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)

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)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

What makes a valid argument valid? Generally speaking, in a valid argument, if the premisses are true, then the conclusion must necessarily also be true. But on its own, this doesn’t tell us all that much. What is truth? And what is necessity? In what follows, I consider answers to these questions proposed by the fourteenth century logician John Buridan († ca. 1358). My central claim is that Buridan’s logic is downstream from his metaphysics. Accordingly, I treat his metaphysical (...) discussions as the key to his logic. As has been often noted, Buridan’s metaphysics are radically anti-realist about universals, though I think the depth and scope of his anti-realism has at times been papered over. Buridan constructs his logic on an amazingly spartan ontology, and this accomplishment is overdue for reconsideration. To the foregoing questions: truth is a feature of propositions, and of propositions only—not of proposition-like states of affairs, or anything like that. It is a function of the reference or supposition (suppositio) of their terms, which depends on predication in a propositional context. And necessary truth is grounded in causation: a predication is necessary if it cannot be falsified by any power, natural or supernatural, without ii annihilating what its terms stand for. “Socrates is a human”, for instance, can only be falsified by annihilating Socrates, and so it is a necessary truth. -/- These considerations provide an ample theoretical basis for a thorough examination of Buridan’s modal logic. This is what the thesis culminates with. In the final chapter, I set forth some novel and surprising findings, chief of which is this: Buridan’s modal syntax and semantics are nothing like Kripke’s—and indeed are incompatible with them. This has significant implications not only for modal logic and metaphysics, but for how we think about medieval logic and philosophy more generally. -/- Throughout the thesis, I advocate a methodology of emphasising the differences, rather than the similarities, between past and present thought. Buridan is wildly unlike what we’re used to, and we should let him speak for himself. (shrink)

The integration challenge for modality states that metaphysical theories of modality tend to fail in one of two ways: either they render the meanings of modal sentences mysterious, or they render modal knowledge mysterious. I argue that there are specific semantic and epistemic constraints on metaphysics implied by the integration challenge and that a plausible metaphysical theory of modality will satisfy both of them. I further argue that no popular metaphysical theory of modality simultaneously satisfies (...) both of the constraints. Therefore, a new metaphysical theory of modality is needed, one that can offer a clear response to the integration challenge. I attempt to supply the needed theory and show that it satisfies the constraints of the integration challenge. The overall result is an argument for a new and unique metaphysical theory of modality that I call constructionism. (shrink)

ABSTRACT We critically review two extant paradigms for understanding the systematic interaction between modality and tense, as well as their respective modifications designed to do justice to the contingency of time’s structure and composition. We show that on either type of theory, as well as their respective modifications, some principles prove logically valid whose truth might sensibly be questioned on metaphysical grounds. These considerations lead us to devise a more general logical framework that allows accommodation of those metaphysical (...) views that its predecessors rule out by fiat. (shrink)

Modal epistemologies that rely on a fallibilism about modal claims have been gaining traction over the years. This paper critically discusses the accounts of Kung (2009; 2010; 2016) and Dohrn (2018; 2019; 2020) and argues that they are invariably susceptible to being read as entailing claims of epistemic possibility. Both Kung and Dohrn seek to ground modal intuitions on non-modal ones, and primarily appeal to the modalizing capacity of imagination to aid in the discovery of (...) class='Hi'>modal truths. However, insofar as inference from non-modal imagination to modal truths remains fallible, then no non-ad hoc distinction can be made between substantiation of fallible metaphysically modal claims and infallible epistemically modal ones. This is because, barring an agent’s infallible knowledge of modal truths, how these truths are asserted must attend the agent’s imperfect epistemic access thereof, therefore entailing claims of modality consistent with her epistemic state – i.e., claims of epistemic possibility. If modal epistemologies in general non-modally ground their modal assertions in this fallible fashion, then they seem inevitably interpretable in terms of epistemic possibility as opposed to some non-epistemic reading of metaphysical possibility. (shrink)

The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth collapses (...) to truth. Then I will propose a different formulation of Carnapian modal arithmetic and establish that it is free of collapse. Noteworthy is that one can retain the standard strong principle of induction. I will occupy myself in the third section with Carnapian epistemic logic and arithmetic. Here too it is claimed that the standard weak principle of induction is invalid and that the alternative principle is valid. In the fourth and last section I will get back to the self-predication principles and I will point to some of the consequences if one adds them to Carnapian Epistemic arithmetic. The interaction of self-predication principles and the strong principle of induction results in a collapse of de re knowability. (shrink)

