The KK Principle

This essay provides a novel account of iterated epistemic states. The essay argues that states of epistemic determinacy might be secured by countenancing iterated epistemic states on the model of fixed points in the modal $\mu$-calculus. Despite the epistemic indeterminacy witnessed by the invalidation of modal axiom 4 in the sorites paradox -- i.e. the KK principle: $\square$$\phi$ $\rightarrow$ $\square$$\square$$\phi$ -- a hyperintensional epistemic $\mu$-automaton permits fixed points to entrain a principled means by which to iterate epistemic states and account (...) thereby for necessary conditions on self-knowledge. The hyperintensional epistemic $\mu$-calculus is applied to the iteration of the epistemic states of a single agent instead of the common knowledge of a group of agents, and is thus a novel contribution to the literature. (shrink)

In his Knowledge and Belief (1962), Hintikka establishes his system of epistemic logic with the KK (Knowing that One Knows, in symbols, Kp→KKp) principle (KK for short). However, his system of epistemic logic and the KK principle are grounded upon his strong notion of knowledge, which requires that knowledge is infallible, that is, it makes further inquiry pointless, and becomes ‘discussion-stopper’; knowledge implies truth, to wit, cognitive agents will not be mistaken in their knowledge; cognitive agents will be ‘perfect logicians’, (...) i.e. they have infinitive capability of logical inference. Hintikka calls the argument for KK from the strong notion of knowledge as the ‘transcendental argument’ for KK. Obviously, the strong notion of knowledge is far away from our ordinary conception of knowledge; based on such a strong sense of knowledge, epistemic logic has met the problem of logical omnipotence, and is difficult to apply in our ordinary cognitive practice. Moreover, there is no close connection of the KK principle with internalism or externalism. (shrink)

Williamson (2000) argues that the KK principle is inconsistent with knowledge of margin for error in cases of inexact perceptual observations. This paper argues, primarily by analogy to a different scenario, that Williamson’s argument is fallacious. Margin for error principles describe the agent’s knowledge as a result of an inexact perceptual event, not the agent’s knowledge state in general. Therefore, epistemic agents can use their knowledge of margin for error at most once after a perceptual event, but not more. This (...) insight blocks a crucial step in Williamson’s original argument. Along the way, the value of standard epistemic logic for analyzing margin for error reasoning is challenged. (shrink)

The various themes explored in this superb collection of essays are organised around one thinker, John McDowell, and one central idea.

The aim of this paper is to analyse and develop how scepticism becomes an intelligible question starting from requirements that epistemologists themselves aim to endorse. We argue for and defend the idea that the root of scepticism is the underdetermination principle by articulating its specificitya respectable epistemic principle and by defending it against objections in current literature. This engagement offers a novel understanding of underdetermination-based scepticism. While most anti-sceptical approaches challenge scepticism by understanding it as postulating uneliminated scenarios of mass (...) deception, or as endorsing unnatural epistemic requirements, we argue here that both contentions are mistaken. Underdetermination-based scepticism targets our beliefs by issuing a genuine question about the rational support they enjoy. If we cannot establish that the sources of our beliefs provide them the required epistemic merit and authority, they lack non-arbitrary grounds. This has a sizable impact on what constitutes a satisfactory anti-sceptical strategy. Strategies that merely focus on the scenario-based aspect of scepticism, or on the truth-functional evaluation of our beliefs, are shown to miss the mark of the sceptical threat. The proposed analysis ultimately provides a shift in perspective concerning the character and reach of philosophical doubt. (shrink)

In On the Trinity 15.12.21, Augustine appears to endorse the KK principle (that if one knows that φ, then one knows that one knows that φ) in the course of giving an argument – the Multiplicity Argument – against the Academic skeptics. Gareth Matthews has disputed Augustine’s endorsement of the KK principle and presented a different reading of the Multiplicity Argument. In this note, I show that Matthews’s construal of the Multiplicity Argument is both interpretively and technically defective and defend (...) the attribution of some form of the KK principle to Augustine. (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)

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)

