In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a “core set” of the so-called “reduction axioms”. In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that the proof system based on this core set of axioms does not completely axiomatize PAL without additional axioms and rules. In fact, many of the intuitive axioms and rules we took for granted could not be derived from the (...) core set. Moreover, we also propose and advocate an alternative yet meaningful axiomatization of PAL without the reduction axioms. The completeness is proved directly by a detour method using the canonical model where announcements are treated as merely labels for modalities as in normal modal logics. This new axiomatization and its completeness proof may sharpen our understanding of PAL and can be adapted to other dynamic epistemic logics. (shrink)

We have several intuitive paradigms of defeating evidence. For example, let E be the fact that Ernie tells me that the notorious pet Precious is a bird. This supports the premise F, that Precious can fly. However, Orna gives me *opposing* evidence. She says that Precious is a dog. Alternatively, defeating evidence might not oppose Ernie's testimony in that direct way. There might be other ways for it to weaken the support that Ernie's testimony gives me for believing F, without (...) the new evidence itself intuitively constituting reasons to believe one way or the other about Precious's flight ability. An example: Ursula tells me that Ernie has no idea what Precious's species is; he's just guessing. She may not herself want to or be in a position to weigh in about Precious's real species or flight ability. I call defeating evidence of this sort *undermining evidence. (shrink)

Diachronic Dutch book arguments seem to support both conditionalization and Bas van Fraassen's Reflection principle. But the Reflection principle is vulnerable to numerous counterexamples. This essay addresses two questions: first, under what circumstances should an agent obey Reflection, and second, should the counterexamples to Reflection make us doubt the Dutch book for conditionalization? In response to the first question, this essay formulates a new "Qualified Reflection" principle, which states that an agent should obey Reflection only if he or she is (...) certain that he or she will conditionalize on veridical evidence in the future. Qualified Reflection follows from the probability calculus together with a few idealizing assumptions. The essay then formulates a "Distorted Reflection" principle that approximates Reflection even in cases where the agent is not quite certain that he or she will conditionalize on veridical evidence. In response to the second question, the essay argues that contrary to a common misconception, not all Dutch books dramatize incoherence—some dramatize a less blameworthy sort of epistemic frailty that the essay calls "self-doubt." The distinction between Dutch books that dramatize incoherence and those that dramatize self-doubt cross-cuts the distinction between synchronic and diachronic Dutch books. The essay explains why the Dutch book for conditionalization reveals true incoherence, whereas the Dutch book for Reflection reveals only self-doubt. (shrink)

Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...) illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology and a notable contribution to the philosophy of mind. (shrink)

Consider the skeptic about the external world. Let’s straightaway concede to such a skeptic that perception gives us no conclusive or certain knowledge about our surroundings. Our perceptual justification for beliefs about our surroundings is always defeasible—there are always possible improvements in our epistemic state which would no longer support those beliefs. Let’s also concede to the skeptic that it’s metaphysically possible for us to have all the experiences we’re now having while all those experiences are false. Some philosophers dispute (...) this, but I do not. The skeptic I want to consider goes beyond these familiar points to the much more radical conclusion that our perceptual experiences can’t give us any knowledge or even justification for believing that our surroundings are one way rather than another. (shrink)

Something about this argument sounds funny. As we’ll see, though, it takes some care to identify exactly what Moore has done wrong. Iwill assume that Moore knows premise (2) to be true. One could inquire into how he knows it, and whether that knowledge can be defeated; but Iwon’t. I’ll focus instead on what epistemic relations Moore has to premise (1) and to his conclusion (3). It may matter which epistemic relations we choose to consider. Some philosophers will diagnose Moore’s (...) argument using Contextualist machinery. They’ll say. (shrink)

We develop a conceptual and formal clarification of notion of surprise as a belief-based phenomenon by exploring a rich typology. Each kind of surprise is associated with a particular phase of cognitive processing and involves particular kinds of epistemic representations (representations and expectations under scrutiny, implicit beliefs, presuppositions). We define two main kinds of surprise: mismatch-based surprise and astonishment. In the central part of the paper we suggest how a formal model of surprise can be integrated with a formal model (...) of belief change. We investigate the role of surprise in triggering the process of belief reconsideration. There are a number of models of surprise developed in the psychology of emotion. We provide several comparisons of our approach with those models. (shrink)

The dominant response to this problem of the criterion focuses on the alleged requirement that we need to know a belief source is reliable in order for us to acquire knowledge by that source. Let us call this requirement, “The KR principle”.

One of the main goals of epistemologists is to provide a substantive and explanatory account of the conditions under which a belief has some desirable epistemic status (typically, justification or knowledge). According to the reliabilist approach to epistemology, any adequate account will need to mention the reliability of the process responsible for the belief, or truth-conducive considerations more generally. Historically, one major motivation for reliabilism—and one source of its enduring interest—is its naturalistic potential. According to reliabilists, epistemic properties can be (...) explained in terms of reliability, which in turn can be understood without reference to any unreduced epistemic notions, such as evidence or knowledge. This article begins by surveying some of the main forms of reliabilism, concentrating on process reliabilism as a theory of justification. It proceeds to review some of the main objections to reliabilism, and some of the responses that have been offered on the reliabilist’s behalf. After canvassing some recent developments in reliabilist epistemology, the article concludes by considering various cousins and spin-offs of reliabilist epistemology, including virtue reliabilism and various evidentialist-reliabilist hybrids. (shrink)