In this article, I seek to assess the extent to which Theism, the claim that there is a God, can provide a true fundamental explanation for the existence of the infinite plurality of concrete and abstract possible worlds, posited by David K. Lewis and Alvin Plantinga. This assessment will be carried out within the (modified) explanatory framework of Richard Swinburne, which will lead to the conclusion that the existence of God provides a true fundamental explanation for these specific entities. And (...) thus, given the truth of this type of explanation, we have another good abductive argument for God’s existence and grounds for affirming a weaker form of the principle of methodological naturalism in our metaphysical theorising. (shrink)

There is a line of thought, neglected in recent philosophy, according to which a priori knowable truths such as those of logic and mathematics have their special epistemic status in virtue of a certain tight connection between their meaning and their truth. Historical associations notwithstanding, this view does not mandate any kind of problematic deflationism about meaning, modality or essence. On the contrary, we should be upfront about it being a highly debatable metaphysical idea, while nonetheless insisting that (...) it be given due consideration. From this standpoint, I suggest that the Finean distinction between essence and modality allows us to refine the view. While liberal about meaning, modality and essence, the view is not without bite: it is reasonable to suppose that it is able to ward off philosophical confusions stemming from the undue assimilation of a priori to empirical knowledge. (shrink)

I propose that we approach the epistemology of modality by putting modal metaphysics first and, specifically, by investigating the metaphysics of essence. Following a prominent Neo-Aristotelian view, I hold that metaphysical necessity depends on the nature of things, namely their essences. I further clarify that essences are core properties having distinctive superexplanatory powers. In the case of natural kinds, which is my focus in the paper, superexplanatoriness is due to the fact that the essence of a kind is (...) what causes all the many properties and behaviors that are typically shared by all the instances of the kind. Accordingly, we know what is necessarily true of kinds by knowing what is essential to them in the sense of actually playing such causal-explanatory roles. Modal reasoning aimed at discovering metaphysical necessity thus proceeds via essentialist deduction: we move from essentialist truths to reach necessary truths. (shrink)

Contingency is the presence of non-actualized possibility in the world. Fatalism is a view of reality on which there is no contingency. Since it is contingency that permits agency, there has traditionally been much interest in contingency. This interest has long been embarrassed by the contention that simple and plausible assumptions about the world lead to fatalism. I begin with an Aristotelian argument as presented by Richard Taylor. Appreciation of this argument has been stultified by a question pertaining to the (...) source of necessity and possibility and a closely related one regarding the nature of metaphysics itself. Answering these questions reveals the crucial issue here, to wit, necessity and possibility in a temporal world. This issue is investigated through an important later criticism of Taylor by David Foster Wallace. Wallace’s critique is significant because it brings to the fore the pivotal notion for understanding contingency in a temporal world, that of synchronic possibility, the idea that incompatible states of affairs are possible at a single moment. This notion provides the basis of distinguishing two systematic accounts of truth, modality and time: two metaphysics of contingency. On one account, Taylor’s Aristotelian argument is straightforwardly valid and compelling; on the other, it is fallacious. In closing, I present reasons why the former account, supporting the Aristotelian views of time and truth, is correct and make some comments to ameliorate this conclusion. (shrink)

In the presentation I will analyse Kant’s conception of modalities and consider its relevance to his critical metaphysics. With his Tables of Judgements and of Categories Kant makes an important division between two kinds of modality, of which the former is only logical and the latter transcendental, i.e., objective. Only judgements that are necessary in both ways are properly metaphysical. This distinction is important for Kant’s distinction between Transcendental Analytic and Transcendental Dialectic, i.e., between acceptable and unacceptable metaphysics. I (...) submit that not only is Kant’s theory of modality useful for properly understanding his arguments in the Dialectic, but that only by distinguishing between the two types of modality can one can make sense of his theory that the ideas of reason are simultaneously inevitable and erroneous. This modal analysis thus offers a new and important point of view to Kant’s metaphysics and its critique. (shrink)

Aim of this paper is to analyse and assess two divergent understandings of metaphysical modality. On one hand, according to the absolutist conception, metaphysical modality is the extreme variety of objective modality and can be characterised in terms of all the varieties of objective modality: for example, p is metaphysically necessary if and only if p is necessary for every variety of objective necessity. The absolutist conception can also be framed in terms of counterfactual inevitability. On the other (...) hand, according to the essentialist conception of metaphysical modality, p is metaphysically necessary if and only if the truth of p is grounded by the essences of some entities. Based on the analysis of these two conceptions, I show that possible worlds are not helpful in characterising metaphysical modality. I finally suggest that in the light of a general principle about philosophical terminology, the essentialist conception has an edge over the absolutist one. (shrink)

