The epistemicist theory aims to explain ignorance due to vagueness by semantic plasticity: the shiftiness of intensions across close possible worlds resulting from shiftiness in usage. This explanation is challenged by the Omniscient Speaker Puzzle (Sennet in Philos Stud 161(2):273–285, 2012). Suppose that an omniscient speaker, Barney, who knows all the facts about usage and how these facts determine the intensions of expressions, cooks up a scheme to stabilise the intension of a normally semantically plastic term like ‘rich’. It seems (...) that ‘rich’ would display all the phenomena associated with vagueness without being semantically plastic, thus making the epistemicist explanation of ignorance due to vagueness insufficient. In this paper, I present a few choice points for epistemicism that arise as a result of the puzzle. (shrink)

This paper generalizes the preface paradox beyond the conjunctive aggregation of beliefs and constructs an analogous paradox for deontic reasoning. The analysis of the deontic case suggests a systematic restriction of intuitive rules for reasoning with obligations. This proposal can be transferred to the epistemic case: it avoids the preface and the lottery paradox and saves one of the two directions of the Lockean Thesis (i.e., high credence is sufficient, but not necessary for rational belief). The resulting account compares favorably (...) to competing proposals; in particular, we can formulate the rules of correct doxastic reasoning without reference to probabilistic features of the involved propositions. (shrink)

Our interest in understanding belief stems partly from our being creatures who think. However, the term ‘belief’ is used to refer to many states: from the fully conscious rational state that partly constitutes knowledge to the fanciful states of alarm clocks. Which of the many ‘belief’ states must a theory of belief be answerable to? This is the scope question. I begin my answer with a reply to a recent argument that belief is invariably weak, i.e., that the evidential standards (...) that are required for belief are low. Although one state we refer to using the term ‘belief’ fits this profile, other ‘belief’ states do not. Crucially, when ‘belief’ is heard in a weak sense, it attributes a state that only a rational creature can be in. I will use this observation as a starting point for an argument that the study of (our) belief should not be constrained by the requirement that the illuminated state be held in common with any non-rational being. This lends support to the Transformative Theory of Rationality, according to which rationality does not merely add powers or complexity to the animal mind, but transforms it into a different kind of mind altogether. (shrink)

I defend an iterated knowledge condition on responsibility for outcomes: one is responsible for a consequence of one's action only if one was in a position to know that, for all one was in a position to know, one's action would have that consequence.

Constructivist epistemology posits that all truths are knowable. One might ask to what extent constructivism is compatible with naturalized epistemology and knowledge obtained from inference-making using successful scientific theories. If quantum theory correctly describes the structure of the physical world, and if quantum theoretic inferences about which measurement outcomes will be observed with unit probability count as knowledge, we demonstrate that constructivism cannot be upheld. Our derivation is compatible with both intuitionistic and quantum propositional logic. This result is implied by (...) the Frauchiger-Renner theorem, though it is of independent importance as well. (shrink)

The received view says that possibility is the dual of necessity: a proposition is (metaphysically, logically, epistemically etc.) possible iff it is not the case that its negation is (metaphysically, logically, epistemically etc., respectively) necessary. This reading is usually taken for granted by modal logicians and indeed seems plausible when dealing with logical or metaphysical possibility. But what about epistemic possibility? We argue that the dual definition of epistemic possibility in terms of epistemic necessity generates tension when reasoning about non-idealized (...) agents and is a problem of concern for most hyperintensional epistemic logics that alleviate the problem of logical omniscience. The tension is particularly evident when knowledge is taken as a primitive to define other epistemic concepts, such as justification and belief, as done in the knowledge-first tradition. We propose a non-dual interpretation of epistemic possibility, employing a hyperintensionality filter similar to the one that makes the corresponding epistemic necessity operator hyperintensional. We employ the proposed semantics to model Stalnaker's belief as epistemic possibility of knowledge and provide a sound and complete axiomatization for a hyperintensional version of his bimodal logic of knowledge and belief. (shrink)

