Epistemic Possibility

This paper argues that the types of intention can be modeled both as modal operators and via a multi-hyperintensional semantics. I delineate the semantic profiles of the types of intention, and provide a precise account of how the types of intention are unified in virtue of both their operations in a single, encompassing, epistemic space, and their role in practical reasoning. I endeavor to provide reasons adducing against the proposal that the types of intention are reducible to the mental states (...) of belief and desire, where the former state is codified by subjective probability measures and the latter is codified by a utility function. I argue, instead, that each of the types of intention -- i.e., intention-in-action, intention-as-explanation, and intention-for-the-future -- has as its aim the value of an outcome of the agent's action, as derived by her partial beliefs and assignments of utility, and as codified by the value of expected utility in evidential decision theory. (shrink)

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

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

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)

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)

In this paper it will be attempted to dissolve the lottery problem based on fallibilism, probabilism and the introduction of a so far widely neglected second context of knowledge. First, it will be argued that the lottery problem is actually an exemplification of the much wider Humean "future knowledge problem" (ch. 1). Two types of inferences and arguments will be examined, compared and evaluated in respect to their ability to fittingly describe the thought processes behind lottery/future knowledge propositions (ch. 2). (...) A second context of knowledge that underlines the importance of fallibilism and probabilism in a somewhat different manner will be introduced (ch. 3) and, based on that "two-context probabilism," the lottery/future knowledge problem will be dissolved (ch. 4). Lastly, it will be hinted at the necessity of adopting not just fallibilism including and two context minding probabilism, but, beyond that, also the even more encompassing position of both ontological and epistemological "gradualism" (ch. 5). (shrink)

Some how-possibly explanations have epistemic value because they are epistemically possible; we cannot rule out their truth. One paradoxical implication of that proposal is that epistemic value may be obtained from mere ignorance. For the less we know, then the more is epistemically possible. This chapter examines a particular class of problematic epistemically possible how-possibly explanations, viz. *epistemically opaque* how-possibly explanations. Those are how-possibly explanations justified by an epistemically opaque process. How could epistemically opaque how-possibly explanations have epistemic value if (...) they result from a process about which we lack knowledge or understanding? This chapter proposes three different strategies to salvage epistemic value from epistemic opacity, namely salvaging value from 1) functional transparency, 2) modal operator interpretation, and 3) pursuitworthiness. It illustrates using cases from deep neural network modeling. (shrink)

We argue that S is in a position to know that p iff S can know that p. Thus, what makes position-to-know-ascriptions true is just a special case of what makes ability-ascriptions true: compossibility. The novelty of our compossibility theory of epistemic modality lies in its subsuming epistemic modality under agentive modality, the modality characterizing what agents can do.

Veltman’s test semantics and developments thereof reject the canon about semantic contents and attitude ascriptions in favor of dynamic alternatives. According to these theories the semantic content of a sentence is not a proposition, but a context change potential (CCP). Similarly, beliefs are not taken to be relations between agents and propositions, but agents and CCPs. These deviations from the canon come at the cost of an elegant explanation about the correctness of belief. Standardly, it is taken that the content (...) of a belief is correct just in case the content of that belief is true. The proponent of the test semantics cannot appeal to this explanation since they hold that certain contents, namely epistemically modalized contents, do not express propositions, and are neither true nor false. After motivating the need for an account of the correctness of belief within the dynamic framework, I argue that the few extant accounts in the literature are unsatisfactory. A novel account is proposed that avoids the problems of competing views. (shrink)

This essay is an accessible introduction to the proof paradox in legal epistemology. -/- In 1902 the Supreme Judicial Court of Maine filed an influential legal verdict. The judge claimed that in order to find a defendant culpable, the plaintiff “must adduce evidence other than a majority of chances”. The judge thereby claimed that bare statistical evidence does not suffice for legal proof. -/- In this essay I first motivate the claim that bare statistical evidence does not suffice for legal (...) proof. I then introduce and motivate a knowledge-centred explanation of this fact. The knowledge-centred explanation rests on two premises. The first is that legal proof requires knowledge of culpability. The second is that one cannot attain knowledge that p from bare statistical evidence that p. To motivate the second premise, I suggest that beliefs based on bare statistical evidence fail to be safe—they could easily be wrong—and bare statistical evidence cannot eliminate relevant alternatives. -/- I then cast doubt on the first premise; I argue that legal proof does not require knowledge. I thereby dispute the knowledge-centred explanation of the inadequacy of bare statistical evidence for legal proof. Instead of appealing to the nature of knowledge, I suggest we should seek a more direct explanation by appealing to those more foundational epistemic properties, such as safety or eliminating relevant alternatives. (shrink)

