Counterfactual skepticism says that most ordinary counterfactuals are false. While few endorse counterfactual skepticism, the precise costs of the view are disputed and not generally well-understood. I have two aims in this paper. My first and primary aim is to establish, on grounds acceptable to all parties, that counterfactual skepticism is not benign. I argue it leads to significant skepticism about the future: if counterfactual skepticism is true, then we can have only very limited knowledge about the future. I give (...) three arguments to this conclusion, taking as premises principles connecting knowledge of indicative conditionals to knowledge of disjunctions; and principles linking knowledge of indicative conditionals to knowledge of counterfactual conditionals.My second aim is to examine the consequences for non-skeptical theories. My arguments indicate that not only are many ordinary counterfactuals true, but that we also know them. How can this be reconciled with the very real tension between counterfactuals and chance? I consider two solutions, one purely epistemic and one contextualist. Together they suggest something like contextualism about knowledge is required to fully resolve the skeptical threat. (shrink)

This paper is about the principle that success entails ability, which I call Success. I argue the status of Success is highly puzzling: when we focus on past instances of actually successful action, Success is very compelling; but it is in tension with the idea that true ability claims require an action be in the agent's control. I make the above tension precise by considering the logic of ability. I argue Success is appealing because it is classically equivalent to two (...) genuinely valid inferences, which I call Past Success and Can't-Entails-Won't; but also that Success itself has counterexamples. I show how to invalidate Success while validating Past Success and Can't-Entails-Won't by connecting the meaning of ‘can’ to facts about what is settled or open. I define an operator W with features attributed to ‘will’ in the literature on future contingents. I then give a conditional analysis of ability ascriptions stated with W-conditionals, where "S can A" says, roughly, there’s some action available to S such that if S does it, then W(S A). I show this semantics invalidates Success while still explaining its appeal. (shrink)

The literature on counterfactuals is dominated by strict accounts and variably strict accounts. Counterexamples to the principle of Antecedent Strengthening were thought to be fatal to SA; but it has been shown that by adding dynamic resources to the view, such examples can be accounted for. We broaden the debate between VSA and SA by focusing on a new strengthening principle, Strengthening with a Possibility. We show dynamic SA classically validates this principle. We give a counterexample to it and show (...) that extra dynamic resources cannot help SA. We then show VSA accounts for the counterexample if it allows for orderings on worlds that are not almost-connected, and that such an ordering naturally falls out of a Kratzerian ordering source semantics. We conclude that the failure of Strengthening with a Possibility tells strongly against Dynamic SA and in favor of an ordering source-based version of VSA. (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)

Know how and ability have a seemingly fraught relationship. I deepen the tension here, by arguing for two new pieces of data concerning know how and ability. First, know how ascriptions have two distinct readings that differ in their entailments to ability: one entails ability, the other does not. Second, in certain cases, the indeterminacy of certain ability claims infects both readings of know how claims. No existing accounts of the relationship between know how and ability captures both data points, (...) I argue; but a certain kind of intellectualism has special resources to account for them. Ascriptions of knowledge of infinitival questions give rise to a distinctive kind of context-sensitivity specific to infinitivals. I show how on an intellectualist view where, very roughly, knowing how to do something is knowing an answer to an infinitival question about your abilities, this context-sensitivity accounts for the relationship between know how and ability. (shrink)

This paper concerns a puzzle about the interaction of epistemic modals and future tense. In cases of predictable forgetfulness, speakers cannot describe their future states of mind with epistemic modals under future tense, but promising theories of epistemic modals do not predict this. In §1, I outline the puzzle. In §2, I argue that it undermines a very general approach to epistemic modals that draws a tight connection between epistemic modality and evidence. In §3, I defend the assumption that tense (...) can indeed scope over epistemic modals. In §4, I outline a new way of determining the domain of quantification of epistemic modals: epistemic modals quantify over the worlds compatible with the information accumulated within a certain interval. Information loss can change which interval is relevant for determining the domain. In §5, I defend the view from some objections. In §6, I explore the connections between my view of epistemic modality and circumstantial modality. (shrink)

