A generalized inclusion frame consists of a set of points W and an assignment of a binary relation $R\sb{w}$ on W to each point w in W. Generalized inclusion frames whose $R\sb{w}$ are partial orders are called comparison frames. Conditional logics of various comparative notions, for example, Lewis's V-logic of comparative possibility and utilitarian accounts of conditional obligation, model the dyadic modal operator $>$ on comparison frames according to the following truth condition: $\alpha > \beta$ "holds at w" iff every (...) point in the truth set of $\alpha$ bears $R\sb{w}$ to some point where $\beta$ holds. ;In this essay I provide a relational frame theory which embraces both accessibility semantics and g.i. semantics as special cases. This goal is achieved via a philosophically significant generalization of universal strict implication which does not assume accessibility as a primitive. Within this very general setting, I provide the first axiomatization of the dyadic modal logic corresponding to the class of all g.i. frames. Various correspondences between dyadic logics and first order definable subclasses of the class of g.i. frames are established. Finally, some general model constructions are developed which allow uniform completeness proofs for important sublogics of Lewis' V. (shrink)

Dispositional essentialism is a non-Humean view about the essences of certain fundamental or natural properties that looms large in recent metaphysics , not least because it promises to explain neatly the natural modalities such as laws of nature, counterfactuals, causation and chance. In the current paper, however, several considerations are presented that indicate a serious tension between its essentialist core thesis and natural “metaphysical” interpretations of its central explanatory claims.

Miracles are extraordinary events that occur in the hands of those who claim to be prophets and which cannot be repeated by others. By these miracles, the prophets prove to society that the truths they convey are of divine origin. The miracles bestowed upon prophets vary according to the scope of the message they deliver and the interests and relevance of the societies with which they deal. Accordingly, Islamic scholars have classified miracles into three groups. The miraculous events that appeal (...) to people’s senses and lead them to the truths they convey by captivating their astonishment are called emotional miracles. Such miracles are events that occur without cause by overcoming the laws of nature, which are in the realm of causes, through the direct intervention of Allāh. On the other hand, spiritual miracles are truths that arouse the interlocutor’s interest in moral conduct and rational conclusions rather than in his sensory perceptions. Since these truths are attained through contemplation, they are not confined to a particular time and place, as in the case of emotional miracles. Some Kalām scholars have also considered the Prophets’ revelational knowledge about events that have occurred in the past or will occur in the future as miracles. They have studied these events that a person could not bear in the past or could not predict for the future under the title of "The news miracle" Among these three types of miracles, scholars have considered spiritual miracles superior to the others both in terms of the breadth of their influence and their continuity. That Prophet Muhammad (PBUH) is the last of the prophets, and that the teachings he received through revelation remain valid until the Day of Judgment necessitates that some of the miracles bestowed upon him must be of a quality that attracts the attention of all people. For this reason, Islamic scholars have placed the permanent miracle of Prophet Muhammad in the category of spiritual miracles. Scholars agree that his greatest miracle that has astonished all humankind is the Qurʾān. The clearest proof of this are the verses in the Qurʾān that challenge the opponents to bring a similar one. Allāh commands the disbelievers first to bring a similitude of the Qurʾān (al-Isrāʾ 17:88), then the equivalent of ten surahs (Hūd 11:13), and finally any surah of the Qurʾān (al-Baqara 2:23). Thus, the deniers are made aware of their inability to meet this challenge under gradually mitigating circumstances. Although scholars agree on the Qurʾānic miracle’s reality, they have expressed different views on its nature and essence. Thus, some scholars have argued that the miracle of the Qurʾān does not arise from some properties special to it but from the direct intervention of Allāh in human who have the ability to bring something like it. Most Islamic scholars, on the other hand, pointed out that the Qurʾān has aspects that exceed human powers in various fields, and they explained the inability to reply in the same vein to the Qurʾān due to its uniquenesses. Accordingly, some scholars have argued that miracles are perceptible, but it is never possible to define them. Other scholars, however, viewed miracles as an identifiable phenomenon and stated that the Qurʾān is an unusual and unique book in terms of verses. In this article, the questions Why was the Quran sent down as a miraculous Kalam with an attribute not found in other divine books and in what way did the Qurʾān make people weak to have a similar of it? were scrutinized, thus, some fundamental questions regarding the nature and character of iʿdjāz al-Qurʾān are elucidated. Since the topic deals with history and literature, scanning sources and data analysis were mainly used as methods in the research. The results can be summerized as follows: Although the Prophet was supported by both emotional and mental miracles in proving the Prophetic case, his greatest miracle is the Quran. The miracle of the Qurʾān is different from the other miracles, based on both the challenging verses and the Prophet's explanations of the miracles. The reason for this difference lies in the fact that the miracle of the Qurʾān is based on reason, unlike the other miracles which are emotional. Most Islamic scholars who deal with the miracle of the Qurʾān emphasize the issues of rhetoric, verse, style, and content. At this point, they emphasized that the Qurʾān has a unique expression and content that cannot be surpassed. (shrink)