According to a recent proposal, the epistemic aim of metaphysics as a discipline is to chart the different viable theories of metaphysical objects of inquiry (e.g. causation, persistence). This paper elaborates on and seeks to improve on that proposal in two related ways. First, drawing on an analogy with how-possibly explanation in science, I argue that we can usefully understand this aim of metaphysics as the charting of epistemically possible answers to metaphysical questions. Second, I argue that in order to (...) account for the epistemic goodness of this aim, one should appeal to the epistemic value it has in virtue of providing resources for non-factive understanding of the objects of metaphysical inquiry.**This paper is part of a special issue of Argumenta on the Epistemology of Metaphysics**. (shrink)

There are currently two legally established criteria for death: the irreversible cessation of circulation and respiration and the irreversible cessation of neurologic function. Recently, there have been technological developments that could undermine the irreversibility requirement. In this paper, I focus both on whether death should be identified as an irreversible state and on the proper scope of irreversibility in the biological definition of death. In this paper, I tackle the distinction between the commonsense definition of death and the biological definition (...) of death to show that even the commonsense concept of death is specified by biological facts. Resting on this argument, I argue that any definition of death is a posteriori. Thus, irreversibility is part of any definition of death because the actual phenomenon of death is irreversible. In addition, I show that the proper domain of irreversibility in a definition of death is circumscribed by physical possibilities and that irreversibility in the definition of death refers to current possibilities for the reversal of relevant biological processes. I conclude that, despite recent technological advancements, death is still irreversible. (shrink)

Counterfactual scepticism holds that most ordinary counterfactuals are false. The main argument for this view appeals to a ‘chance undermines would’ principle: if ψ would have some chance of not obtaining had ϕ obtained, then ϕ □→ ψ is false. This principle seems to follow from two fairly weak principles, namely, that ‘chance ensures could’ and that ϕ □→ ψ and ϕ ⋄→ ¬ ψ clash. Despite their initial plausibility, I show that these principles are independently problematic: given some modest (...) closure principles, they entail absurdities. Moreover, on the most promising strategy for saving these principles, they do not, in the relevant sense, entail the chance-undermines-would principle. Instead, they entail a principle that only supports counterfactual indeterminism, the view that most ordinary counterfactuals are chancy, that is, not settled true. I demonstrate this by developing an indeterminist semantics that vindicates the clash and chance-ensures-could principles but not the chance-undermines-would principle. This view, I argue, offers a better account of our credal and linguistic judgements than counterfactual scepticism. (shrink)

ABSTRACT – Epistemic Injustice in the Education of People with Mental Disabilities. This article offers a perspective on inclusive education based on Fricker’s conception of epistemic injustice. What is the relationship be- tween inclusive education and epistemic injustice in the case of students with mental deficiencies? By adapting Fricker’s thesis to this extreme case, epistemic injustice can be explored via the social model of disability (SMD). Accordingly, we propose that epistemic injustice harms the entire educa- tional community and society. -/- (...) . (shrink)

RESUMEN ‒ Injusticias Epistémicas en la Educación de Personas con Dis- capacidad Mental. Se ofrece en este artículo una perspectiva de la educa- ción inclusiva a partir de la concepción de las injusticias epistémicas de Fricker. Se pregunta cuál es la relación entre la educación inclusiva y la in- justicia epistémica en el caso de estudiantes con deficiencias mentales. Es necesario adaptar las tesis de Fricker a este caso límite, por lo que se debe pensar la injusticias epistémicas a partir (...) del modelo social de la discapaci- dad. Se propone que la injusticia epistémica perjudica a toda la comunidad educativa y a la sociedad. -/- . (shrink)