In this paper I propose and motivate a logic of the interdefined concepts of making true and control, understood as intensional propositional operators to be indexed to an agent. While bearing a resemblance to earlier logics in the tradition, the motivations, semantics, and object language theory differ on crucial points. Applying this logic to widespread formal theories of agency, I use it as a framework to argue against the ubiquitous assumption that the strongest actions or options available to a given (...) agent must always be pairwise incompatible. The conclusion is that this assumption conflicts with failures of higher order control of agents over their degree or precision of control, failures exhibited by such imperfect agents as ourselves. I discuss models in this setting for understanding such imperfectly self-controlling agents. In an appendix, I prove several relevant results about the logic described, including soundness and completeness both for it and for certain natural extensions. (shrink)

Standard models in epistemic game theory make strong assumptions about agents’ knowledge of their own beliefs. Agents are typically assumed to be introspectively omniscient: if an agent believes an event with probability p, she is certain that she believes it with probability p. This paper investigates the extent to which this assumption can be relaxed while preserving some standard epistemic results. Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth” axiom, together with the property of balancedness, a significant (...) relaxation of introspective omniscience. I provide an example which shows that Geanakoplos’s statement is incorrect. I then introduce a new property, local balancedness, which allows us both to correct Geanakoplos’s result, and to extend it to cases where the truth axiom may fail. I exploit this general Agreement Theorem to provide novel epistemic conditions for correlated and Nash equilibrium, both of which relax the assumption of introspective omniscience. In all three cases, the results are also extended to infinite state spaces. (This is Chapter 5 of my 2014 Oxford DPhil (PhD) thesis.). (shrink)

There is a large literature exploring how accuracy constrains rational degrees of belief. This paper turns to the unexplored question of how accuracy constrains knowledge. We begin by introducing a simple hypothesis: increases in the accuracy of an agent’s evidence never lead to decreases in what the agent knows. We explore various precise formulations of this principle, consider arguments in its favour, and explain how it interacts with different conceptions of evidence and accuracy. As we show, the principle has some (...) noteworthy consequences for the wider theory of knowledge. First, it implies that an agent cannot be justified in believing a set of mutually inconsistent claims. Second, it implies the existence of a kind of epistemic blindspot: it is not possible to know that one’s evidence is misleading. (shrink)

This paper explores the consequences of applying two natural ideas from epistemology to decision theory: (1) that knowledge should guide our actions, and (2) that we know a lot of non-trivial things. In particular, we explore the consequences of these ideas as they are applied to standard decision theoretic puzzles such as the St. Petersburg Paradox. In doing so, we develop a “knowledge-first” decision theory and we will see how it can help us avoid fanaticism with regard to the St. (...) Petersburg puzzle and related puzzles. The result will be a decision theory that gives a novel, but well-motivated, reason for discounting small probabilities when making decisions. We examine the merits and demerits of such a decision theory. (shrink)

We propose a new topological semantics for evidence, evidence-based justifications, belief, and knowledge. Resting on the assumption that an agent’s rational belief is based on the available evidence, we try to unveil the concrete relationship between an agent’s evidence, belief, and knowledge via a rich formal framework afforded by topologically interpreted modal logics. We prove soundness, completeness, decidability, and the finite model property for the associated logics, and apply this setting to analyze key epistemological issues such as “no false lemma” (...) Gettier examples, misleading defeaters, undefeated justification versus undefeated belief, as well as the defeasibility theories of knowledge. (shrink)

kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K⁠, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weakK¬K⁠, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weakK¬K are much stronger than (...) they initially appear. Jointly, they entail kk and K¬K⁠. And they are susceptible to variants of the standard arguments against kk and K¬K⁠. This has interesting implications for the debate on positive introspection and for deeper issues concerning the structure and limits of knowability. (shrink)

Recent research has identified a tension between the Safety principle that knowledge is belief without risk of error, and the Closure principle that knowledge is preserved by competent deduction. Timothy Williamson reconciles Safety and Closure by proposing that when an agent deduces a conclusion from some premises, the agent’s method for believing the conclusion includes their method for believing each premise. We argue that this theory is untenable because it implies problematically easy epistemic access to one’s methods. Several possible solutions (...) are explored and rejected. (shrink)

We offer a general framework for theorizing about the structure of knowledge and belief in terms of the comparative normality of situations compatible with one’s evidence. The guiding idea is that, if a possibility is sufficiently less normal than one’s actual situation, then one can know that that possibility does not obtain. This explains how people can have inductive knowledge that goes beyond what is strictly entailed by their evidence. We motivate the framework by showing how it illuminates knowledge about (...) the future, knowledge of lawful regularities, knowledge about parameters measured using imperfect instruments, the connection between knowledge, belief, and probability, and the dynamics of knowledge and belief in response to new evidence. (shrink)