In this comprehensive study of Wittgenstein's modal theorizing, Bradley offers a radical reinterpretation of Wittgenstein's early thought and presents both an interpretive and a philosophical thesis. A unique feature of Bradley's analysis is his reliance on Wittgenstein's Notebooks, which he believes offer indispensable guidance to the interpretation of difficult passages in the Tractatus. Bradley then goes on to argue that Wittgenstein's account of modality--and the related notion of possible worlds--is in fact superior to any of the currently popular theories (...) in this area. In this context, he examines and critiques the work of such figures as Adams, Carnap, Hintikka, Lewis, Rescher, and Stalnaker. (shrink)

This book defends a radical new theory of contingency as a physical phenomenon. Drawing on the many-worlds approach to quantum theory and cutting-edge metaphysics and philosophy of science, it argues that quantum theories are best understood as telling us about the space of genuine possibilities, rather than as telling us solely about actuality. When quantum physics is taken seriously in the way first proposed by Hugh Everett III, it provides the resources for a new systematic metaphysical framework encompassing possibility, necessity, (...) actuality, chance, counterfactuals, and a host of related modal notions. -/- Rationalist metaphysicians argue that the metaphysics of modality is strictly prior to any scientific investigation; metaphysics establishes which worlds are possible, and physics merely checks which of these worlds is actual. Naturalistic metaphysicians respond that science may discover new possibilities and new impossibilities. This book's quantum theory of contingency takes naturalistic metaphysics one step further, allowing that science may discover what it is to be possible. As electromagnetism revealed the nature of light, as acoustics revealed the nature of sound, as statistical mechanics revealed the nature of heat, so quantum physics reveals the nature of contingency. (shrink)

The paper pinpoints certain unrecognized difficulties that surface for recombination and duplication in modal realism when we ask whether the following inter-world fixity claims hold true: 1) A property is perfectly natural in a world iff it is perfectly natural in every world where it is instantiated; 2) Something is mereologically atomic in a world iff all of its duplicates in every world are atomic. In connection to 1), the hypothesis of idlers prompts four variants of Lewis’s doctrine (...) of perfectly natural properties, all deemed unsatisfactory for the purposes of duplication and recombination. By means of 2), instead, we show that the principle of recombination does not countenance the atomicity or non-atomicity of duplicates; but it should, because it is genuinely possible that: a) something, which is atomic, is non-atomic; and b) something, which is non-atomic, is atomic. In discussing 1) and 2), the paper substantiates a tension in Lewis’s metaphysics between modal intuitions and the reliance on the natural sciences. (shrink)

Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. (...) I prove soundness and completeness theorems with respect to Hodes’ semantics, as well as semantics with fewer restrictions on the accessibility relation. (shrink)

Ontic structural realism is the view that structures are what is real in the first place in the domain of fundamental physics. The structures are usually conceived as including a primitive modality. However, it has not been spelled out as yet what exactly that modality amounts to. This paper proposes to fill this lacuna by arguing that the fundamental physical structures possess a causal essence, being powers. Applying the debate about causal vs categorical properties in analytic metaphysics to (...) ontic structural realism, I show that the standard argument against categorical and for causal properties holds for structures as well. Structural realism, as a position in the metaphysics of science that is a form of scientific realism, is committed to causal structures. The metaphysics of causal structures is supported by physics, and it can provide for a complete and coherent view of the world that includes all domains of empirical science. (shrink)

