal of Philosophical Logic - If updating with E has the same result across all epistemically possible worlds, then the agent has no uncertainty as to the behavior of the update, and we may call...