John Cook Wilson is an important predecessor of contemporary knowledge first epistemologists: among other parallels, he claimed that knowledge is indefinable. We reconstruct four arguments for this claim discernible in his work, three of which find no clear analogues in contemporary discussions of knowledge first epistemology. We pay special attention to Cook Wilson’s view of the relation between knowledge and forms of thinking (like belief). Claims of Cook Wilson’s that support the indefinability of knowledge include: that knowledge, unlike belief, straddles (...) an active/passive divide; that, rather than entailing belief, knowledge excludes belief; and that understanding forms of thinking other than knowledge (such as belief) depends on understanding knowledge. Reflecting on Cook Wilson’s framework highlights underappreciated concerns relevant to any attempt to define knowledge. (shrink)

In this paper, we propose a unified account of conditionals inspired by Frank Ramsey. Most contemporary philosophers agree that Ramsey’s account applies to indicative conditionals only. We observe against this orthodoxy that his account covers subjunctive conditionals as well—including counterfactuals. In light of this observation, we argue that Ramsey’s account of conditionals resembles Robert Stalnaker’s possible worlds semantics supplemented by a model of belief. The resemblance suggests to reinterpret the notion of conditional degree of belief in order to overcome a (...) tension in Ramsey’s account. The result of the reinterpretation is a tenable account of conditionals that covers indicative and subjunctive as well as qualitative and probabilistic conditionals. (shrink)

According to an influential recent view, S is propositionally justified in believing p iff S is in no position to know that S is in no position to know p. I argue that this view faces compelling counterexamples.

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

Sven Rosenkranz’s Justification as Ignorance shows how a strongly internalist conception of justification can be derived from a strongly externalist conception of knowledge, given an identification of justification with second-order ignorance and a set of structural principles concerning knowing and being in a position to know. Among these principles is an epistemic analogue of the Geach modal schema which states that one is always in a position to know that one doesn’t know p or in a position to know that (...) one doesn’t know not-p. Even suitably refined, the principle faces a range of counterexamples in which it misleadingly and persistently seems to one that one knows whether p without it seeming to one that one knows p nor that one knows not-p. These cases also threaten the book’s case for the luminosity of second-order ignorance, which is in turn central to its derivation of strongly internalist principles of justification. (shrink)

Abstract. Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological models of knowledge (...) and belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB-logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. (shrink)

This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...) constructions; comparisons with other semantics for modal logic ; neighborhood semantics for first-order modal logic, applications in game theory ; applications in epistemic logic ; and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic ; or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory. (shrink)

Philosophical Perspectives, Volume 35, Issue 1, Page 206-228, December 2021.

A variety of recent work in epistemology employs a notion of normality to provide novel theories of knowledge or justification. While such theories are commonly advertised as affording particularly strong epistemic logics, they often make substantive assumptions about the background notion of normality and its logic. This article takes recent normality-based defences of the KK principle as a case study to submit such assumptions to scrutiny. After clarifying issues regarding the natural language use of normality claims, the article isolates a (...) number of choice points regarding the role of contingency, context-sensitivity and similarity in our theorizing with normality. It turns out that both weaker and stronger logics of normality can be motivated depending on how such choices are resolved. And yet securing logics of normality strong enough for normality to play its envisaged role in epistemology may have unwelcome downstream consequences for the resultant theories of knowledge or justification. (shrink)

Recent work has argued that belief is weak: the level of rational credence required for belief is relatively low. That literature has contrasted belief with assertion, arguing that the latter requires an epistemic state much stronger than (weak) belief---perhaps knowledge or even certainty. We argue that this is wrong: assertion is just as weak as belief. We first present a variety of new arguments for this, and then show that the standard arguments for stronger norms are not convincing. Finally, we (...) sketch an alternative picture on which the fundamental norm of assertion is to say what you believe, but both belief and assertion are weak. To help make sense of this, we propose that both belief and assertion involve navigating a tradeoff between accuracy and informativity, and so it can makes sense to believe/say something you only have weak evidence for, if it is informative enough. (shrink)