We often claim to know what might be—or probably is—the case. Modal knowledge along these lines creates a puzzle for information-sensitive semantics for epistemic modals. This paper develops a solution. We start with the idea that knowledge requires safe belief: a belief amounts to knowledge only if it could not easily have been held falsely. We then develop an interpretation of the modal operator in safety that allows it to non-trivially embed information-sensitive contents. The resulting theory avoids various paradoxes that (...) arise from other accounts of modal knowledge. It also delivers plausible predictions about modal Gettier cases. (shrink)

I present a cumulative case for the thesis that we only know propositions that are certain for us. I argue that this thesis can easily explain the truth of eight plausible claims about knowledge: -/- (1) There is a qualitative difference between knowledge and non-knowledge. (2) Knowledge is valuable in a way that non-knowledge is not. (3) Subjects in Gettier cases do not have knowledge. (4) If S knows that P, P is part of S’s evidence. (5) If S knows (...) that P, ~P is epistemically impossible for S. (6) If S knows that P, S can rationally act as if P. (7) If S knows that P, S can rationally stop inquiring whether P. (8) If S knows each of {P1, P2, … Pn}, and competently deduces Q from these propositions, S knows that Q. -/- I then argue that the skeptical costs of this thesis are outweighed by its explanatory power. (shrink)

Ephecticism is the tendency towards suspension of belief. Epistemology often focuses on the error of believing when one ought to doubt. The converse error—doubting when one ought to believe—is relatively underexplored. This essay examines the errors of undue doubt. I draw on the relevant alternatives framework to diagnose and remedy undue doubts about rape accusations. Doubters tend to invoke standards for belief that are too demanding, for example, and underestimate how farfetched uneliminated error possibilities are. They mistake seeing how incriminating (...) evidence is compatible with innocence for a reason to withhold judgement. Rape accusations help illuminate the causes and normativity of doubt. I propose a novel kind of epistemic injustice, for example, wherein patterns of unwarranted attention to farfetched error possibilities can cause those error possibilities to become relevant. Widespread unreasonable doubt thus renders doubt reasonable and makes it harder to know rape accusations. Finally, I emphasise that doubt is typically a conservative force and I argue that the relevant alternatives framework helps defend against pernicious doubt-mongers. (shrink)

Physicists Brian Greene and Max Tegmark both make variants of the claim that if the universe is infinite and matter is roughly uniformly distributed, then there are infinitely many “people with the same appearance, name and memories as you, who play out every possible permutation of your life choices.” In this paper I argue that--while our current best theories in astrophysics may allow one to conclude that we have infinitely many duplicates whose lives are identical to our own from start (...) to finish--without either further advances in physics or advances in fields like biology, psychology, neuroscience, and philosophy, Greene’s and Tegmark’s claims about the ways in which our duplicates lives will differ from our own are not a consequence of our best current scientific theories. Rather, I argue that Greene and Tegmark’s conclusions rely on philosophically imprecise usages of the language of “possibility.”. (shrink)

A Benacerraf–Field challenge is an argument intended to show that common realist theories of a given domain are untenable: such theories make it impossible to explain how we’ve arrived at the truth in that domain, and insofar as a theory makes our reliability in a domain inexplicable, we must either reject that theory or give up the relevant beliefs. But there’s no consensus about what would count here as a satisfactory explanation of our reliability. It’s sometimes suggested that giving such (...) an explanation would involve showing that our beliefs meet some modal condition, but realists have claimed that this sort of modal interpretation of the challenge deprives it of any force: since the facts in question are metaphysically necessary and so obtain in all possible worlds, it’s trivially easy, even given realism, to show that our beliefs have the relevant modal features. Here I show that this claim is mistaken—what motivates a modal interpretation of the challenge in the first place also motivates an understanding of the relevant features in terms of epistemic possibilities rather than metaphysical possibilities, and there are indeed epistemically possible worlds where the facts in question don’t obtain. (shrink)