The starting point of this paper concerns the apparent difference between what we might call absolute truth and truth in a model, following Donald Davidson. The notion of absolute truth is the one familiar from Tarski’s T-schema: ‘Snow is white’ is true if and only if snow is white. Instead of being a property of sentences as absolute truth appears to be, truth in a model, that is relative truth, is evaluated in terms of the relation between sentences and models. (...) I wish to examine the apparent dual nature of logical truth (without dwelling on Davidson), and suggest that we are dealing with a distinction between a metaphysical and a linguistic interpretation of truth. I take my cue from John Etchemendy, who suggests that absolute truth could be considered as being equivalent to truth in the ‘right model’, i.e., the model that corresponds with the world. However, the notion of ‘model’ is not entirely appropriate here as it is closely associated with relative truth. Instead, I propose that the metaphysical interpretation of truth may be illustrated in modal terms, by metaphysical modality in particular. One of the tasks that I will undertake in this paper is to develop this modal interpretation, partly building on my previous work on the metaphysical interpretation of the law of non-contradiction (Tahko 2009). After an explication of the metaphysical interpretation of logical truth, a brief study of how this interpretation connects with some recent important themes in philosophical logic follows. In particular, I discuss logical pluralism and propose an understanding of pluralism from the point of view of the metaphysical interpretation. (shrink)

Drawing an analogy between modal structuralism about mathematics and theism, I o er a structuralist account that implicitly de nes theism in terms of three basic relations: logical and metaphysical priority, and epis- temic superiority. On this view, statements like `God is omniscient' have a hypothetical and a categorical component. The hypothetical component provides a translation pattern according to which statements in theistic language are converted into statements of second-order modal logic. The categorical component asserts the logical (...) possibility of the theism struc- ture on the basis of uncontroversial facts about the physical world. This structuralist reading of theism preserves objective truth-values for theistic statements while remaining neutral on the question of ontology. Thus, it o ers a way of understanding theism to which a naturalist cannot object, and it accommodates the fact that religious belief, for many theists, is an essentially relational matter. (shrink)

This essay expands upon the suggestion that Lessing's infamous ‘ditch’ is actually three ditches: temporal, metaphysical, and existential gaps. It examines the complex problems these ditches raise, and then proposes that Kierkegaard's Fragments and Postscript exhibit a similar triadic organizational structure, which may signal a deliberate attempt to engage and respond to Lessing's three gaps. Viewing the Climacean project in this way offers an enhanced understanding of the intricacies of Lessing's rationalist approach to both religion and historical truth, and (...) illuminates Climacus's subjective response to Lessing. (shrink)

During the last quarter of a century, a number of philosophers have become attracted to the idea that necessity can be analyzed in terms of a hyperintensional notion of essence. One challenge for proponents of this view is to give a plausible explanation of our modal knowledge. The goal of this paper is to develop a strategy for meeting this challenge. My approach rests on an account of modality that I developed in previous work, and which analyzes modal (...) properties in terms of the notion of a metaphysical law. I discuss what information about the metaphysical laws is required for modal knowledge. Moreover, I describe two ways in which we might be able to acquire this information. The first way employs inference to the best explanation. The metaphysical laws, including the essential truths, play a crucial role in causal and grounding explanations and we can gain knowledge of these laws by abductive inferences from facts of which we have perceptual or a priori knowledge. The second way of gaining information about the metaphysical laws rests on knowledge that is partly constitutive of competence with the concepts that are needed to express the relevant information. Finally, I consider how knowledge of the metaphysical laws can be used to establish modal claims, paying special attention to the much-discussed connection between conceiving and possibility. (shrink)

We review some of the major accounts in the current epistemology of modality and identify some shared issues that plague all of them. In order to provide insight into the nature of modal statements in science, philosophy, and beyond, a satisfactory epistemology of modality would need to be suitably applicable to practical and theoretical contexts by limited beings. However, many epistemologies of modality seem to work only when we have access to the kind of knowledge that is at least (...) currently beyond our reach. Or, in the extreme case, it is argued that even if we knew all the relevant information about the respective domain – or even the entire state of the world – there would still remain a special class of modal truths that would be left unaccounted for. Neither picture bodes well for practical applicability, nor for the philosophical justification of these epistemologies. This is especially the case as we hold that one of the main motivations for modal inquiry typically arises in cases of imperfect information and limited cognitive resources. We close by providing a partial remedy to the situation by suggesting an overall framework of relative modality (RM) that can be used to both unify some existing modal epistemologies and, at the same time, make them more metaphysically modest. (shrink)

This paper targets a series of potential issues for the discussion of, and modal resolution to, the alethic paradoxes advanced by Scharp (2013). I proffer four novel extensions of the theory, and detail five issues that the theory faces.