The Qualitative Thesis says that if you leave open P, then you are sure of if P, then Q just in case you are sure of the corresponding material conditional. We argue the Qualitative Thesis provides compelling reasons to accept a thesis that we call Conditional Locality, which says, roughly, the interpretation of an indicative conditional depends, in part, on the conditional’s local embedding environment. In the first part of the paper, we present an argument—due to Ben Holguín—showing that, without (...) Conditional Locality, the Qualitative Thesis is in tension with a margin for error principle on rational sureness. We show Conditional Locality reconciles the Qualitative Thesis with the margin for error principle. In the second part, we argue the full range of data supports what we call the Strong Qualitative Thesis. Without Conditional Locality, the Strong Qualitative Thesis has unacceptable consequences. But with Conditional Locality, it is tenable. (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)

One of the central arguments for the knowledge norm of assertion appeals to the fact that it is typically legitimate to respond to an assertion with “How do you know?”, intended as a challenge to the assertion. The legitimacy of the challenge is taken as evidence in favor of the idea that permissible assertion requires knowledge. In this paper, I argue that if the legitimacy of “How do you know?” challenges supports a knowledge norm for assertion, it also supports the (...) controversial KK thesis. I further argue that data from assertion prompts likewise supports KK. This is an unwelcome consequence for many proponents of the knowledge norm of assertion who reject KK. At the same time, it constitutes new evidence from conversational patterns in favor of the KK thesis. (shrink)

Kevin Dorst has recently pointed out an apparently puzzling consequence of denying epistemic luminosity: given some natural-sounding bridging principles between knowledge, credence, and indicative conditionals, the denial of epistemic luminosity licenses the knowledge and assertability of abominable-sounding conditionals of the form ⌜If I don’t know that ϕ, then ϕ⌝. We provide a general and systematic examination of this datum by testing Dorst’s claim against various semantics for the indicative conditional in the setting of epistemic logic. Our conclusion is that, regardless (...) of whether knowledge is luminous, the knowability of these conditionals is highly sensitive to the correct semantic analysis of the indicative conditional. Moreover, standard pragmatic resources can explain away the infelicity of such assertions. As it stands, the datum does not tell against epistemic non-luminosity. (shrink)

According to the seventh-century C.E. philosopher Kumārila Bhat.t.a, epistemic agents are warranted in taking their world-presenting experiences as veridical, if they lack defeaters. For him, these experiences are defeasibly sources of knowledge without the agent reflecting on their content or investigating their causal origins. This position is known as svatah prāmāṇya in Sanskrit (henceforth the SP principle). -/- As explicated by the eleventh-century commentator, Pārthasārathi Misŕa, this position entails that epistemic agents know things without simultaneously knowing that they know them, (...) or being in a position to know that they know. In contrast, some contemporary Anglo-analytic philosophers argue for the “knows-knows principle” (KK principle), in which if someone knows that p, then that person also knows that they know that p, or that person is in a position to know that they know p. Despite some apparent similarities, the SP principle is not a version of the KK principle, nor would Pārthasārathi’s Kumārila have held the KK principle. -/- Recently, Daniel Immerman (2018) has argued that the SP principle is a position-to-know version of the “knows-knows principle” (KK-pos principle). By examining Kumārila’s response to his Buddhist opponent, who challenges the veracity of Vedic testimony, we will see that Kumārila understands higher-order knowing as involving an independent check on one’s epistemic processes, through an epistemic instrument known as postulation (arthāpatti). This precludes him from holding the KK-pos principle. (shrink)

Why should we avoid incoherence? An influential view tells us that incoherent combinations of attitudes are such that it is impossible for all of those attitudes to be simultaneously vindicated by the evidence. But it is not clear whether this view successfully explains what is wrong with certain akratic doxastic states. In this paper I flesh out an alternative response to that question, one according to which the problem with incoherent combinations of attitudes is that it is impossible for all (...) of those attitudes to be simultaneously knowledgeable. This alternative response explains what is wrong with akratic combinations of attitudes using commonly accepted epistemological theses. The paper still shows how this proposal is able to explain the badness of incoherent combinations involving the absence of attitudes, suspended judgment and credence. These explanations deploy the notions of knowledge and being in a position to know, instead of the notion of responding properly to the evidence. Finally, I suggest that this picture can be generalized to the realm of practical rationality as well. (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)