This paper explores the principle that knowledge is fragile, in that whenever S knows that S doesn’t know that S knows that p, S thereby fails to know p. Fragility is motivated by the infelicity of dubious assertions, utterances which assert p while acknowledging higher-order ignorance whether p. Fragility is interestingly weaker than KK, the principle that if S knows p, then S knows that S knows p. Existing theories of knowledge which deny KK by accepting a Margin for Error (...) principle can be conservatively extended with Fragility. (shrink)

I explore the motivation and logical consequences of the idea that we have some (limited) ability to know contingent facts about the future, even in presence of the assumption that the future is objectively unsettled or indeterminate. I start by formally characterizing skepticism about the future. This analysis nudges the anti-skeptic towards the idea that if some propositions about the future are objectively indeterminate, then it may be indeterminate whether a suitably positioned agent knows them. -/- Philosophical Perspectives, Volume 35, (...) Issue 1, Page 50-69, December 2021. (shrink)

Abstract. The aim of this paper is to show that the topological interpretation of knowledge as an interior kernel operator K of a topological space (X, OX) comes along with a partially ordered family of belief modalities B that fit K in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB logic of knowledge and belief with the exception of the contentious axiom of negative introspection (NI). The new belief modalities B introduced in this paper are (...) defined with the help of the (dense) nuclei of the Heyting algebra OX of open subsets on the topological space (X, OX). In this way, the natural context for the belief operators B related to topological knowledge operator K is shown to be the Heyting algebra NUC(OX) of the nuclei of the Heyting algebra OX.1 More precisely, the dense nuclei of NUC(OX) can be used to define a variety of bimodal logics of knowledge operators K and belief operators B. The operators K and B are compatible with each other in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB system with the exception of the axiom (NI). Therefore, for (X, OX), one obtains a bounded, partially ordered family of belief operators B defined by the elements of NUC(OX). (shrink)

Formal models of appearance and reality have proved fruitful for investigating structural properties of perceptual knowledge. This paper applies the same approach to epistemic justification. Our central goal is to give a simple account of The Preface, in which justified belief fails to agglomerate. Following recent work by a number of authors, we understand knowledge in terms of normality. An agent knows p iff p is true throughout all relevant normal worlds. To model The Preface, we appeal to the normality (...) of error. Sometimes, it is more normal for reality and appearance to diverge than to match. We show that this simple idea has dramatic consequences for the theory of knowledge and justification. Among other things, we argue that a proper treatment of The Preface requires a departure from the internalist idea that epistemic justification supervenes on the appearances and the widespread idea that one knows most when free from error. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal and hyperintensional cognitivism and modal and hyperintensional expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics, comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are categorically dual. I examine five methods for modeling the dynamics of conceptual (...) engineering for intensions and hyperintensions. I develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. I examine then the virtues unique to the modal and hyperintensional expressivist approaches here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of$$T \times W$$T×Wmodels, and the (...) proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper. (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)

The most widespread models of rational reasoners (the model based on modal epistemic logic and the model based on probability theory) exhibit the problem of logical omniscience. The most common strategy for avoiding this problem is to interpret the models as describing the explicit beliefs of an ideal reasoner, but only the implicit beliefs of a real reasoner. I argue that this strategy faces serious normative issues. In this paper, I present the more fundamental problem of logical omnipotence, which highlights (...) the normative content of the problem of logical omniscience. I introduce two developments of the notion of implicit belief (accessible and stable belief ) and use them in two versions of the most common strategy applied to the problem of logical omnipotence. (shrink)

This paper provides a conceptual exploration of the implication of Jeffrey’s rule of belief revision to account for rule-following behavior in a game-theoretic framework. Jeffrey’s rule reflects the fact that in many cases learning something new does not imply that one has full assurance about the true content of the information. In other words, the same information may be both perceived and interpreted in several different ways. I develop an account of rule-following behavior according to which, in the context of (...) strategic interactions, following a rule is defined by two conditions. First, that agents must frame the interaction in a sufficiently similar way and be aware of the same salient properties, i.e. they must have the same partition of the event. Second, they must ascribe to others the same revised probabilities to what they take to be the common partition. In a game-theoretic framework, this also indicates that rule-following behavior cannot be identified merely to the existence of a common prior. (shrink)