This book contributes to two debates and it does so by bringing them together. The first is a debate in metaethics concerning normative reasons, the considerations that serve to justify a person’s actions and attitudes. The second is a debate in epistemology concerning the norms for belief, the standards that govern a person’s beliefs and by reference to which they are assessed. The book starts by developing and defending a new theory of reasons for action, that is, of practical reasons. (...) The theory belongs to a family that analyses reasons by appeal to the normative notion of rightness (fittingness, correctness); it is distinctive in making central appeal to modal notions, specifically, that of a nearby possible world. The result is a comprehensive framework that captures what is common to and distinctive of reasons of various kinds: justifying and demanding; for and against, possessed and unpossessed; objective and subjective. The framework is then generalized to reasons for belief, that is, to epistemic reasons, and combined with a substantive, first-order commitment, namely, that truth is the sole right-maker for belief. The upshot is an account of the various norms governing belief, including knowledge and rationality, and the relations among them. According to it, the standards to which belief is subject are various, but they are unified by an underlying principle. (shrink)

To reject skepticism and lay the foundation for the certainty of knowledge, Kant raised the question of how synthetic a priori proposition is possible. In his solution, the new content of knowledge comes from the syntheses of experience a posteriori, and the universal necessity of knowledge is guaranteed by it’s a priority. Under the influence of Kant, the concept of a priori and necessity has long been regarded as coextensive. But Saul Kripke believes that this will confuse different philosophical fields: (...) a priori is an epistemological concept, which involves the way or means of acquiring knowledge, and necessity is a metaphysical concept, which involves the possible ways or states of the world. The key point is that, on Kripke, there is no necessary connection between these two fields. He raised some famous examples of the necessary a posteriori. More remarkably, in his explanation of necessary a posteriori, although he did not clearly propose the distinction between epistemic possibility and metaphysical possibility, he had laid the foundation for this distinction. Furthermore, on Manuel Garcia-Carpintero and Josep Macia, when Kripke talks about necessary a posteriori by appealing to two relevant expressions, what he proposed can be taken as kind of ‘blueprint for 2-D accounts’. (Manuel Garcia-Carpintero and Josep Macia, 2006, p.2) There are different forms of two-dimensionalism in semantics. I will focus on David Chalmers’s epistemic version and Scott Soames’ criticism. With the framework of possible world semantics established by Kripke and others, David Chalmers’ epistemic two-dimensionalism deals with the relationship between epistemic and metaphysical modalities from a quite different perspective, and then gives an elegant definition to necessary a posteriori and other modal concepts. Scott Soames criticized two-dimensionalism based on Kripke's modal realism and essentialism, and developed Kripke's account of necessary a posteriori. But according to Chalmers, Soames also uses a two-dimensional system himself to analyze cases of the necessary a posteriori. In the first two part of this paper I will briefly introduce the epistemic two-dimensionalism and specify the similarities between Kripke-Soames and Chalmers when they interpret necessary a posteriori. In the third part I turn to their difference by the analysis of relationship between epistemic possibility and metaphysical possibility which is the key issue for illuminating necessary a posteriori. (shrink)

The epistemology of risk examines how risks bear on epistemic properties. A common framework for examining the epistemology of risk holds that strength of evidential support is best modelled as numerical probability given the available evidence. In this essay I develop and motivate a rival ‘relevant alternatives’ framework for theorising about the epistemology of risk. I describe three loci for thinking about the epistemology of risk. The first locus concerns consequences of relying on a belief for action, where those consequences (...) are significant if the belief is false. The second locus concerns whether beliefs themselves—regardless of action—can be risky, costly, or harmful. The third locus concerns epistemic risks we confront as social epistemic agents. I aim to motivate the relevant alternatives framework as a fruitful approach to the epistemology of risk. I first articulate a ‘relevant alternatives’ model of the relationship between stakes, evidence, and action. I then employ the relevant alternatives framework to undermine the motivation for moral encroachment. Finally, I argue the relevant alternatives framework illuminates epistemic phenomena such as gaslighting, conspiracy theories, and crying wolf, and I draw on the framework to diagnose the undue skepticism endemic to rape accusations. (shrink)