This essay proposes a new theory of agentive modals: ability modals and their duals, compulsion modals. After criticizing existing approaches—the existential quantificational analysis, the universal quantificational analysis, and the conditional analysis—it presents a new account that builds on both the existential and conditional analyses. On this account, the act conditional analysis, a sentence like ‘John can swim across the river’ says that there is some practically available action that is such that if John tries to do it, he swims across (...) the river. The essay argues that the act conditional analysis avoids the problems faced by existing accounts of agentive modality and shows how the act conditional analysis can be extended to an account of generic agentive modal claims. The upshot is a new vantage point on the role of agentive modal ascriptions in practical discourse: ability ascriptions serve as a kind of hypothetical guarantee, and compulsion ascriptions as a kind of nonhypothetical guarantee. (shrink)

We propose a new analysis of ability modals. After briefly criticizing extant approaches, we turn our attention to the venerable but vexed conditional analysis of ability ascriptions. We give an account that builds on the conditional analysis, but avoids its weaknesses by incorporating a layer of quantification over a contextually supplied set of actions.

From religion to philosophy to science, all human systems of definition are formed by human brains. The nature and limits of the human brain are the nature and limits of those systems. This essay shows how the human brain works normally then unusually, and what this reveals about the limits of human knowledge. There are many conditions and instances where the brain processes information unusually, including mental disorders, physical events, and drug use. This essay focuses on the neurological events called (...) mystical experiences. (shrink)

Philosophers of language have drawn on metamathematical results in varied ways. Extensionalist philosophers have been particularly impressed with two, not unrelated, facts: the existence, due to Frege/Tarski, of a certain sort of semantics, and the seeming absence of intensional contexts from mathematical discourse. The philosophical import of these facts is at best murky. Extensionalists will emphasize the success and clarity of the model theoretic semantics; others will emphasize the relative poverty of the mathematical idiom; still others will question the aptness (...) of the standard extensional semantics for mathematics. In this paper I investigate some implications of the Gödel Second Incompleteness Theorem for these positions. I argue that the realm of mathematics, proof theory in particular, has been a breeding ground for intensionality and that satisfactory intensional semantic theories are implicit in certain rigorous technical accounts. (shrink)

Recent objections to epistemic permissivism have a metaepistemic flavor. Impermissivists argue that their view best accounts for connections between rationality, planning and deference. Impermissivism is also taken to best explain the value of rational belief and normative assessment. These objections pose a series of metaepistemic explanatory challenges for permissivism. In this paper, I illustrate how permissivists might meet their explanatory burdens by developing two permissivist metaepistemic views which fare well against the explanatory challenges.

Representationalists argue that phenomenal states are intentional states of a special kind. This paper offers an account of the kind of intentional state phenomenal states are: I argue that they are underived intentional states. This account of phenomenal states is equivalent to two theses: first, all possible phenomenal states are underived intentional states; second, all possible underived intentional states are phenomenal states. I clarify these claims and argue for each of them. I also address objections which touch on a range (...) of topics, including meaning holism and concept empiricism. I conclude with a brief discussion of the consequences of the proposed view for the project of naturalizing consciousness. (shrink)

The model of human intelligence that is most widely adopted derives from psychometrics and behavioral genetics. This standard approach conceives intelligence as a general cognitive ability that is genetically highly heritable and describable using quantitative traits analysis. The paper analyzes intelligence within the debate on natural kinds and contends that the general intelligence conceptualization does not carve psychological nature at its joints. Moreover, I argue that this model assumes an essentialist perspective. As an alternative, I consider an HPC theory of (...) intelligence and evaluate how it deals with essentialism and with intuitions coming from cognitive science. Finally, I highlight some concerns about the HPC model as well, and conclude by suggesting that it is unnecessary to treat intelligence as a kind in any sense. (shrink)

[This is an edited version of a keynote talk at the conference on Neural Information Processing Systems (NeurIPS) on November 28, 2022, with some minor additions and subtractions.] -/- There has recently been widespread discussion of whether large language models might be sentient or conscious. Should we take this idea seriously? I will break down the strongest reasons for and against. Given mainstream assumptions in the science of consciousness, there are significant obstacles to consciousness in current models: for example, their (...) lack of recurrent processing, a global workspace, and unified agency. At the same time, it is quite possible that these obstacles will be overcome in the next decade or so. I conclude that while it is somewhat unlikely that current large language models are conscious, we should take seriously the possibility that successors to large language models may be conscious in the not-too-distant future. (shrink)