In this paper, I will defend the thesis that fundamental natural laws are distinguished from accidental empirical generalizations neither by metaphysical necessity, 147–155, 2005, 2007) nor by contingent necessitation. The only sort of modal force that distinguishes natural laws, I will argue, arises from the peculiar physical property of mutual independence of elementary interactions exemplifying the laws. Mutual independence of elementary interactions means that their existence and their nature do not depend in any way on which other interactions (...) presently occur. It is exactly this general physical property of elementary interactions in the actual world that provides natural laws with their specific modal force and grounds the experience of nature’s ‘recalcitrance’. Thus, the modal force of natural laws is explained by contingent non-modal properties of nature. In the second part of the paper, I deal with some alleged counterexamples to my approach: constraint laws, compositional laws, symmetry principles and conservation laws. These sorts of laws turn out to be compatible with my approach: constraint laws and compositional laws do not represent the dynamics of interaction-types by themselves, but only as constitutive parts of a complete set of equations, whereas symmetry principles and conservation laws do not represent any specific dynamics, but only impose general constraints on possible interactions. (shrink)

This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

ABSTRACTHegel's Phenomenology of Spirit provides a fascinating picture of individual minds caught up in “recognitive” relations so as to constitute a realm—“spirit”—which, while necessarily embedded in nature, is not reducible to it. In this essay I suggest a contemporary path for developing Hegel's suggestive ideas in a way that broadly conforms to the demands of his own system, such that one moves from logic to a philosophy of mind. Hence I draw on Hegel's “subjective logic”, understood in the light of (...) modern modal logic, in an attempt to model the way minds might be thought as connected by way of shared intentional contents. Here, we should not be surprised at some of the parallels that emerge between the approaches of Hegel and the modal logician Arthur Prior, as Prior had testified to the influence of his teacher, John N. Findlay, who himself had strong Hegelian leanings. In the final section, Robert Stalnaker's version of possible-world semantics is suggested as a framework within which Hegel's recognitive account of the mind might be understood. (shrink)

In a recent paper, Tuomas Tahko has argued for a hybrid view of the laws of nature, according to which some physical laws are metaphysically necessary, while others are metaphysically contingent. In this paper, we show that his criterion for distinguishing between these two kinds of laws — which crucially relies on the essences of natural kinds — is on its own unsatisfactory. We then propose an alternative way of drawing the metaphysically necessary/contingent distinction for laws of physics based (...) on the central kinematical/dynamical distinction used in physical theorising, and argue that the criterion can be used to amend Tahko’s own account, but also that it can be combined with different metaphysical views about the source of necessity. (shrink)

We can formalize judgments as logical formulas. Judgment aggregation deals with judgments of several agents, which need to be aggregated to a collective judgment. There are several logical formalizations of judgment aggregation. This paper focuses on a modal formalization which nicely expresses classical properties of judgment aggregation rules and famous results of social choice theory, like Arrow’s impossibility theorem. A natural deduction system for modal logic of judgment aggregation is presented in this paper. The system is sound and complete. (...) As an example of derivation, a formal proof of Arrow’s impossibility theorem is given. (shrink)

The concept of "nature as inner principle of change" is fundamental to Aristotle's theory of the physical world; it is the object of the present thesis to substantiate this claim by tracing the effects of this idea in Aristotle's rejection of materialism, in his doctrine of "natural places", in his definition of change and process in general, and in his notion of agency in general and the supreme Unmoved Mover in particular ). Aristotle elucidates "natural" by. contrast with (...) "artificial" - ), holding that natural substances not merely collectively - ) but as individuals each possess an 'innate impulse of change'. But this must be explained so as to allow for the fact that no change is entirely independent of external conditions - ). If, however, change were totally dependent on external conditions, its occurrence would be inexplicable - ), and the very concept of "change" would be incoherent. This latter conclusion emerges from an examination of the ancient paradox of becoming and Aristotle's treatment of it - ). The paradox is expounded -). Aristotle answers it by showing that language assumes a continuing subject of change - ). But this assumption meets the problem only if the metaphysical category of substance is also assumed, and along with it some distinction between substance-constitutive and non-substance-constitutive characteristics - ). The former mark off their subject as a thing of a certain causal type; thus change, in presupposing a substantial subject, presupposes one that makes some causal contribution to its own changes - ). But Aristotle means more than this by 'nature as inner principle'. He holds a natural substance to be the autonomous determinant of certain changes; these therefore are "natural", as manifesting the substantial nature - ). This problematic notion is taken for granted by Aristotle in the Vhys-ics - ), but can be seen to rest on his metaphysic of substance. It is a consequence of this that the natural change of a given substance be of one kind and display a unitary pattern reflecting the unity of the substance ). This view cripples scientific method as we understand it ), but Aristotle's idea of substance anyway cuts him off from the approaches successfully operated in later mechanics and chemistry - ). A summary of the ground so far covered ) introduces a further sense in which Aristotle's natures are "inner" principles of change: the subject of change is not external to the being which is the source of change - ). (shrink)

We present systems of Natural Deduction based on Strict Implication for the main normal modal logics between K and S5. In this work we consider Strict Implication as the main modal operator, and establish a natural correspondence between Strict Implication and strict subproofs.