There is a common approach to metaphysical disputes, which takes language as its starting point, and leads to a view about the range of acceptable metaphysical positions in any such dispute. I argue that this approach rests on accepting what I call the Strong Linguistic Thesis (SLT). In the metaphysical debate about time I argue that the new B-theory has rejected SLT, and for good reasons. The metaphysical debate about modality parallels the early metaphysical debate (...) about time. I argue that a position analogous to the new B-theory of time is available in the modal debate, and has some advantages over its rivals. (shrink)

Recent work on the philosophy of modality has tended to pass over questions about iterated modalities in favour of constructing ambitious metaphysical theories of possibility and necessity, despite the central importance of iterated modalities to modal logic. Yet there are numerous unresolved but fundamental issues involving iterated modalities: Chandler and Salmon have provided forceful arguments against the widespread assumption that all necessary truths are necessarily necessary, for example. The current paper examines a range of ways in which (...) one might seek to identify limited regions within which some of the most well-known principles featuring iterated modalities may safely be assumed. (shrink)

In his influential Naming and Necessity lectures, Saul Kripke made new sense of modal statements: “Kant might have been a bachelor”, “Königsberg is necessarily identical with Kaliningrad”. Many took the notions he introduced-metaphysical necessity and rigid designation -- to herald new metaphysical issues and have important consequences. In fact, the Kripkean insight is at bottom semantic, rather than metaphysical: it is part of how proper names work that they purport to refer to individuals to whom (...) class='Hi'>modal properties can be ascribed. We can see this by reflecting on analytic truths that ground modal claims like the two examples above. (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)

Some metaphysicians believe that metaphysical modality is explainable by the essences of objects. In §II, I spell out the definitional view of essence, and in §III, a working notion of metaphysical explanation. Then, in §IV, I consider and reject five natural ways to explain necessity by essence: in terms of the principle that essential properties can't change, in terms of the supposed obviousness of the necessity of essential truth, in terms of the logical necessity of definitions, in terms (...) of Fine's logic of essence, and in terms of the theory of real definitions. I will conclude that the present evidence favours rejecting the hypothesis that modality is explainable by essence. (shrink)

Resolving the Ross and Prior paradoxes proved to be a difficult task. Its first two stages, involving the identification of the true natures of the implication and truth values, are described in the articles "Solving the Paradox of Material Implication – 2024" and "Solving Jörgensen's Dilemma – 2024". This article describes the third stage, which involves the discovery of missing modal operators and the Classical Modal Calculus. Finally, procedures for solving both paradoxes are provided.

Leibniz' first problem with contingency stems from his doctrine of divine creation (not his later doctrine of truth) and is solved via his concepts of necessity per se, etc. (not via his later concept of infinite analysis). I scrutinize some of the earliest texts in which the first problem and its solution occur. I compare his "per se modal concepts" with his concept of analysis and with the traditional concept of metaphysical necessity. I then identify and remove the (...) main obstacle to Leibniz' employment of these concepts by reflecting on his concept of a world and comparing and contrasting it with contemporary conceptions. Finally I sketch the place that this early problem and its solution had in the context of his mature philosophy. A disagreement between Sleigh and Adams which hinges on the assumption that there is just one problem with competing solutions is seen to dissolve in this light. (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)

I provide a case-by-case definition of essential truths based on the notions of metaphysical necessity and ontological dependence. Relying on suggestions in the literature, I adopt a definition of the latter notion in terms of the notion of ground. The resulting account is adequate in the sense that it is not subject to Kit Fine’s famous counterexamples to the purely modal account of essence. In addition, it provides us with a novel conception of truths pertaining to (...) the essence of objects, which might help to dispel doubts on the legitimacy of the notion of essence itself. (shrink)

I develop a psychological account for how it is that we use imagination to metaphysically modalize, i.e., to reach conclusions about metaphysical modality. Specifically, I argue that Nichols and Stich’s (2003) cognitive theory of imagination can be extended to metaphysical modalizing. I then use the extension to explicate philosophical disagreements about whether a scenario is metaphysically possible. Thereafter, I address Nichols’ (2006) objection that psychologizing imagination makes it clear that imagination is unreliable when used to metaphysically modalize. The (...) end result is a naturalistic account for how imagination enables us to metaphysically modalize. (shrink)