There is a very plausible principle linking abilities and possibilities: If S is able to Φ, then it is metaphysically possible that S Φ’s. Jack Spencer recently proposed a class of counterexamples to this principle involving the ability to know certain propositions. I renew an argument against these counterexamples based on the unknowability of Fitch propositions. In doing so, I provide a new argument for the unknowability of Fitch propositions and show that Spencer’s counterexamples are in tension with a principle (...) weaker than the one linking abilities and possibilities. (shrink)

The present paper argues that there is a knowledge norm for conversational implicature: one may conversationally implicate p only if one knows p. Linguistic data about the cancellation behavior of implicatures and the ways they are challenged and criticized by speakers is presented to support the thesis. The knowledge norm for implicature is then used to present a new consideration in favor of the KK thesis. It is argued that if implicature and assertion have knowledge norms, then assertion requires not (...) only knowledge but iterated knowledge: knowing that you know that you know that... you know. Such a condition on permissible assertion is argued to be plausible only if the KK thesis is true. (shrink)

In Knowing and Seeing, Michael Ayers presents a view of what he calls primary knowledge according to which one who knows in that way both knows perspicuously and knows how they know. Here, I use some general considerations about seeing, knowing, and knowing how one knows in order to raise some questions about this view. More specifically, I consider some putative limits on one’s capacity to know how one knows. The main question I pursue concerns whether perspicuity should be thought (...) of either (i) as a condition of sensory experience, (ii) as a condition of sense-based cognition, or (iii) as an interface condition, involving interrelations between sensory experience and sense-based cognition. (shrink)

The Surprise Exam Paradox is well-known: a teacher announces that there will be a surprise exam the following week; the students argue by an intuitively sound reasoning that this is impossible; and yet they can be surprised by the teacher. We suggest that a solution can be found scattered in the literature, in part anticipated by Wright and Sudbury, informally developed by Sorensen, and more recently discussed, and dismissed, by Williamson. In a nutshell, the solution consists in realising that the (...) teacher's announcement is a blindspot that can only be known if the week is at least 2 days long. Along the way, we criticise Williamson's own treatment of the paradox. In Williamson's view, the Surprise is similar to the Paradox of the Glimpse and, because of their similarities, both these paradoxes ought to receive a uniform treatment-one that involves locating an illicit application of the KK Principle. We argue that there's no deep analogy between the Surprise and the Glimpse and that, even if there were, the Surprise reasoning reaches a paradoxical conclusion before the KK Principle is used. Rather, in both the Surprise and the Glimpse, the blame should be put on other epistemic principles-respectively, a knowledge retention and a margin for error principle. (shrink)

Editors' preface to the book symposium on Michael Ayers' Knowing and Seeing. Groundwork for a New Empiricism (OUP 2019).

This paper draws out and connects two neglected issues in Kant’s conception of a priori knowledge. Both concern topics that have been important to contemporary epistemology and to formal epistemology in particular: knowability and luminosity. Does Kant commit to some form of knowability principle according to which certain necessary truths are in principle knowable to beings like us? Does Kant commit to some form of luminosity principle according to which, if a subject knows a priori, then they can know that (...) they know a priori? I defend affirmative answers to both of these questions, and by considering the special kind of modality involved in Kant’s conceptions of possible experience and the essential completability of metaphysics, I argue that his combination of knowability and luminosity principles leads Kant into difficulty. (shrink)

A mental state is luminous if, whenever an agent is in that state, they are in a position to know that they are. Following Timothy Williamson’s Knowledge and Its Limits, a wave of recent work has explored whether there are any non-trivial luminous mental states. A version of Williamson’s anti-luminosity appeals to a safety- theoretic principle connecting knowledge and confidence: if an agent knows p, then p is true in any nearby scenario where she has a similar level of confidence (...) in p. However, the relevant notion of confidence is relatively underexplored. This paper develops a precise theory of confidence: an agent’s degree of confidence in p is the objective chance they will rely on p in practical reasoning. This theory of confidence is then used to critically evaluate the anti-luminosity argument, leading to the surprising conclusion that although there are strong reasons for thinking that luminosity does not obtain, they are quite different from those the existing literature has considered. In particular, we show that once the notion of confidence is properly understood, the failure of luminosity follows from the assumption that knowledge requires high confidence, and does not require any kind of safety principle as a premise. (shrink)