In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge. Building on Stalnaker’s core insights, we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and what is knowable; we argue that the foundational axioms of Stalnaker’s system rely intuitively on both of these notions. More precisely, we argue that the plausibility of the (...) principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an “evidence-in-hand” conception of knowledge and a weaker “evidence-out-there” notion of what could come to be known. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker’s postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics. (shrink)

We consider a basic logic with two primitive uni-modal operators: one for certainty and the other for plausibility. The former is assumed to be a normal operator, while the latter is merely a classical operator. We then define belief, interpreted as “maximally plausible possibility”, in terms of these two notions: the agent believes \ if she cannot rule out \ ), she judges \ to be plausible and she does not judge \ to be plausible. We consider four interaction properties (...) between certainty and plausibility and study how these properties translate into properties of belief. We then prove that all the logics considered are minimal logics for the highlighted theorems. We also consider a number of possible interpretations of plausibility, identify the corresponding logics and show that some notions considered in the literature are special cases of our framework. (shrink)

This paper argues that two widely accepted principles about the indicative conditional jointly presuppose the falsity of one of the most prominent arguments against epistemological iteration principles. The first principle about the indicative conditional, which has close ties both to the Ramsey test and the “or‐to‐if” inference, says that knowing a material conditional suffices for knowing the corresponding indicative. The second principle says that conditional contradictions cannot be true when their antecedents are epistemically possible. Taken together, these principles entail that (...) it is impossible to be in a certain kind of epistemic state: namely, a state of ignorance about which of two partially overlapping bodies of knowledge corresponds to one's actual one. However, some of the more popular “margin for error” style arguments against epistemological iteration principles suggest that such states are not only possible, but commonplace. I argue that the tension between these views runs deep, arising just as much for non‐factive attitudes like belief, presupposition, and certainty. I also argue that this is worse news for those who accept the principles about the indicative conditional than it is for those who reject epistemological iteration principles. (shrink)

We present a framework for epistemic logic, modeling the logical aspects of System 1 and System 2 cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the logical consequences (...) of such knowledge and beliefs, by paying a cognitive cost. The framework is applied to three instances of limited rationality, widely discussed in cognitive psychology: Stereotypical Thinking, the Framing Effect, and the Anchoring Effect. (shrink)

This paper explores the relationship between dynamic and truth conditional semantics for epistemic modals. It provides a generalization of a standard dynamic update semantics for modals. This new semantics derives a Kripke semantics for modals and a standard dynamic semantics for modals as special cases. The semantics allows for new characterizations of a variety of principles in modal logic, including the inconsistency of ‘p and might not p’. Finally, the semantics provides a construction procedure for transforming any truth conditional semantics (...) for modals into a dynamic semantics for modals with similar properties. (shrink)

There is much to like about the idea that justification should be understood in terms of normality or normic support (Smith 2016, Goodman and Salow 2018). The view does a nice job explaining why we should think that lottery beliefs differ in justificatory status from mundane perceptual or testimonial beliefs. And it seems to do that in a way that is friendly to a broadly internalist approach to justification. In spite of its attractions, we think that the normic support view (...) faces two serious challenges. The first is that it delivers the wrong result in preface cases. These cases suggest that the view is either too sceptical or too externalist. The second is that the view struggles with certain kinds of Moorean absurdities. It turns out that these problems can easily be avoided. If we think of normality as a condition on *knowledge*, we can characterise justification in terms of its connection to knowledge and thereby avoid the difficulties discussed here. The resulting view does an equally good job explaining why we should think that our perceptual and testimonial beliefs are justified when lottery beliefs cannot be. Thus, it seems that little could be lost and much could be gained by revising the proposal and adopting a view on which it is knowledge, not justification, that depends directly upon normality. (shrink)

KK is the thesis that if you can know p, you can know that you can know p. Though it’s unpopular, a flurry of considerations has recently emerged in its favour. Here we add fuel to the fire: standard resources allow us to show that any failure of KK will lead to the knowability and assertability of abominable indicative conditionals of the form ‘If I don’t know it, p’. Such conditionals are manifestly not assertable—a fact that KK defenders can easily (...) explain. I survey a variety of KK-denying responses and find them wanting. Those who object to the knowability of such conditionals must either deny the possibility of harmony between knowledge and belief, or deny well-supported connections between conditional and unconditional attitudes. Meanwhile, those who grant knowability owe us an explanation of such conditionals’ unassertability—yet no successful explanations are on offer. Upshot: we have new evidence for KK. (shrink)