Dispositionalism is the theory of modality according to which all (metaphysical and natural) modal truths are made true by some actual irreducibly dispositional property. The relationship between Dispositionalism and time is yet to be satisfactorily explored. In this paper we contribute to this task by examining how Dispositionalism deals with ‘dated truths’: propositions involving a specific time, e.g. “It might rain at 12.30”. We examine two possible accounts: the first, 'Dated Manifestations Strategy', is the idea that (...) powers are very fine-grained, and tend towards temporally very specific manifestations. We argue that such strategy should not be adopted, for it leads to unnecessary violations of ontological parsimony; it is unable to accommodate an ontology of platonic universals; and it is incapable of offering a principled explanation of the forward-looking nature of powers. We offer an alternative account, the "Duration Strategy", which relies on an independently determined arrow of time and the existence of some “duration facts” that specify how long a power takes to bring about its manifestation. We argue that the Duration Strategy is to be preferred. We then flesh out the account by exploring the connection between powers, duration facts, and processes. (shrink)

Metaphysics-first approaches dominate the current literature in the epistemology of modality. According to metaphysics-firsters, metaphysical theses have an important role in the justification of modal epistemologies. For example, the thesis that essentialist truths constitute the metaphysical grounds of modal truths is meant to have an important role in the justification of essentialist modal epistemologies. In this article, we argue against this approach. We first pick up some of the groundwork on behalf of the (...) metaphysics-firsters and explicitly spell out potential arguments for their view. However, despite some initial plausibility, these arguments are ultimately found wanting. We conclude that the metaphysics-first approach lacks motivation and puts far too stringent demands upon modal epistemologists. (shrink)

Modal dimensionalism is realism about spaces, times and worlds—metaphysical indices that make objects spatial, temporal and modal, respectively, and that play the role of alethic relativizers, i.e. items to which matters of truth are relativized. This paper examines several arguments against MD and shows that MD offers a feasible way to understand modal discourse.

In a lot of domains in metaphysics the tacit assumption has been that whichever metaphysical principles turn out to be true, these will be necessarily true. Let us call necessitarianism about some domain the thesis that the right metaphysics of that domain is necessary. Necessitarianism has flourished. In the philosophy of maths we find it held that if mathematical objects exist, then they do of necessity. Mathematical Platonists affirm the necessary existence of mathematical objects (see for instance Hale and (...) Wright 1992 and 1994; Wright 1983 and 1988; Schiffer 1996; Resnik 1997; Shapiro 1997 and Zalta 1988) while mathematical nominalists, usually in the form of fictionalists, hold that necessarily such objects fail to exist (see for instance Balaguer 1996 and 1998; Rosen 2001 and Yablo 2005). In metaphysics more generally, until recently it was more or less assumed that whatever the right account of composition—the account of under what conditions some xs compose a y—that account will be necessarily true (for a discussion of theories of composition see Simons 1987 and van Inwagen 1987 and 1990; the modal status of the composition relation is explicitly addressed in Schaffer 2007; Parsons 2006 and Cameron 2007). Similarly, it has generally been assumed that whatever the right account is of the nature of properties, whether they be universals, tropes, or whether nominalism is true, that account will be necessarily true (though see Rosen 2006 for a recent suggestion to the contrary). In considering theories of persistence it has been widely held that whether objects endure or perdure through time is a matter of necessity (Sider 2001; though see Lewis 1999 p227 who defends contingent perdurantism). And with respect to theories of time it is frequently held that whichever of the A- or B-theory is true is necessarily true. A-theorists often argue that there is time in a world only if the A-theory is true at that world (see for instance McTaggart 1903; Markosian 2004; Bigelow 1996; Craig 2001) while B-theorists often argue that the A-theory is internally inconsistent (Smart 1987; Mellor 1998; Savitt 2000 and Le Poidevin 1991). Once again, we find a few recent contingentist dissenters. Bourne (2006) suggests that it is a contingent feature of time that it is tensed, and thus that the A-theory is contingently true. Worlds in which there exist only B-theoretic properties are worlds with time, it is just that time in those worlds time is radically different to the way it is actually. Other defenders of the B-theory, though not expressly contingentists, do offer arguments against versions of the A-theory that try to show that such A-theories theories are inconsistent with the actual laws of nature (see for instance Saunders 2002 and Callender 2000); these arguments, at least, leave room for the possibility that the A-theories in question are contingently false (at least on the assumption that the laws of nature are themselves contingent, an assumption that not everyone accepts). Despite some notable exceptions, necessitarianism has flourished in many, if not most, domains in metaphysics. One such exception is Lewis’ famous defence of Humean supervenience as a contingent claim about our world. Lewis does not argue that necessarily, the supervenience base for all matters of fact in a world is nothing but a vast mosaic of local matters of particular fact. Rather, he thinks that we have reason to think that our world is one in which Humean supervenience holds (see Lewis 1986 p9-10 and 1994). Another exception to the necessitarian orthodoxy is to be found in the lively debate about the modal status of the laws of nature. Here, if anything, contingentism has been the dominating force, with it generally being held that there are possible worlds in which different laws of nature hold (this view is defended by, among others, Lewis 1986 and 2010; Schaffer 2005 and Sidelle 2002). Necessitarian dissenters hold that the laws of nature are necessary, frequently because they think it is necessary that fundamental properties have the causal or nomic profiles they do (see for instance Shoemaker 1980 and 1988; Swoyer 1982; Bird 1995; Ellis and Lierse 1994). Nevertheless, when it comes to thinking about the nature of the laws themselves, the necessitarian presumption is back on firm footing. Though there is disagreement about whether the laws are generalisations that feature in the most virtuous true axiomatisation of all the particular matters of fact (often known as the Humean view of laws and defended by Ramsey 1978; Lewis 1986 and Beebee 2000) or whether laws are relations of necessity that hold between universals (a view defended by Armstrong 1983; Dretske 1977; Tooley 1977 and Carroll 1990) no one has seriously suggested that it might be a contingent matter which of these is the right account of laws. The necessitarian orthodoxy is not surprising since metaphysics is largely an a priori process. While a priori reasoning may be used to determine whether a proposition is necessary or contingent, it is not well placed (in the absence of a posteriori evidence) to determine whether a contingent proposition is actually true or false. Since metaphysicians aim to tell us which principles are true in which worlds, on the face of it the discovery that metaphysical principles are contingent seems to make part of the task of metaphysics epistemically intractable. In what follows I consider two reasons one might end up embracing contingentism and whether this would lead one into epistemic difficulty. The following section considers a route to contingent metaphysical truths that proceeds via a combination of conceptual necessities and empirical discoveries. Section 3 considers whether there might be synthetic contingent metaphysical truths, and the final section raises the question of whether if there were such truths we would be well placed to come to know them. (shrink)