This paper explains and defends a belief-first view of the relationship between belief and credence. On this view, credences are a species of beliefs, and the degree of credence is determined by the content of what is believed. We begin by developing what we take to be the most plausible belief-first view. Then, we offer several arguments for it. Finally, we show how it can resist objections that have been raised to belief-first views. We conclude that the belief-first view is (...) more plausible than many have previously supposed. (shrink)

An influential proposal is that knowledge involves safe belief. A belief is safe, in the relevant sense, just in case it is true in nearby metaphysically possible worlds. In this paper, I introduce a distinct but complementary notion of safety, understood in terms of epistemically possible worlds. The main aim, in doing so, is to add to the epistemologist’s tool-kit. To demonstrate the usefulness of the tool, I use it to advance and assess substantive proposals concerning knowledge and justification.

According to a common conception of legal proof, satisfying a legal burden requires establishing a claim to a numerical threshold. Beyond reasonable doubt, for example, is often glossed as 90% or 95% likelihood given the evidence. Preponderance of evidence is interpreted as meaning at least 50% likelihood given the evidence. In light of problems with the common conception, I propose a new ‘relevant alternatives’ framework for legal standards of proof. Relevant alternative accounts of knowledge state that a person knows a (...) proposition when their evidence rules out all relevant error possibilities. I adapt this framework to model three legal standards of proof—the preponderance of evidence, clear and convincing evidence, and beyond reasonable doubt standards. I describe virtues of this framework. I argue that, by eschewing numerical thresholds, the relevant alternatives framework avoids problems inherent to rival models. I conclude by articulating aspects of legal normativity and practice illuminated by the relevant alternatives framework. (shrink)

The paper explores the project of an ambitious modal epistemology that attempts to combine the a priori methods of Chalmers’ 2D semantics with Kripke’s modal metaphysics. I argue that such a project is not viable. The ambitious modal epistemology involves an inconsistent triad composed of (1) Modal Monism, (2) Two-Dimensionalism, and what I call (3) “Metaphysical Kripkeanism”. I present the three theses and show how only two of those can be true at a time. There is a fundamental incompatibility between (...) Chalmers’ Modal Rationalism and Kripke’s modal metaphysics. Specifically, Chalmers’ conceivability entails possibilities that a Kripkean rejects as genuinely metaphysical. However, three positive stances in modal epistemology emerge from the combinations that the triad allows. One of those offers a promising way forward for 2D modal epistemologies. But it comes with a cost, as it requires abandoning modal monism and reshaping the scope of what a priori conceivability can give us access to. (shrink)

Some people might be tempted by modal ontological arguments from the possibility that God exists to the conclusion that God in fact exists. They might also be tempted to support the claim that possibly God exists by appealing to the conceivability of God’s existence. In this chapter, I introduce three constraints on an adequate theory of philosophical conceivability. I then consider and develop both imagination-based accounts of conceivability and conceptual coherence-based accounts of conceivability. Finally, I return to the modal ontological (...) argument and consider whether the premise that possibly God exists can be supported by some conceiving. (shrink)

In the introduction to the Critique of Pure Reason (2nd edition), Kant claims that a transcendental cognition is a one ‘that is occupied not so much with objects but rather with our mode of cognition of objects insofar as is this ought to be possible a priori (a priori möglich sein soll)’. In this paper, I argue that Kant scholarship should take into account the specific signification of the term ‘sollen’, which might require us to reconsider the usual distinction between (...) the system of freedom and the system of nature. Following a Fichtean perspective, I will try to show that, even if ‘sollen’ in this context does not refer to a duty in the strict sense, it does refer to the demand that transcendental philosophy itself be possible. I will argue that this demand is contingent at its very origin and, accordingly, expresses a particular kind of ‘freedom’. On this basis I will consider the tribunal of reason enacted in the Critique of Pure Reason as a tribunal that emerges from a free decision, in which the transcendental philosopher imagines its own possibility. Because it is a ‘free’ and ‘contingent’ tribunal, it cannot exceed the status of a problematic philosophical strategy. (shrink)