Lipsey and Lancaster's "general theory of second best" is widely thought to have significant implications for applied theorizing about the institutions and policies that most effectively implement abstract normative principles. It is also widely thought to have little significance for theorizing about which abstract normative principles we ought to implement. Contrary to this conventional wisdom, I show how the second-best theorem can be extended to myriad domains beyond applied normative theorizing, and in particular to more abstract theorizing about the normative (...) principles we should aim to implement. I start by separating the mathematical model used to prove the second-best theorem from its familiar economic interpretation. I then develop an alternative normative-theoretic interpretation of the model, which yields a novel second best theorem for idealistic normative theory. My method for developing this interpretation provides a template for developing additional interpretations that can extend the reach of the second-best theorem beyond normative theoretical domains. I also show how, within any domain, the implications of the second-best theorem are more specific than is typically thought. I conclude with some brief remarks on the value of mathematical models for conceptual exploration. (shrink)

Reductive representationalism is the view that the qualitative properties associated with conscious experience are properties of the objects of the experience, and not of the experience itself. A prima facie problem for this view arises from dreams and hallucinations, in which qualitative properties are experienced but not instantiated in external objects of perception. I argue that representationalist attempts to solve it by appeal to actually uninstantiated properties are guilty of an absurdity akin to that which Ryle accused Descartes of in (...) the latter’s doctrine of immaterial substance. (shrink)

A diagnostic process is an investigative process that takes a clinical picture as input and outputs a diagnosis. We propose a method for distinguishing diagnoses that are warranted from those that are not, based on the cognitive processes of which they are the outputs. Processes designed and vetted to reliably produce correct diagnoses will output what we shall call ‘warranted diagnoses’. The latter are diagnoses that should be trusted even if they later turn out to have been wrong. Our work (...) is based on the recently developed Cognitive Process Ontology and further develops the Ontology of General Medical Science. It also has applications in fields such as intelligence, forensics, and predictive maintenance, all of which rely on vetted processes designed to secure the reliability of their outputs. (shrink)

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The categorical duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The hyperintensional profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal and hyperintensional profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely (...) logical. Second, the foregoing provides a hyperintensional account of the interpretation of mathematical and metamathematical vocabulary. (shrink)

Failure of substitutivity of coreferential terms, one of the hallmarks of referential opacity, is standardly explained in terms of the presence of an expression (such as a verb of propositional attitude, a modal adverb or quotation marks) with opacity-inducing properties. It is thus assumed that any term in a complex expression for which substitutivity fails will be within the scope of an expression of one of these types, and that where there is an expression of one of these types there (...) will be failure of substitutivity for terms within its scope. I shall discuss a series of examples that have been thought to challenge this explanation by exhibiting failure of substitutivity of coreferential terms for positions not within the scope of any of the standard opacity-inducing expressions. If these examples are genuine, then the usual explanations of opacity are either incomplete – because there are sources of opacity other than those standardly identified, or completely mistaken – because the standardly identified expressions are not causes of opacity. I will argue, however, that the examples only exhibit failure of substitutivity of non-coreferential terms, and, hence, do not present a challenge to standard explanations of opacity. (shrink)

What are the philosophical views of professional philosophers, and how do these views change over time? The 2020 PhilPapers Survey surveyed around 2000 philosophers on 100 philosophical questions. The results provide a snapshot of the state of some central debates in philosophy, reveal correlations and demographic effects involving philosophers' views, and reveal some changes in philosophers' views over the last decade.

This paper examines the philosophical significance of the consequence relation defined in the $\Omega$-logic for set-theoretic languages. I argue that, as with second-order logic, the hyperintensional profile of validity in $\Omega$-Logic enables the property to be epistemically tractable. Because of the duality between coalgebras and algebras, Boolean-valued models of set theory can be interpreted as coalgebras. In Section \textbf{2}, I demonstrate how the hyperintensional profile of $\Omega$-logical validity can be countenanced within a coalgebraic logic. Finally, in Section \textbf{3}, the philosophical (...) significance of the characterization of the hyperintensional profile of $\Omega$-logical validity for the philosophy of mathematics is examined. I argue (i) that $\Omega$-logical validity is genuinely logical, and (ii) that it provides a hyperintensional account of formal grasp of the concept of `set'. Section \textbf{4} provides concluding remarks. (shrink)