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 it a transparent update. If an agent is uncertain about the behavior of an update, we may call it opaque. In order to model the uncertainty an agent has about the result of an update, the same update must behave differently across different possible worlds. In this paper, I study opaque (...) updates using a simple system of dynamic epistemic logic suitably modified for that purpose. The paper highlights the connection between opaque updates and the dynamic-epistemic principles Perfect-Recall and No-Miracles. I argue that opaque updates are central to contemporary discussions in epistemology, in particular to externalist theories of knowledge and to the related problem of epistemic bootstrapping, or easy knowledge. Opaque updates allow us to explicitly investigate a dynamic form of uncertainty, using simple and precise logical tools. (shrink)

ABSTRACTRational agents have consistent beliefs. Bayesianism is a theory of consistency for partial belief states. Rational agents also respond appropriately to experience. Dogmatism is a theory of how to respond appropriately to experience. Hence, Dogmatism and Bayesianism are theories of two very different aspects of rationality. It's surprising, then, that in recent years it has become common to claim that Dogmatism and Bayesianism are jointly inconsistent: how can two independently consistent theories with distinct subject matter be jointly inconsistent? In this (...) essay I argue that Bayesianism and Dogmatism are inconsistent only with the addition of a specific hypothesis about how the appropriate responses to perceptual experience are to be incorporated into the formal models of the Bayesian. That hypothesis isn't essential either to Bayesianism or to Dogmatism, and so Bayesianism and Dogmatism are jointly consistent. That leaves the matter of how experiences and credences are related, a... (shrink)

This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book (...) develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science. (shrink)

I argue that its appearing to you that P does not provide justification for believing that P unless you have independent justification for the denial of skeptical alternatives – hypotheses incompatible with P but such that if they were true, it would still appear to you that P. Thus I challenge the popular view of ‘dogmatism,’ according to which for some contents P, you need only lack reason to suspect that skeptical alternatives are true, in order for an experience as (...) of P to justify belief that P. I pursue three lines of objection to dogmatism, having to do with probabilistic reasoning, considerations of future or hypothetically available justification, and epistemic circularity. I briefly sketch a fall-back position which avoids the problems raised. (shrink)

An introductory overview of the main issues in the epistemology of perception.

How do rational minds make contact with the world? The empiricist tradition sees a gap between mind and world, and takes sensory experience, fallible as it is, to provide our only bridge across that gap. In its crudest form, for example, the traditional idea is that our minds consult an inner realm of sensory experience, which provides us with evidence about the nature of external reality. Notoriously, however, it turns out to be far from clear that there is any viable (...) conception of experience which allows it to do the job. The original problem is to show that thought is rationally constrained by external reality. If sensory experience is to provide the solution--in particular, if it is to provide the answer to sceptical challenges--it must therefore meet two criteria. First, it must itself be `receptive'--i.e., appropriately constrained by external reality. Second, it must be the kind of thing that can enter into a logical or rational relationship with belief--it must already be `conceptual,' in other words. In arguing against the idea that anything could serve both roles, Wilfred Sellars termed this conception of experience "the Myth of the Given.". (shrink)

This essay surveys the varieties of disjunctivism about perceptual experience. Disjunctivism comes in two main flavours, metaphysical and epistemological.

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event (...) models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall , No Miracles , and Bisimulation Invariance . We then focus on new issues of completeness . One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...) the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (shrink)

Cases of inexact observations have been used extensively in the recent literature on higher-order evidence and higher-order knowledge. I argue that the received understanding of inexact observations is mistaken. Although it is convenient to assume that such cases can be modeled statically, they should be analyzed as dynamic cases that involve change of knowledge. Consequently, the underlying logic should be dynamic epistemic logic, not its static counterpart. When reasoning about inexact knowledge, it is easy to confuse the initial situation, the (...) observation process, and the result of the observation; I analyze the three separately. This dynamic approach has far reaching implications: Williamson’s influential argument against the KK principle loses its force, and new insights can be gained regarding synchronic and diachronic introspection principles. (shrink)

In this article, we present a new logical framework to think about surprise. This research does not just aim to better understand, model and predict human behaviour, but also attempts to provide tools for implementing artificial agents. Moreover, these artificial agents should then also be able to reap the same epistemic benefits from surprise as humans do. We start by discussing the dominant literature regarding propositional surprise and explore its shortcomings. These shortcomings are of both an empirical and a conceptual (...) nature. Next, we propose a philosophical solution to the problems that ail these systems, based on the notion of issue of epistemic interest. Finally, we give a formal framework to think about surprise. More specifically, we develop a probabilistic dynamic epistemic logic that succeeds at formalizing the relevant philosophical concepts. This will be done through an issue management system grounded in topology. As an added bonus, the additional expressive power allows us to capture a richer variety of scenarios, and it also enables a more careful analysis of said scenarios. (shrink)

It has been argued recently that dogmatism in epistemology is incompatible with Bayesianism. That is, it has been argued that dogmatism cannot be modelled using traditional techniques for Bayesian modelling. I argue that our response to this should not be to throw out dogmatism, but to develop better modelling techniques. I sketch a model for formal learning in which an agent can discover a posteriori fundamental epistemic connections. In this model, there is no formal objection to dogmatism.

The bootstrapping problem poses a general challenge, afflicting even strongly internalist theories. Even if one must always know that one’s source is reliable to gain knowledge from it, bootstrapping is still possible. I survey some solutions internalists might offer and defend the one I find most plausible: that bootstrapping involves an abuse of inductive reasoning akin to generalizing from a small or biased sample. I also argue that this solution is equally available to the reliabilist. The moral is that the (...) issues raised by bootstrapping are orthogonal to questions about internalism and basic knowledge, having more to do with the nature of good inductive reasoning. (shrink)

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event (...) models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall, No Miracles, and Bisimulation Invariance. We then focus on new issues of completeness. One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)