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

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

The paper offers an integrative interpretation of the different lines of thought Wittgenstein was inspecting in On Certainty and what he might have been looking for through them. It suggests that we may have been focusing our attention too strongly in the wrong place and comes to a new conclusion about where the real import of these reflections lies. This leads to an answer to the initially posed question of Foundationalism that revises the way in which there can be said (...) to be a grounding intention in On Certainty. (shrink)

Do other earthly forms of life evolved to the level of intelligent life? Cancer and resistance to antibiotics obliged to ask this question. Signs of intelligence are found at its simplest levels. We try to see if logic is used at these levels. Peter of Spain’s suppositio materialis is applied to the chemical signals of cells. Dynamic Logic is used to understand these chemical communications. <System of communications> is used, instead of “language”. The development of life appears as the development (...) of an axiomatic system. The rights of unborn humans and God’s rights over His own creation appear as the most powerful arguments for conservationism. (shrink)

In “Knowledge and epistemic necessity,” John Hawthorne gives a defense of what he rightly calls the “standard approach” to epistemic possibility against what he calls a new “competing idea” presented by Dougherty and Rysiew which he notes has been “endorsed and elaborated upon” by Fantl and McGrath. According to the standard approach, roughly, p is epistemically possible for S if S doesn’t know that not-p. The new approach has it that p is epistemically possible if p has a non-zero epistemic (...) probability. Both approaches, he notes, would explain the oddness of CKAs, utterances of the form “p, but possibly not p.” However, he offers a number of arguments designed to show that the standard approach has other advantages. In this paper, we undermine Hawthorne’s reasons for favoring the standard approach over Dougherty and Rysiew’s alternative approach. (shrink)

One of Moore’s paradoxical sentence types is ‘P, but I believe ~P’. Mooreans have assumed that all tokens of that sentence type are absurd in some way: epistemically, pragmatically, semantically, or assertively. And then they proceed to debate what the absurdity really is. I argue that if one has the appropriate philosophical views, then one can rationally assert tokens of that sentence type, and one can be epistemically reasonable in the corresponding compound belief as well.

In §18 of Principles of Nature and Grace, Based on Reason, Leibniz says: ”Thus our happiness will never consist, and must never consist, in complete joy, in which nothing is left to desire, and which would dull our mind, but must consist in a perpetual progress to new pleasures and new perfections.” -/- This passage is typical in Leibniz’s Nachlass. Universal perfection creates in us joy or pleasure of the mind and its source is our creator, God. When this joy (...) is constant, we reach happiness and wisdom which is a kind of standing state of virtue, readiness to practice charity in the best of all possible worlds. However, it also indicates that our knowledge is never perfect. Perfecting our knowledge is a never-ending process which gives us joy in itself and motivates us to act in imitation of God. In this way some passions advance our knowledge and we can create ourselves a passionate habit of knowing more about the world and its perfection. In this paper I try to see this process of self-perfection from a cognitive rather than ethical point of view. While it is clear that in the final stage of wisdom we act mostly on our volitions which are founded on clear and distinct perceptions, it is less clear what cognitive status is to be attributed to our initial perceptions of perfection, our emotions and finally, the intellectual emotions which lead us to perfection and God. I will also reflect the role of the minute perceptions in our struggle for happiness. My argument is that a central cognitive role in Leibniz’s views on self-perfection is held by clear, but confused perfections which are subjective, undemonstrable impressions, shades, feelings. Therefore our ethical action is largely founded on passing, minute feelings rather than on deliberated conscious volitions, although the goal in Leibniz’s moral theory is to change this fact. -/- My discussion is founded on several texts from Leibniz’s later philosophy, such as the discussion following from New System of the Nature and the Communication of Substances of 1695, Leibniz’s letter to Queen Sophie Charlotte of 1702 (also known as On What is Independent in Sense and Matter), New Essays on Human Understanding (1704), Theodicy (1710) and naturally Leibniz’s most important epistemological text, Meditations of Truth, Knowledge and Ideas (1684). (shrink)