Artificial intelligence has historically been conceptualized in anthropomorphic terms. Some algorithms deploy biomimetic designs in a deliberate attempt to effect a sort of digital isomorphism of the human brain. Others leverage more general learning strategies that happen to coincide with popular theories of cognitive science and social epistemology. In this paper, I challenge the anthropomorphic credentials of the neural network algorithm, whose similarities to human cognition I argue are vastly overstated and narrowly construed. I submit that three alternative supervised learning (...) methods—namely lasso penalties, bagging, and boosting—offer subtler, more interesting analogies to human reasoning as both an individual and a social phenomenon. Despite the temptation to fall back on anthropomorphic tropes when discussing AI, however, I conclude that such rhetoric is at best misleading and at worst downright dangerous. The impulse to humanize algorithms is an obstacle to properly conceptualizing the ethical challenges posed by emerging technologies. (shrink)

Does the Ship of Theseus present a genuine puzzle about persistence due to conflicting intuitions based on “continuity of form” and “continuity of matter” pulling in opposite directions? Philosophers are divided. Some claim that it presents a genuine puzzle but disagree over whether there is a solution. Others claim that there is no puzzle at all since the case has an obvious solution. To assess these proposals, we conducted a cross-cultural study involving nearly 3,000 people across twenty-two countries, speaking eighteen (...) different languages. Our results speak against the proposal that there is no puzzle at all and against the proposal that there is a puzzle but one that has no solution. Our results suggest that there are two criteria—“continuity of form” and “continuity of matter”— that constitute our concept of persistence and these two criteria receive different weightings in settling matters concerning persistence. (shrink)

What constitutes numerically one and the same tradition diachronically, at different times? This question is the focus of often violent dispute in societies. Is it capable of a rational resolution? Many accounts attempt that resolution with a diagnosis of ambiguity of the disputed concept-Islam, Marxism, or democracy for example. The diagnosis offered is in terms of vagueness, namely the vague criteria for sameness or similarity of central beliefs and practices.

The arguments of Fodor, Garret, Walker and Parkes [(1980) Against definitions, Cognition, 8, 263-367] are the source of widespread skepticism in cognitive science about lexical semantic structure. Whereas the thesis that lexical items, and the concepts they express, have decompositional structure (i.e. have significant constituents) was at one time "one of those ideas that hardly anybody [in the cognitive sciences] ever considers giving up" (p. 264), most researchers now believe that "[a]ll the evidence suggests that the classical [(decompositional)] view is (...) wrong as a general theory of concepts" [Smith, Medin & Rips (1984) A psychological approach to concepts: comments on Rey, Cognition, 17, 272], and cite Fodor et al. (1980) as "sounding the death knell for decompositional theories" [MacNamara & Miller (1989) Attributes of theories of meaning, Psychological Bulletin, 106, 360]. I argue that the prevailing skepticism is unmotivated by the arguments in Fodor et al. Fodor et al. misrepresent the form, function and scope of the decompositional hypothesis, and the procedures they employ to test for the psychological reality of definitions are flawed. I argue, further, that decompositional explanations of the phenomena they consider are preferable to their primitivist alternatives, and, hence, that there is prima facie reason to accept them as evidence for the existence of decompositional structure. Cognitive scientists would, therefore, do well to revert to their former commitment to the decompositional hypothesis. (shrink)

What are the philosophical views of contemporary professional philosophers? We surveyed many professional philosophers in order to help determine their views on 30 central philosophical issues. This article documents the results. It also reveals correlations among philosophical views and between these views and factors such as age, gender, and nationality. A factor analysis suggests that an individual's views on these issues factor into a few underlying components that predict much of the variation in those views. The results of a metasurvey (...) also suggest that many of the results of the survey are surprising: philosophers as a whole have quite inaccurate beliefs about the distribution of philosophical views in the profession. (shrink)

There is a difference between merely thinking that P and really grasping that P. For example, Jackson's (1982) black-and-white Mary cannot (before leaving her black-and-white room) fully grasp what it means to say that fire engines are red, but she can perfectly well entertain the thought that fire engines are red. The contrast between merely thinking and grasping is especially salient in the context of certain moral decisions. For example, an individual who grasps the plight of starving children thanks to (...) evocative images seems much more likely to donate for the children's benefit than someone who is merely told about their plight. This paper offers a phenomenal account of grasping according to which grasping a content (whether a proposition or concept) consists in one's thoughts about the content being constituted by phenomenal experiences of constituents of the content. This account improves on earlier phenomenal accounts of grasping (Bourget 2017a, 2018) by allowing for partial grasping and generalizing to concepts. The paper also addresses objections to phenomenal accounts of grasping, including the objection that recent developments in AI technology show that consciousness is irrelevant to grasping and understanding. (shrink)