This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal profile of (...) rational intuition; and to the types of intention, when the latter is interpreted as a modal 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 epistemic two-dimensional hyperintensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic 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, by contrast to availing of modal axiom 4 (i.e. the KK principle). 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 chapter \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 intensions of epistemic two-dimensional semantics solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between topic-sensitive epistemic two-dimensional truthmaker semantics, 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. Chapter \textbf{9} examines the modal profile of $\Omega$-logic in set theory. Chapter \textbf{10} examines the modal commitments of abstractionism, in particular necessitism, and epistemic modality and the epistemology of abstraction. Chapter \textbf{11} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of epistemic two-dimensional semantics in order to account for the interaction of the interpretational and objective modalities thereof. Chapter \textbf{12} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal semantics for the different types of intention and the relation of the latter to evidential decision theory. The multi-hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is applied in chapters \textbf{7}, \textbf{8}, \textbf{10}, \textbf{11}, \textbf{12}, and \textbf{14}.}. (shrink)

This paper concerns a distinction between circumstantial truths that hold because of the circumstances and acircumstantial truths that hold regardless of, or transcend, the circumstances. Previous discussions of the distinction tended to focus on its applications, such as to modality, logical truth, and essence. This paper focuses on developing the distinction largely, but not entirely, in abstraction from its potential applications. As such, the paper’s main contribution is to further clarify the distinction itself. An indirect contribution is to (...) help guide its future applications. (shrink)

We propose a semantic analysis of the particles afinal (European Portuguese) and alla fine (Italian) in terms of the notion of truth unpersistence, which combines both epistemic modality and constraints on discourse structure. We argue that the felicitous use of these modal particles requires that the truth of a proposition p* fail to persist through a temporal succession of epistemic states, where p* is incompatible with the proposition modified by afinal/alla fine, and that the interlocutors share knowledge of a (...) previous epistemic attitude toward p*. We analyze two main cases, that of plan-related propositions and that of propositions without plans. We also discuss the connections between truth unpersistence and evidentiality. (shrink)