Many epistemologists call themselves ‘fallibilists’. But many philosophers of language hold that the meaning of epistemic usages of ‘possible’ ensures a close knowledge- possibility link : a subject’s utterance of ‘it’s possible that not-p’ is true only if the subject does not know that p. This seems to suggest that whatever the core insight behind fallibilism is, it can’t be that a subject could have knowledge which is, for them, possibly false. I argue that, on the contrary, subjects can have (...) such possibly false knowledge. My ultimate aim, then, is to vindicate a very robust form of fallibilism. Uniquely, however, the account I offer does this while also allowing that concessive knowledge attributions – sentences of the form “I know that p, but it’s possible that not-p” – are not only infelicitous but actually false whenever uttered. The account predicts this result without conceding KPL. I argue that my account has the resources to explain some related cases for which the KPL account yields the wrong predictions. Taken as a whole, the linguistic data not only do not support the proposal that subjects cannot have possibly false knowledge, but indeed positively favor the proposal that they can. (shrink)

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that (...) are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (shrink)

Probabilistic theories of “should” and “ought” face a predicament. At first blush, it seems that such theories must provide different lexical entries for the epistemic and the deontic interpretations of these modals. I show that there is a new style of premise semantics that can avoid this consequence in an attractively conservative way.

Seth Yalcin has pointed out some puzzling facts about the behaviour of epistemic modals in certain embedded contexts. For example, conditionals that begin ‘If it is raining and it might not be raining, … ’ sound unacceptable, unlike conditionals that begin ‘If it is raining and I don’t know it, … ’. These facts pose a prima facie problem for an orthodox treatment of epistemic modals as expressing propositions about the knowledge of some contextually specified individual or group. This paper (...) develops an explanation of the puzzling facts about embedding within an orthodox framework. (shrink)

Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll (...) argue that agents can fail to know trivial consequences of what they know, but never determinately. Such cases are epistemic oversights on behalf of the agent in question, and the facts about epistemic oversights are always indeterminate facts. As a result, we are never in a position to assert that such-and-such constitutes an epistemic oversight for agent i (for we may rationally assert only determinate truths). I then develop formal epistemic models according to which epistemic accessibility relations are vague. Given these models, we can show that epistemic oversights always concern indeterminate cases of knowledge. (shrink)

My aim in this paper is to give a philosophical analysis of the relationship between contingently available technology and the knowledge that it makes possible. My concern is with what specific subjects can know in practice, given their particular conditions, especially available technology, rather than what can be known “in principle” by a hypothetical entity like Laplace’s Demon. The argument has two parts. In the first, I’ll construct a novel account of epistemic possibility that incorporates two pragmatic conditions: responsibility and (...) practicability. For example, whether subjects can gain knowledge depends in some circumstances on whether they have the capability of gathering relevant evidence. In turn, the possibility of undertaking such investigative activities depends in part on factors like ethical constraints, economical realities, and available technology. In the second part of the paper, I’ll introduce “technological possibility” to analyze the set of actions made possible by available technology. To help motivate the problem and later test my proposal, I’ll focus on a specific historical case, one of the earliest uses of digital electronic computers in a scientific investigation. I conclude that the epistemic possibility of gaining access to scientific knowledge about certain subjects depends (in some cases) on the technological possibility for making responsible investigations. (shrink)

This chapter examines modality in the history of analytic philosophy. There were, in this history, two principal types of reductionism or eliminativism about modality, and two corresponding phases in the rejection of anti-modal stances. First, the founders of analytic philosophy, Frege, Moore, and Russell, took necessity and possibility to be reducible to more fundamental logical notions, where logic for these thinkers consists of truths about a mind- and language-independent reality extending beyond the empirical world. Against this reductionism, C. I. Lewis (...) and Wittgenstein argued that logic itself requires modal notions. Second, Carnap advanced a pragmatically motivated account of modal terms as expressing pseudo-object properties, which appear to be properties of objects but can be construed as properties of their designations. Quine criticized this account and proposed a thoroughgoing elimination of modality. Quine’s well-known claim that quantifying into modal contexts is unintelligible without resorting to essentialism cannot be fully understood independently of Carnap’s notion of pseudo-object property. Against Quine, Ruth Marcus and Saul Kripke argued for the coherence of modal concepts and their entrenchment in ordinary language and thought, leading to the now dominant view that modal properties are mind- and language-independent features of the world. (shrink)