Closure principles say that if you know some proposition which entails a second and you meet further conditions then you know the second. In this paper I construct an argument against closure principles which turns on the idea that knowing a proposition requires that one’s belief-forming process be reliable. My argument parallels an influential argument offered by Timothy Williamson against KK principles–principles that say that if you know some proposition and you meet further conditions then you know that you know (...) the proposition. After offering my argument, I provisionally assess its damage to closure principles and also look at how responses to my argument against closure principles can be used to generate responses to Williamson’s argument against KK principles. (shrink)

Many of our sources of knowledge only afford us knowledge that is inexact. When trying to see how tall something is, or to hear how far away something is, or to remember how long something lasted, we may come to know some facts about the approximate size, distance or duration of the thing in question but we don’t come to know exactly what its size, distance or duration is. In some such situations we also have some pointed knowledge of how (...) inexact our knowledge is. That is, we can knowledgeably pinpoint some exact claims that we do not know. We show that standard models of inexact knowledge leave little or no room for such pointed knowledge. We devise alternative models that are not afflicted by this shortcoming. (shrink)

According to the KK-principle, knowledge iterates freely. It has been argued, notably in Greco, that accounts of knowledge which involve essential appeal to normality are particularly conducive to defence of the KK-principle. The present article evaluates the prospects for employing normality in this role. First, it is argued that the defence of the KK-principle depends upon an implausible assumption about the logical principles governing iterated normality claims. Once this assumption is dropped, counter-instances to the principle can be expected to arise. (...) Second, it is argued that even if the assumption is maintained, there are other logical properties of normality which can be expected to lead to failures of KK. Such failures are noteworthy, since they do not depend on either a margins-for-error principle or safety condition of the kinds Williamson appeals to in motivating rejection KK. “Introduction: KK and Being in a Position to Know” Section formulates two versions of the KK-Principle; “Inexact Knowledge and Margins for Error” Section presents a version of Williamson’s margins-for-error argument against it; “Knowledge and Normality” and “Iterated Normality” Sections discuss the defence of the KK-Principle due to Greco and show that it is dependent upon the implausible assumption that the logic of normality ascriptions is at least as strong as K4; finally, “Knowledge in Abnormal Conditions” and “Higher-Order Ignorance Inside the Margins” Sections argue that a weakened version of Greco’s constraint on knowledge is plausible and demonstrate that this weakened constraint will, given uncontentious assumptions, systematically generate counter-instances to the KK-principle of a novel kind. (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)

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)

The early literature on epistemic logic in philosophy focused on reasoning about the knowledge or belief of a single agent, especially on controversies about "introspection axioms" such as the 4 and 5 axioms. By contrast, the later literature on epistemic logic in computer science and game theory has focused on multi-agent epistemic reasoning, with the single-agent 4 and 5 axioms largely taken for granted. In the relevant multi-agent scenarios, it is often important to reason about what agent A believes about (...) what agent B believes about what agent A believes; but it is rarely important to reason just about what agent A believes about what agent A believes. This raises the question of the extent to which single-agent introspection axioms actually matter for multi-agent epistemic reasoning. In this paper, we formalize and answer this question. To formalize the question, we first define a set of multi-agent formulas that we call agent-alternating formulas, including formulas like Box_a Box_b Box_a p but not formulas like Box_a Box_a p. We then prove, for the case of belief, that if one starts with multi-agent K or KD, then adding both the 4 and 5 axioms (or adding the B axiom) does not allow the derivation of any new agent-alternating formulas—in this sense, introspection axioms do not matter. By contrast, we show that such conservativity results fail for knowledge and multi-agent KT, though they hold with respect to a smaller class of agent-nonrepeating formulas. (shrink)

This paper examines the relationship between the KK principle and the epistemological theses of externalism and internalism. In particular we examine arguments from Okasha (Analysis 73(1):80–86, 2013) and Greco (J Philos 111(4):169–197, 2014) which deny that we can derive the denial of the KK principle from externalism.