Call a thought whose expression involves the utterance of an indexical an indexical thought. Thus, my thoughts that I’m annoyed, that now is not the right time, that this is not acceptable, are all indexical thoughts. Such thoughts present a prima facie problem for the thesis that thought contents are phenomenally individuated -- i.e., that each distinct thought type has a proprietarily cognitive phenomenology such that its having that phenomenology makes it the thought that it is -- given the assumption (...) that phenomenology is intrinsically determined. My concern in this paper is to blunt standard intuitions concerning the external individuation of indexical thought contents, and to defend a conception of indexical thought content that is entirely phenomenal and internalist. (shrink)

Does consciousness collapse the quantum wave function? This idea was taken seriously by John von Neumann and Eugene Wigner but is now widely dismissed. We develop the idea by combining a mathematical theory of consciousness (integrated information theory) with an account of quantum collapse dynamics (continuous spontaneous localization). Simple versions of the theory are falsified by the quantum Zeno effect, but more complex versions remain compatible with empirical evidence. In principle, versions of the theory can be tested by experiments with (...) quantum computers. The upshot is not that consciousness-collapse interpretations are clearly correct, but that there is a research program here worth exploring. (shrink)

What follows is a first step towards an ontology of conscious mental processes. We provide a theoretical foundation and characterization of conscious mental processes based on a realist theory of intentionality and using BFO as our top-level ontology. We distinguish three components of intentional mental process: character, directedness, and objective referent, and describe several features of the process character and directedness significant to defining and classifying mental processes. We arrive at the definition of representational mental process as a process that (...) is the bringing into being, sustaining, modifying, or terminating of a mental representation. We conclude by outlining some benefits and applications of this approach. (shrink)

Inspired by Rudolf Carnap's Der Logische Aufbau Der Welt, David J. Chalmers argues that the world can be constructed from a few basic elements. He develops a scrutability thesis saying that all truths about the world can be derived from basic truths and ideal reasoning. This thesis leads to many philosophical consequences: a broadly Fregean approach to meaning, an internalist approach to the contents of thought, and a reply to W. V. Quine's arguments against the analytic and the a (...) priori. Chalmers also uses scrutability to analyze the unity of science, to defend a conceptual approach to metaphysics, and to mount a structuralist response to skepticism. Based on the 2010 John Locke lectures, Constructing the World opens up debate on central philosophical issues involving language, consciousness, knowledge, and reality. This major work by a leading philosopher will appeal to philosophers in all areas. This entry contains uncorrected proofs of front matter, chapter 1, and first excursus. (shrink)

A discussion of three central ideas in action theory; trying to act, doing or acting, one's action causing further consequences.

This paper concentrates on a particular sort of case where it’s plausible that epistemic requirements can conflict: cases where an agent’s higher-order evidence supports doubting her reliability in reacting to her ordinary evidence. Conflicting epistemic requirements can be seen as generating epistemic dilemmas. The paper examines two ways that people have sought to recognize conflicting requirements without allowing them to generate epistemic dilemmas: separating epistemic norms into two different varieties, and positing rational indeterminacy in cases where principles conflict. It argues (...) that these views incur costs, and that the sense in which they avoid dilemmas does not gain them an advantage over a view that simply recognizes dilemmas as a natural outgrowth of agents’ rational reflection on their own thinking. (shrink)

In this paper, I argue for a modified version of what Devitt calls the Representational Thesis. According to RT, syntactic rules or principles are psychologically real, in the sense that they are represented in the mind/brain of every linguistically competent speaker/hearer. I present a range of behavioral and neurophysiological evidence for the claim that the human sentence processing mechanism constructs mental representations of the syntactic properties of linguistic stimuli. I then survey a range of psychologically plausible computational models of comprehension (...) and show that they are all committed to RT. I go on to sketch a framework for thinking about the nature of the representations involved in sentence processing. My claim is that these are best characterized not as propositional attitudes but, rather, as subpersonal states whose representational properties are determined by their functional role. Finally, I distinguish between explicit and implicit representations and argue that the latter can be drawn on as data by the algorithms that constitute our sentence processing routines. I conclude that skepticism concerning the psychological reality of grammars cannot be sustained. (shrink)