Assume that it is your evidence that determines what opinions you should have. I argue that since you should take peer disagreement seriously, evidence must have two features. (1) It must sometimes warrant being modest: uncertain what your evidence warrants, and (thus) uncertain whether you’re rational. (2) But it must always warrant being guided: disposed to treat your evidence as a guide. Surprisingly, it is very difficult to vindicate both (1) and (2). But diagnosing why this is so leads to (...) a proposal—Trust—that is weak enough to allow modesty but strong enough to yield many guiding features. In fact, I claim that Trust is the Goldilocks principle—for it is necessary and sufficient to vindicate the claim that you should always prefer to use free evidence. Upshot: Trust lays the foundations for a theory of disagreement and, more generally, an epistemology that permits self-doubt—a modest epistemology. (shrink)

The paper explores a structural account of propositional justification in terms of the notion of being in a position to know and negation. Combined with a non-normal logic for being in a position to know, the account allows for the derivation of plausible principles of justification. The account is neutral on whether justification is grounded in internally individuated mental states, and likewise on whether it is grounded in facts that are already accessible by introspection or reflection alone. To this extent, (...) it is compatible both with internalism and with externalism about justification. Even so, the account allows for the proof of principles that are commonly conceived to depend on an internalist conception of justification. The account likewise coheres both with epistemic contextualism and with its rejection, and is compatible both with the knowledge-first approach and with its rejection. Despite its neutrality on these issues, the account makes propositional justification luminous and so is controversial. However, it proves quite resilient in the light of recent anti-luminosity arguments. (shrink)

The notion of an ideal reasoner has several uses in epistemology. Often, ideal reasoners are used as a parameter of (maximum) rationality for finite reasoners (e.g. humans). However, the notion of an ideal reasoner is normally construed in such a high degree of idealization (e.g. infinite/unbounded memory) that this use is unadvised. In this dissertation, I investigate the conditions under which an ideal reasoner may be used as a parameter of rationality for finite reasoners. In addition, I present and justify (...) the research program of computational epistemology, which investigates the parameter of maximum rationality for finite reasoners using computer simulations. (shrink)

Some people commonly know a proposition just in case they all know it, they all know that they all know it, they all know that they all know that they all know it, and so on. They commonly believe a proposition just in case they all believe it, they all believe that they all believe it, they all believe that they all believe that they all believe it, and so on. A long tradition in economic theory, theoretical computer science, linguistics (...) and philosophy has held that people have some approximation of common knowledge or common belief in a range of circumstances, for example, when they are looking at an object together, or when they have just discussed something explicitly in conversation. In this paper, I argue that people do not have any approximation of common knowledge or common belief in these circumstances. The argument suggests that people never have any approximation of common knowledge or common belief. (shrink)

The Lockean Thesis says that you must believe p iff you’re sufficiently confident of it. On some versions, the 'must' asserts a metaphysical connection; on others, it asserts a normative one. On some versions, 'sufficiently confident' refers to a fixed threshold of credence; on others, it varies with proposition and context. Claim: the Lockean Thesis follows from epistemic utility theory—the view that rational requirements are constrained by the norm to promote accuracy. Different versions of this theory generate different versions of (...) Lockeanism; moreover, a plausible version of epistemic utility theory meshes with natural language considerations, yielding a new Lockean picture that helps to model and explain the role of beliefs in inquiry and conversation. Your beliefs are your best guesses in response to the epistemic priorities of your context. Upshot: we have a new approach to the epistemology and semantics of belief. And it has teeth. It implies that the role of beliefs is fundamentally different than many have thought, and in fact supports a metaphysical reduction of belief to credence. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Dorr et al. present a case that poses a challenge for a number of plausible principles about knowledge and objective chance. Implicit in their discussion is an interesting new argument against KK, the principle that anyone who knows p is in a position to know that they know p. We bring out this argument, and investigate possible responses for defenders of KK, establishing new connections between KK and various knowledge-chance principles.