Augment the propositional language with two modal operators: □ and ■. Define ⧫ to be the dual of ■, i.e. ⧫=¬■¬. Whenever (X) is of the form φ → ψ, let (X⧫) be φ→⧫ψ . (X⧫) can be thought of as the modally qualified counterpart of (X)—for instance, under the metaphysical interpretation of ⧫, where (X) says φ implies ψ, (X⧫) says φ implies possibly ψ. This paper shows that for various interesting instances of (X), fairly weak assumptions suffice for (...) (X⧫) to imply (X)—so, the modally qualified principle is as strong as its unqualified counterpart. These results have surprising and interesting implications for issues spanning many areas of philosophy. (shrink)

An important question in epistemology is whether the KK principle is true, i.e., whether an agent who knows that p is also thereby in a position to know that she knows that p. We explain how a “transparency” account of self-knowledge, which maintains that we learn about our attitudes towards a proposition by reflecting not on ourselves but rather on that very proposition, supports an affirmative answer. In particular, we show that such an account allows us to reconcile a version (...) of the KK principle with an “externalist” or “reliabilist” conception of knowledge commonly thought to make that principle particularly problematic. (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.

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s paradox. The references (...) and recommended readings provide gateways for further exploration. (shrink)

Knows-knows principles in epistemology say that if you know some proposition, then you are in a position to know that you know it. This paper examines the viability of analogous principles in ethics, which I call ought-ought principles. Several epistemologists have recently offered new defences of KK principles and of other related principles, and there has recently been an increased interest in examining analogies between ethics and epistemology, and so it seems natural to examine whether defences of KK and related (...) principles carry over to OO principles. In this paper, I introduce two OO principles, and I show how some arguments in favour of KK carry over to them. Then I show how these OO principles can be used to shed light on a much-discussed case in ethics, that of Professor Procrastinate. (shrink)

In a recent paper, Murali Ramachandran endorses a principle that he thinks can help us solve the surprise test puzzle and cause problems for a Williamsonian argument against KK principles. But in this paper I argue that his principle is false and as a result it cannot do either.

This essay defends a principle that promises to help illuminate the nature of reflective knowledge. The principle in question belongs to a broader category called knows-knows principles, or KK principles for short. Such principles say that if you know some proposition, then you're in a position to know that you know it.KK principles were prominent among various historical philosophers and can be fruitfully integrated with many views in contemporary epistemology and beyond—and yet almost every contemporary analytic epistemologist thinks that they (...) are false.Regarding their historical pedigree: they've been endorsed by Plato, Aristotle, Augustine, Averroes, Aquinas, Spinoza, and Schopenhauer, among others.1Regarding... (shrink)

Suppose you’d like to believe that p, whether or not it’s true. What can you do to help? A natural initial thought is that you could engage in Intentionally Biased Inquiry : you could look into whether p, but do so in a way that you expect to predominantly yield evidence in favour of p. This paper hopes to do two things. The first is to argue that this initial thought is mistaken: intentionally biased inquiry is impossible. The second is (...) to show that reflections on intentionally biased inquiry strongly support a controversial ‘access’ principle which states that, for all p, if p is part of our evidence, then that p is part of our evidence is itself part of our evidence. (shrink)

Roy Sorensen introduced the concept of an epistemic blindspot in the 1980s. A proposition is an epistemic blindspot for some individual at some time if and only if that proposition is consistent but unknowable by that individual at that time. In the first half of this paper, I extend Sorensen work on blindspots by arguing that there exist blindspots that essentially involve hopes. In the second half, I show how such blindspots can contribute to and impair different pursuits of self-understanding. (...) My arguments throughout this paper draw on Luc Bovens’s account of hope. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine 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 cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (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} are 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 my 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. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that 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 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 the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent 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 while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. 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)

The KK-principle can be defined as follows: “For any subject x : if x knows that p, then she is always in a position to know that she knows that p ”. This principle has been widely accepted in the history of philosophy. However, in contemporary epistemology it is considered controversial and regarded as an important part of the debate concerning the nature of knowledge. One of the arguments against the KK-principle has been presented by Timothy Williamson and it involves (...) the so-called “safety principle”. In this paper, I argue against this account. My argument consists of two parts: in the first part, it is argued that the safety principle presented by Williamson contradicts Dretske’s account of knowledge. In the second part, I claim that the safety principle, as defined by Williamson, is not precise enough, which enables one to argue that it does not contradict the KK-principle. (shrink)