The contract review process can be a costly and time-consuming task for lawyers and clients alike, requiring significant effort to identify and evaluate the legal implications of individual clauses. To address this challenge, we propose the use of natural language processing techniques, specifically text classification based on deontic tags, to streamline the process. Our research question is whether natural language processing techniques, specifically dense vector embeddings, can help semi-automate the contract review process and reduce time and costs for (...) legal professionals reviewing deontic modalities in contracts. In this study, we create a domain-specific dataset and train both baseline and neural network models for contract sentence classification. This approach offers a more efficient and cost-effective solution for contract review, mimicking the work of a lawyer. Our approach achieves an accuracy of 0.90, showcasing its effectiveness in identifying and evaluating individual contract sentences. (shrink)

This paper gives an outline of truthmaker semantics for natural language against the background of standard possible-worlds semantics. It develops a truthmaker semantics for attitude reports and deontic modals based on an ontology of attitudinal and modal objects and on a semantic function of clauses as predicates of such objects. It also présents new motivations for 'object-based truthmaker semantics' from intensional transitive verbs such as ‘need’, ‘look for’, ‘own’, and ‘buy’ and gives an outline of their semantics. This paper (...) is a commissioned 'target' article, with commentaries by W. Davis, B. Arsenijevic, K. Moulton, K. Liefke, M. Kaufmann, R. Matthews, P. Portner and A. Rubinstein, P. Elliott, G. Ramchand and my reply. (shrink)

The interpretation of quantum mechanics due to Everett (1957) postulates the existence of many worlds. The analysis of modality due to Lewis (1986) is supported.

The sentential calculus SC of Kalish and Montague is extended to modal sentences. Rules of inference and a derivation procedure are added. The resultant natural deduction system SMC is like a system for S4 due to Fitch, but SMC is for S5 and the restriction on necessity derivation concerns.terminations of such derivations whereas the restriction on strict subordinate proof in Fitch's system concerns the line-by-line development of such proofs. An axiomatic system AxMC for S5 founded on SC is presented (...) and it is shown that SMC and AxMC are equivalent : what ever is derivable in one system is derivable in the other. (shrink)

We address the thesis recently proposed by Andy Clark, that skill-mediated access to modality implies phenomenal feel. We agree that a skill theory of perception does indeed offer the possibility of a satisfactory account of the feel of perception, but we claim that this is not only through explanation of access to modality but also because skill actually provides access to perceptual property in general. We illustrate and substantiate our claims by reference to the recently proposed 'sensorimotor contingency' (...) theory of visual awareness. We discuss why this theory offers a distinctively attractive access-based approach to perceptual consciousness because it 'dereifies' experience and permits otherwise problematic aspects of phenomenal perceptual consciousness to be explained. We suggest our approach thus offers the prospect of 'naturalizing phenomenology'. (shrink)

In this paper, I will defend the thesis that fundamental natural laws are distinguished from accidental empirical generalizations neither by metaphysical necessity (e.g. Ellis 1999, 2001; Bird in Analysis, 65(2), 147–155, 2005, 2007) nor by contingent necessitation (Armstrong 1983). The only sort of modal force that distinguishes natural laws, I will argue, arises from the peculiar physical property of mutual independence of elementary interactions exemplifying the laws. Mutual independence of elementary interactions means that their existence and their nature (...) do not depend in any way on which other interactions presently occur. It is exactly this general physical property of elementary interactions in the actual world that provides natural laws with their specific modal force and grounds the experience of nature’s ‘recalcitrance’. Thus, the modal force of natural laws is explained by contingent non-modal properties of nature. In the second part of the paper, I deal with some alleged counterexamples to my approach: constraint laws, compositional laws, symmetry principles and conservation laws. These sorts of laws turn out to be compatible with my approach: constraint laws and compositional laws do not represent the dynamics of interaction-types by themselves, but only as constitutive parts of a complete set of equations, whereas symmetry principles and conservation laws do not represent any specific dynamics, but only impose general constraints on possible interactions. (shrink)

