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 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 epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-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 μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-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 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 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 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 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 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 Ω-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 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 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 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 13 examines modal responses to the alethic paradoxes. Chapter 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 is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the modal $\mu$-calculus. Via correspondence results between fixed point modal propositional logic and the bisimulation-invariant fragment of monadic second-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the modal operators regimenting the (...) notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via a topic-sensitive epistemic two-dimensional truthmaker semantics. (shrink)

This dissertation concerns the foundations of epistemic modality. 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 dissertation demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...) epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the apriori-aposteriori distinction; to the modal profile of rational propositional intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Examining the nature of epistemic logic itself, I develop a novel approach to conditions of self-knowledge in the setting of the modal μ-calculus, as well as novel epistemicist solutions to Curry's, the liar, and the knowability paradoxes. Solutions to previously intransigent issues concerning the first-person concept; the distinction between fundamental and derivative truths; and the unity of intention and its role in decision theory, are developed along the way. (shrink)

We provide new findings that add to the growing body of empirical evidence that important epistemic intuitions converge across cultures. Specifically, we selected three recent studies conducted in the US that reported surprising effects of knowledge attribution among English speakers. We translated the vignettes used in those studies into Mandarin Chinese and Korean and then ran the studies with participants in Mainland China, Taiwan, and South Korea. We found that, strikingly, all three of the effects first obtained in the US (...) also emerged in the East Asian cultures we studied. Our findings not only cohere with but also provide—at least moderate—support for the existence of extensive convergences of important epistemic intuitions across cultures. (shrink)

The possibility of justified true belief without knowledge is normally motivated by informally classified examples. This paper shows that it can also be motivated more formally, by a natural class of epistemic models in which both knowledge and justified belief are represented. The models involve a distinction between appearance and reality. Gettier cases arise because the agent's ignorance increases as the gap between appearance and reality widens. The models also exhibit an epistemic asymmetry between good and bad cases that sceptics (...) seem to ignore or deny. (shrink)

In recent years, there has been increasing discussion of whether philosophy actually makes progress. This discussion has been prompted, in no small part, by the depth and persistence of disagreement among philosophers on virtually every major theoretical issue in the field. In this paper, I examine the role that the Method of Cases – the widespread philosophical method of testing and revising theories by comparing their verdicts against our intuitions in particular cases – plays in creating and sustaining theoretical disagreements (...) in philosophy. Drawing on work from cognitive psychology, I argue that there is a fundamental incompatibility between the structure of the theories that philosophers seek to construct using the MoC and the structure of the concepts on which our case-specific intuitions are based. This incompatibility renders MoC-based philosophical theorizing unable ever to succeed by the very standards of adequacy that it sets for itself. And this, in turn, helps to explain the depth and persistence of theoretical disagreements – and, in certain ways, the lack of progress – in the many areas of philosophy where the MoC plays an important role. (shrink)

Champions of the methodological movement of experimental philosophy have challenged the long-standing practice of relying on intuitive verdicts on cases in philosophical inquiry. They argue that th...

We report and discuss the results of a series of experiments that address a contrast effect exhibited by folk judgments about knowledge ascriptions. The contrast effect, which was first reported by Schaffer and Knobe, is an important aspect of our folk epistemology. However, there are competing theoretical accounts of it. We shed light on the various accounts by providing novel empirical data and theoretical considerations. Our key findings are, firstly, that belief ascriptions exhibit a similar contrast effect and, secondly, that (...) the contrast effect is systematically sensitive to the content of what is in contrast. We argue that these data pose significant challenges to contrastivist accounts of the contrast effect. Furthermore, some of the data set provides, in conjunction with some non-empirical epistemological arguments, some limited evidence for what we call a focal bias account of the data. According to the focal bias account, the contrast effects arise at least in part because epistemically relevant facts are not always adequately processed when they are presented in certain ways. (shrink)

Do philosophers use intuitions? Should philosophers use intuitions? Can philosophical methods (where intuitions are concerned) be improved upon? In order to answer these questions we need to have some idea of how we should go about answering them. I defend a way of going about methodology of intuitions: a metamethodology. I claim the following: (i) we should approach methodological questions about intuitions with a thin conception of intuitions in mind; (ii) we should carve intuitions finely; and, (iii) we should carve (...) to a grain to which we are sensitive in our everyday philosophising. The reason is that, unless we do so, we don’t get what we want from philosophical methodology. I argue that what we want is information that will aid us in formulating practical advice concerning how to do philosophy responsibly/well/better. (shrink)

The central question for this dissertation is, how do we do moral philosophy well from within a broadly naturalist framework? Its main goal is to lay the groundwork for a methodological approach to moral philosophy that integrates traditional, intuition-driven approaches to ethics with empirical approaches that employ empirical data from biology and cognitive science. Specifically, it explores what restrictions are placed on our moral theorizing by findings in evolutionary biology, psychology, neuroscience, and other fields, and how we can integrate this (...) data while still offering a fully normative account of ethics. To that end, the dissertation explores the methodological assumptions behind both traditional and more empirical or experimental approaches to ethics, to find where these assumptions cannot be properly supported and need to be re-examined. Chapter 1 explores the science-based objections that have been raised to traditional approaches, with a particular focus on questions concerning the reliability of moral intuitions. Chapter 2 examines three fundamental assumptions supporting the empirical approach to moral philosophy, and how those assumptions ultimately do not fit with how we ought to understand the project of ethics. In chapter 3, I discuss the fact/value distinction, and the restrictions that are placed on our moral theorizing by our commitment to this distinction. Chapter 4 offers a defense of ‘companions in guilt’ arguments, and uses these arguments to draw an analogy between moral philosophy and epistemology that will be used to help defend moral philosophy against empirical debunking arguments. Chapter 5 explores the ways in which epistemologists’ methods of incorporating empirical data into their research while maintaining the normativity of their accounts can be adapted to allow moral philosophers to do the same, and brings together the various methodological concerns addressed up to this point to lay out a methodological approach I call empirically-informed moral philosophy. (shrink)