The paper proposes a strategy for understanding metaphysical grounding in deflationary terms and, more generally, proposes a form of methodological deflationism with respect to the notions of ground. The idea is to define a deflationary is grounded in-predicate by appeal to the two-place non-causal connective ‘because’ and a deflationary truth predicate. To this end, we discuss the explanatory role of the truth-predicate in non-causal explanations and develop a theory of truth for the language of the ‘because’-connective. We argue that (...) at least from a logical perspective our deflationary notion of ground is up to the task. (shrink)

The essays collected in this volume are all concerned with the connection between fiction and truth. This question is of utmost importance to metaphysics, philosophy of language, philosophical logic and epistemology, raising in each of these areas and at their intersections a large number of issues related to creation, existence, reference, identity, modality, belief, assertion, imagination, pretense, etc. All these topics and many more are addressed in this collection, which brings together original essays written from various points of view by (...) philosophers of diverse trends. These essays constitute major contributions to the current debates that the connection between truth and fiction continually enlivens, and give a sense of the directions in which research on this question is heading. Contributors: Fred Adams, Frederick Kroon, Robert Howell, Brendan Murday, Terence Parsons, Graham Priest, Erich Rast, Manuel Rebuschi, Marion Renauld, R.M. Sainsbury, Grant Tavinor, Alberto Voltolini. (shrink)

Kit Fine famously objected against the idea that essence can be successfully analyzed in terms of de re necessity. In response, I want to explore a novel, interesting, but controversial modal account of essence in terms of intrinsicality and grounding. In the first section, I will single out two theoretical requirements that any essentialist theory should meet—the essentialist desideratum and the essentialist challenge—in order to clarify Fine’s objections. In the second section, I will assess Denby’s improved modal account, (...) which appeals to the notion of intrinsicality, and argue that it is untenable. In the third section, I will explain how, when combined with a modal-existential criterion, a hyperintensional account of intrinsicality—in the same vein as Bader (J Philos 110(10): 525–563, 2013) and Rosen (in: Hale and Hoffman (eds) Modality: Metaphysics, logic, and epistemology, Oxford, OUP, 2010)—can help successfully address Fine’s counterexamples. In the fourth section, I will evaluate how this novel analysis of essence stands with respect to sortal, origin, and natural kinds essentialism and discuss potential objections and difficulties. (shrink)

In this paper, we consider recent attempts to metaphysically explain agentive modality in terms of conditionals. We suggest that the best recent accounts face counterexamples, and more worryingly, they take some agentive modality for granted. In particular, the ability to perform basic actions features as a primitive in these theories. While it is perfectly acceptable for a semantics of agentive modal claims to take some modality for granted in getting the extension of action claims correct, a metaphysical explanation (...) of agentive modality cannot, at least not in the way that conditional approaches to agentive modality do. We argue that this problem was present even in the classical conditional analysis. By a pessimistic induction, we suggest that, probably, no conditional approach to agentive modality will succeed. (shrink)

Modal epistemologists parse modal conditions on knowledge in terms of metaphysical possibilities or ways the world might have been. This is problematic. Understanding modal conditions on knowledge this way has made modal epistemology, as currently worked out, unable to account for epistemic luck in the case of necessary truths, and unable to characterise widely discussed issues such as the problem of religious diversity and the perceived epistemological problem with knowledge of abstract objects. Moreover, there (...) is reason to think that this is a congenital defect of orthodox modal epistemology. This way of characterising modal epistemology is however optional. It is shown that one can non-circularly characterise modal conditions on knowledge in terms of epistemic possibilities, or ways the world might be for the target agent. Characterising the anti-luck condition in terms of epistemic possibilities removes the impediment to understanding epistemic luck in the case of necessary truths and opens the door to using these conditions to shed new light on some longstanding epistemological problems. (shrink)

In a recent article forthcoming in *Mind*, Leech (2020) presents a challenge for essentialist accounts of metaphysical modality: why should it be that essences imply corresponding necessities? Leech’s main focus is to argue that one cannot overcome the challenge by utilizing an account of essence in terms of generalized identity due to Correia and Skiles (2019), on pain of circularity. In this reply, we will show how to use identity-based essentialism to bridge ‘epistemic’ and ‘explanatory’ understandings of this alleged (...) essence-to-necessity gap without circularity, Leech’s arguments notwithstanding. We do so by first presenting a novel proof that generalized identities imply corresponding necessities. We then propose several substantive identity-based explanations of how it is, exactly, that essences imply necessities. -/- . (shrink)