Bohmian mechanics is a realistic interpretation of quantum theory. It shares the same ontology of classical mechanics: particles following continuous trajectories in space through time. For this ontological continuity, it seems to be a good candidate for recovering the classical limit of quantum theory. Indeed, in a Bohmian framework, the issue of the classical limit reduces to showing how classical trajectories can emerge from Bohmian ones, under specific classicality assumptions. In this paper, we shall focus on a technical problem that (...) arises from the dynamics of a Bohmian system in bounded regions; and we suggest that a possible solution is supplied by the action of environmental decoherence. However, we shall show that, in order to implement decoherence in a Bohmian framework, a stronger condition is required rather than the usual one. (shrink)

This chapter examines how epistemic norms could be social norms, with a reliance on work on the philosophy and social science of social norms from Bicchieri (on the one hand) and Brennan, Eriksson, Goodin and Southwood (on the other hand). We explain how the social ontology of social norms can help explain the rationality of epistemic cooperation, and how one might begin to model epistemic games.

I argue that the two-dimensional hyperintensions of epistemic topic-sensitive two-dimensional truthmaker semantics provide a compelling solution to the access problem. I countenance an abstraction principle for epistemic hyperintensions based on Voevodsky's Univalence Axiom and function type equivalence in Homotopy Type Theory. I apply, further, modal rationalism in modal epistemology to solve the access problem. Epistemic possibility and hyperintensionality, i.e. conceivability, can be a guide to metaphysical possibility and hyperintensionality, when (i) epistemic worlds or epistemic hyperintensional states are interpreted as being (...) centered metaphysical worlds or hyperintensional states, i.e. indexed to an agent, when (ii) the epistemic (hyper-)intensions and metaphysical (hyper-)intensions for a sentence coincide, i.e. the hyperintension has the same value irrespective of whether the worlds in the argument of the functions are considered as epistemic or metaphysical, and when (iii) sentences are said to consist in super-rigid expressions, i.e. rigid expressions in all epistemic worlds or states and in all metaphysical worlds or states. I argue that (i) and (ii) obtain in the case of the access problem. (shrink)

This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I introduce a novel epistemic two-dimensional truthmaker semantics. I argue that the interaction between the two-dimensional framework and the mereological parthood relation, which is super-rigid, enables epistemic possibilities and truthmakers with regard to parthood to be a guide to its metaphysical profile. I specify, further, a two-dimensional formula encoding the relation between the epistemic possibility and verification of essential properties obtaining (...) and their metaphysical possibility or verification. I then generalize the approach to haecceitistic properties, and examine the Julius Caesar problem as a test case. (shrink)

This paper aims to contribute to the analysis of the nature of mathematical modality and hyperintensionality, and to the applications of the latter to absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the priority (...) and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance a topic-sensitive epistemic two-dimensional truthmaker semantics, if hyperintensional approaches are to be preferred to possible worlds semantics. I examine the relation between two-dimensional hyperintensional states and epistemic set theory, providing two-dimensional hyperintensional formalizations of the modal logic of ZFC, large cardinal axioms, $\Omega$-logic, and the Epistemic Church-Turing Thesis. (shrink)

How should one react when one has a belief, but knows that other people—who have roughly the same evidence as one has, and seem roughly as likely to react to it correctly—disagree? This paper argues that the disagreement of other competent inquirers often requires one to be much less confident in one’s opinions than one would otherwise be.

Conceptual engineering is the design, implementation, and evaluation of concepts. Conceptual engineering includes or should include de novo conceptual engineering (designing a new concept) as well as conceptual re-engineering (fixing an old concept). It should also include heteronymous (different-word) as well as homonymous (same-word) conceptual engineering. I discuss the importance and the difficulty of these sorts of conceptual engineering in philosophy and elsewhere.

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)

How should one react when one has a belief, but knows that other people—who have roughly the same evidence as one has, and seem roughly as likely to react to it correctly—disagree? This paper argues that the disagreement of other competent inquirers often requires one to be much less confident in one’s opinions than one would otherwise be.