When a proposition might be the case, for all an agent knows, we can say that the proposition is epistemically possible for the agent. In the standard possible worlds framework, we analyze modal claims using quantification over possible worlds. It is natural to expect that something similar can be done for modal claims involving epistemic possibility. The main aim of this paper is to investigate the prospects of constructing a space of worlds—epistemic space—that allows us to model what is epistemically (...) possible for ordinary, non-ideally rational agents like you and me. I will argue that the prospects look dim for successfully constructing such a space. In turn, this will make a case for the claim that we cannot use the standard possible worlds framework to model what is epistemically possible for ordinary agents. (shrink)

So far, T×W frames have been employed to provide a semantics for a language of tense logic that includes a modal operator that expresses historical necessity. The operator is defined in terms of quantification over possible courses of events that satisfy a certain constraint, namely, that of being alike up to a given point. However, a modal operator can as well be defined without placing that constraint. This paper outlines a T×W logic where an operator of the latter kind is (...) used to express the epistemic property of definiteness. Section 1 provides the theoretical background. Sections 2 and 3 set out the semantics. Sections 4 and 5 show, drawing on established results, that there is a sound and complete axiomatization of the logic outlined. (shrink)

There is a lot that we don’t know. That means that there are a lot of possibilities that are, epistemically speaking, open. For instance, we don’t know whether it rained in Seattle yesterday. So, for us at least, there is an epistemic possibility where it rained in Seattle yesterday, and one where it did not. It’s tempting to give a very simple analysis of epistemic possibility: • A possibility is an epistemic possibility if we do not know that it does (...) not obtain. But this is problematic for a few reasons. One issue, one that we’ll come back to, concerns the first two words. The analysis appears to quantify over possibilities. But what are they? As we said, that will become a large issue pretty soon, so let’s set it aside for now. A more immediate problem is that it isn’t clear what it is to have de re attitudes towards possibilities, such that we know a particular possibility does or doesn’t obtain. Let’s try rephrasing our analysis so that it avoids this complication. (shrink)

In a possible world framework, an agent can be said to know a proposition just in case the proposition is true at all worlds that are epistemically possible for the agent. Roughly, a world is epistemically possible for an agent just in case the world is not ruled out by anything the agent knows. If a proposition is true at some epistemically possible world for an agent, the proposition is epistemically possible for the agent. If a proposition is true at (...) all epistemically possible worlds for an agent, the proposition is epistemically necessary for the agent, and as such, the agent knows the proposition. -/- This framework presupposes an underlying space of worlds that we can call epistemic space. Traditionally, worlds in epistemic space are identified with possible worlds, where possible worlds are the kinds of entities that at least verify all logical truths. If so, given that epistemic space consists solely of possible worlds, it follows that any world that may remain epistemically possible for an agent verifies all logical truths. As a result, all logical truths are epistemically necessary for any agent, and the corresponding framework only allows us to model logically omniscient agents. This is a well-known consequence of the standard possible world framework, and it is generally taken to imply that the framework cannot be used to model non-ideal agents that fall short of logical omniscience. -/- A familiar attempt to model non-ideal agents within a broadly world involving framework centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in epistemic space, it is easy to avoid logical omniscience. If any logical falsehood is true at some impossible world, then any logical falsehood may remain epistemically possible for some agent. As a result, we can use an impossible world involving framework to model extremely non-ideal agents that do not know any logical truths. -/- A much harder, and considerably less investigated challenge is to ensure that the resulting epistemic space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out impossible worlds that verify obvious logical falsehoods. To model such agents, we need a construction of a non-trivial epistemic space that partly consists of impossible worlds where not "anything goes". This involves imposing substantive constraints on impossible worlds to eliminate from epistemic space, say, trivially impossible worlds that verify obvious logical falsehoods. -/- The central aim of this dissertation is to investigate the nature of such non-trivially impossible worlds and the corresponding epistemic spaces. To flag my conclusions, I argue that successful constructions of epistemic spaces that can safely navigate between the Charybdis of logical omniscience and the Scylla of of “anything goes” are hard, if not impossible to find. (shrink)