The field of experimental philosophy has received considerable attention, essentially for producing results that seem highly counter-intuitive and at the same time question some of the fundamental methods used in philosophy. A substantial part of this attention has focused on the role of intuitions in philosophical methodology. One of the major contributions of experimental philosophy on this topic has been concrete evidence in support of intuitional diversity; the idea that intuitions vary systematically depending on variables such as ethnicity, socioeconomic background, (...) or gender. Because of the important implications, these findings have been the subject of extensive debate. Despite the seeming significance of the findings and despite all the debates that the experimental philosophy movement has prompted, what has not been examined systematically is the reproducibility of the results. Instead, the reported findings have been simply accepted as established facts. We set out to replicate a wide range of experiments and surprisingly failed to reproduce many of the reported findings, some of which are from the most cited and attention grabbing papers of the field. We draw two conclusions from our findings. The first is that the instability of intuitions has been exaggerated by experimental philosophers. Intuitions appear to be more uniform across different demographic groups. The argument that intuitions need to be discarded because they depend on arbitrary factors such as ethnicity, socioeconomic background, or gender does not seem tenable anymore. The second conclusion is that experimental philosophy needs a better system to ensure the reproducibility of published findings. The current research-publication system of various empirical fields, especially those employing statistical methods, leads to an overproduction of false-positive findings in the published literature. Unless changes are made to the current research-publication system, this overproduction is likely to continue, in experimental philosophy as well as other disciplines. (shrink)

Cognitive scientists have revealed systematic errors in human reasoning. There is disagreement about what these errors indicate about human rationality, but one upshot seems clear: human reasoning does not seem to fit traditional views of human rationality. This concern about rationality has made its way through various fields and has recently caught the attention of philosophers. The concern is that if philosophers are prone to systematic errors in reasoning, then the integrity of philosophy would be threatened. In this paper, I (...) present some of the more famous work in cognitive science that has marshaled this concern. Then I present reasons to think that those with training in philosophy will be less prone to certain systematic errors in reasoning. The suggestion is that if philosophers could be shown to be less prone to such errors, then the worries about the integrity of philosophy could be constrained. Then I present evidence that, according to performance on the CRT (Frederick 2005), those who have benefited from training and selection in philosophy are indeed less prone to one kind of systematic error: irrationally arbitrating between intuitive and reflective responses. Nonetheless, philosophers are not entirely immune to this systematic error, and their proclivity for this error is statistically related to their responses to a variety of philosophical questions. So, while the evidence herein puts constraints on the worries about the integrity of philosophy, it by no means eliminates these worries. The conclusion, then, is that the present evidence offers prima facie reasons to ascribe a mitigated privilege to philosophers' ability to rationally arbitrate between intuitive and reflective responses. (shrink)

In this thesis, I will explore the epistemological evolutionary debunking arguments in meta-ethics. I will defend these arguments by accomplishing two tasks: I will offer the best way to understand the EDA and I will also respond to two strongest objections to the EDA. Firstly, in Part I of this thesis, I will offer my account of how the EDA should be best formulated. I will start from how evolution has significantly influenced our moral beliefs. I will then explain why, (...) due to their evolutionary origin, our moral beliefs are not tracking the moral truth reliably. Furthermore, I will argue that the fact that our moral beliefs are not tracking the moral truth also provides an undercutting and a higher-order defeater for those beliefs. As a result, I will conclude that the epistemic status of our moral beliefs is undermined because of these two kinds of defeaters. Secondly, in Part II of this thesis, I will turn my attention to the two strongest objections to the EDA – the Conceptual Truth Objection and the Third Factor Objection. I will first offer two responses to the Conceptual Truth Objection and, based on these two responses, I will argue that the Conceptual Truth Objection fails as a challenge to the EDA. I will then also argue that there currently doesn’t exist an acceptable version of the Third Factor Objection and it is also unlikely that such a version could be constructed in the future. I will finally conclude that both objections are problematic and they are thus unable to give us reason to doubt the EDA. (shrink)

We provide new findings that add to the growing body of empirical evidence that important epistemic intuitions converge across cultures. Specifically, we selected three recent studies conducted in the US that reported surprising effects of knowledge attribution among English speakers. We translated the vignettes used in those studies into Mandarin Chinese and Korean and then ran the studies with participants in Mainland China, Taiwan, and South Korea. We found that, strikingly, all three of the effects first obtained in the US (...) also emerged in the East Asian cultures we studied. Our findings not only cohere with but also provide—at least moderate—support for the existence of extensive convergences of important epistemic intuitions across cultures. (shrink)