One main argument that has been offered in support of the Knowledge Account of Assertion is that it successfully makes sense of a variety of Moorean-paradoxical claims. David Sosa has objected to the Knowledge Account by arguing that it does not generalize satisfactorily to make sense of the oddity of iterated conjunctions of the form “p but I don’t know whether I know that p”. Recently, Martin Montminy has offered a defense of the Knowledge Account. In this paper, I show (...) that both Montminy’s and Sosa’s arguments fail. First, I argue that Montminy does not offer a good reply to Sosa; then I show that Sosa’s objection actually does not constitute a real threat to the Knowledge Account. (shrink)

This paper argues for several related theses. First, the epistemological position that knowledge requires safe belief can be motivated by views in the philosophy of science, according to which good explanations show that their explananda are robust. This motivation goes via the idea—recently defended on both conceptual and empirical grounds—that knowledge attributions play a crucial role in explaining successful action. Second, motivating the safety requirement in this way creates a choice point—depending on how we understand robustness, we'll end up with (...) different conceptions of safety in epistemology. Lastly, and most controversially, there's an attractive choice at this point that will not vindicate some of the most influential applications of the safety-theoretic framework in epistemology, e.g., Williamson's arguments against the KK principle, and luminosity. (shrink)

The status of the knowledge iteration principles in the account provided by Lewis in “Elusive Knowledge” is disputed. By distinguishing carefully between what in the account describes the contribution of the attributor’s context and what describes the contribution of the subject’s situation, we can resolve this dispute in favour of Holliday’s claim that the iteration principles are rendered invalid. However, that is not the end of the story. For Lewis’s account still predicts that counterexamples to the negative iteration principle ) (...) come out as elusive: such counterexamples can occur only in possibilities which the attributors of knowledge are ignoring. This consequence is more defensible than it might look at first sight. (shrink)

_ Source: _Page Count 12 In a previous article, I argued against the widespread reluctance of philosophers to treat skeptical challenges to our a priori knowledge of necessary truths with the same seriousness as skeptical challenges to our a posteriori knowledge of contingent truths. Hamid Vahid has recently offered several reasons for thinking the unequal treatment of these two kinds of skepticism is justified, one of which is a priori skepticism’s seeming dependence upon the widely scorned kk thesis. In the (...) present article, I defend a priori skepticism against Vahid’s criticisms. (shrink)

Some time ago I wrote a paper about conceivability and knowledge. An anonymous referee rejected it on the grounds that the result had already been established in a short story by Jorge Luis Borges. Intrigued, I looked for the story but found no mention of it in Louis and Ziche’s extensive bibliography. I spent months consulting archives and electronic records to no avail. I had begun to doubt whether the story even existed when I had the curious good luck to (...) encounter Sir Thomas Browne of Pembroke College, Oxford, who assured me of the piece’s authenticity and introduced me to Brother Christian Rosenkreuz of Invisible College who in turn generously put me into correspondence with Borges himself. The literary defects in what follows reflect not a diminution of Borges’s undoubted power as a storyteller, but merely my limited ability as an amateur translator. Whatever the translation’s literary faults may be, I hope the story’s philosophical interest—i.e., an argument that ideal conceivers have higher-order knowledge of necessary truths—remains. [Trans.]. (shrink)

In this paper I present a qualified defense of the KK principle. In section one I introduce two popular arguments against the KK principle, along with an example in which these arguments seem to prove too much. In section two I provide a simple formal model of knowledge in which KK holds, and which I argue provides an attractive analysis of the example from section one. I go on argue that when this model is combined with contextualism, we can retain (...) our attractive analysis of the example, while also explaining away the appeal of the aforementioned arguments against KK. I use the same maneuver contextualists have used to defend epistemic closure principles--I argue that KK holds within contexts, but can fail across contexts. (shrink)

In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.

The knowledge account of assertion - roughly: one should not assert what one does not know - can explain a variety of Moorean conjunctions, a fact often cited as evidence in its favor. David Sosa ("Dubious Assertions," Phil Studies, 2009) has objected that the account does not generalize satisfactorily, since it cannot explain the infelicity of certain iterated conjunctions without appealing to the controversial "KK" principle. This essay responds by showing how the knowledge account can handle such conjunctions without use (...) of the KK principle. (shrink)