Dispositionalism is the theory of modality that grounds all modal truths in powers: all metaphysically possible and necessary truths are to be explained by pointing to some actual power, or absence thereof. One of the main reasons to endorse dispositionalism is that it promises to deliver an especially desirable epistemology of modality. However, so far this issue has not be fully investigated with the care it is due. The aim of this paper is to fill this gap. (...) We will cast some doubts on whether the dispositionalist really is in a better position to explain our modal knowledge. In fact, we argue that there is a tension between some core tenets of a powers metaphysics and the very features that make dispositionalism the ideal backdrop for a desirable epistemology of modality. We conclude that this leaves dispositionalists who want to deliver the promised epistemology with a hard, currently unfulfilled, task. (shrink)

Growing-Block theorists hold that past and present things are real, while future things do not yet exist. This generates a puzzle: how can Growing-Block theorists explain the fact that some sentences about the future appear to be true? Briggs and Forbes develop a modal ersatzist framework, on which the concrete actual world is associated with a branching-time structure of ersatz possible worlds. They then show how this branching structure might be used to determine the truth values of future contingents. (...) They point out three different ways of interpreting the logical connectives, which give rise to three different logics of the open future: one supervaluationist, one corresponding to Lukasiewicz's strong Kleene logic, and one intuitionist. (shrink)

In this paper I will be concerned with the question as to whether expressivist theories of meaning can coherently be combined with deflationist theories of truth. After outlining what I take expressivism to be and what I take deflationism about truth to be, I’ll explain why I don’t take the general version of this question to be very hard, and why the answer is ‘yes’. Having settled that, I’ll move on to what I take to be a more pressing and (...) interesting version of the question, arising from a prima facie tension between deflationism about truth and the motivations underlying expressivism for what I take to be two of its most promising applications: to indicative conditionals and epistemic modals. Here I’ll argue that the challenge is substantive, but that there is no conceptual obstacle to its being met, provided that one’s expressivism takes the right form. (shrink)

It is not uncommon in educational research and social science in general either to eschew the word truth or to put it in scare quotes in order to signify scepticism about it. After the initial wave of relativism in the philosophy of natural science, a second wave has developed in social science with the rise of postmodernism and poststructuralism. The tendency here is to relativise truth or to bracket out questions of truth. In contradistinction, this paper revindicates the metaphysical (...) nature of truth. Truth is a transcendental precondition of educational inquiry and is best understood as a formal, regulative norm. Realism about truth enjoins a defence of the correspondence theory, which is provided here. At the same time, however, the development of realism in the social sciences has ironically followed the postmodernists in its scepticism about truth and its rejection of the correspondence theory. This paper critically appraises such recent developments, since all research is unintelligible without realism about the social world and whether our substantive knowledge-claims correspond with it. (shrink)

I distinguish (§1) two projects in modal epistemology—one about how we come to know modal truths, and one about why we have the ability so to come to know. The latter, I suggest, (§§2–3) is amenable to an evolutionary treatment in terms of general capacities developed to evaluate quotidian modal claims. I compare (§4) this approach to a recent suggestion in a similar spirit by Christopher Hill and Timothy Williamson, emphasizing counterfactual conditionals instead of quotidian modals; (...) I argue that while there are some reasons to prefer the quotidian modals approach, there are none favoring the Hill/Williamson counterfactual approach. I conclude (§5) with a suggestion that the remaining questions both approaches leave unanswered ought not to be too troubling. (shrink)

A number of philosophers have recently found it congenial to talk in terms of grounding. Grounding discourse features grounding sentences that are answers to questions about what grounds what. The goal of this article is to explore and defend a counterpart-theoretic interpretation of grounding discourse. We are familiar with David Lewis's applications of the method of counterpart theory to de re modal discourse. Counterpart-theoretic interpretations of de re modal idioms and grounding sentences share similar motivations, mechanisms, and applications. (...) I shall explain my motivations and describe two applications of a counterpart theory for grounding discourse. But, in this article, my main focus is on counterpart-theoretic mechanisms. (shrink)

Let an iterated essentialist statement be a statement of the form 'It lies in the nature of x1,x2,... that it lies in the nature of y1,y2,... that φ'. Let Iteration be the thesis that there are true iterated essentialist statements. Iteration has recently been disputed by Dasgupta (2014) and Glazier (2017). Both authors take the falsity of Iteration to be central to the explanatory role of essentialist truths. An important consequence that is not explicitly noted by them is that (...) the falsity of Iteration would entail that metaphysical necessity is not reducible to essence in the manner suggested by Fine (1994). This paper defends Iteration against these challenges, drawing attention to some features of the collective essences of properties, propositions, and logical operations that have been largely neglected in discussions about essence. (shrink)