What grounds the truth of modal statements? And how do we get to know about what is possible or necessary? One of the most prominent anti-realist perspectives on the nature of modality, due to Peter Menzies, is the response-dependent account of modal concepts. Typically, offering a response-dependent account of a concept means defining it in terms of dispositions to elicit certain mental states from suitable agents under suitable circumstances. Menzies grounded possibility and necessity in the conceivability-response of ideal conceivers: (...) P is possible iff an ideal conceiver could conceive that P. I will draw attention to three major objections that can be identified in the modal metaphysics and epistemology literature: Chalmers’ Incoherency Objection, Sherratt’s Transparency Objection and Geirsson’s Irrelevancy Objection. Each of these objections raises a different worry regarding Menzies’ account: that the notion of an ideal conceiver is incoherent, that the account implies a controversial thesis, and that it fails to offer an explanation of our knowledge of modality. The aim of this paper is to defend the response-dependent account of modality against these three objections. (shrink)

In this paper, I will present a Fitch–style natural deduction proof theory for modal paralogics (modal logics with gaps and/or gluts for negation). Besides the standard classical subproofs, the presented proof theory also contains modal subproofs, which express what would follow from a hypothesis, in case it would be true in some arbitrary world.

The Nature of Contingency: Quantum Physics as Modal Realism. By Wilson Alastair.

_ The Nature of Contingency _: _ Quantum Physics as Modal Realism _, by AlastairWilson. Oxford: Oxford University Press, 2020. Pp. xi + 219.

We show, first, that the normalization procedure for S4 modal logic presented by Dag Prawitz in [5] does not work. We then develop a new natural deduction system for S4 classical modal logic that is logically equivalent to that of Prawitz, and we show that every derivation in this new system can be transformed into a normal derivation.

In this paper we study natural deduction for the intuitionistic and classical (normal) modal logics obtained from the combinations of the axioms T, B, 4 and 5. In this context we introduce a new multi-contextual structure, called T-sequent, that allows to design simple labelfree natural deduction systems for these logics. After proving that they are sound and complete we show that they satisfy the normalization property and consequently the subformula property in the intuitionistic case.

We show, first, that the normalization procedure for S4 modal logic presented by Dag Prawitz in [5] does not work. We then develop a new natural deduction system for S4 classical modal logic that is logically equivalent to that of Prawitz, and we show that every derivation in this new system can be transformed into a normal derivation.

The paper contains an exposition of standard ND-formalizations for modal logics. For the sake of simplicity, it is limited to propositional monomodal logics because focus is on methods not on logics. Some of the discussed approaches, however, may be easily extended to first order modal logics of different sorts or to multimodal logics . Natural Deduction is understood in the strict sense, explained below; neither Gentzen Sequent Calculus, nor Tableau Systems belong to that group. Moreover, some ND-systems with generalized (...) apparatus, like [2] or [3] are also omitted in this survey. There are four basic approaches to modality via NDformalization, which are compared and evaluated with respect to their generality: modalization of assumptions, modalization of reiteration rule, modalization of rules, application of modal assumptions. We focus on practical matters, especially on the applicability of discussed approaches, the only exception is the discussion of independent rules for necessity and possibility in the last section. (shrink)

Theories of modality which invoke possible worlds have recently been challenged by accounts that appeal to dispositional properties. A prominent strand of the accounts maintains that there is an intimate link between dispositions and possibility. The link is said to be captured by the proposition that, at first approximation, a state of affairs is possible just in case there is some actual disposition whose manifestation is the state. Focusing on the most detailed exposition and defence of this approach, put (...) forward by Barbara Vetter, I critically examine the adequacy of the view of dispositional properties on which it rests and which seems to be required by any plausible dispositionalist account of possibility. In the course of doing so, I offer arguments in favour of the causal nature of dispositions. (shrink)

This book proposes a novel position in the debate on scientific realism: Modal Empiricism. Modal empiricism is the view that the aim of science is to provide theories that correctly delimit, in a unified way, the range of experiences that are naturally possible given our position in the world. The view is associated with a pragmatic account of scientific representation and an original notion of situated modalities, together with an inductive epistemology for modalities. It purports to provide a faithful account (...) of scientific practice and of its impressive achievements, and defuses the main motivations for scientific realism. More generally, Modal Empiricism purports to be the precise articulation of a pragmatist stance towards science. This book is of interest to any philosopher involved in the debate on scientific realism, or interested in how to properly understand the content, aim and achievements of science. (shrink)

This volume contains eighteen papers, three with new postscripts, that were written over the past 35 years. Five of the papers have not been previously published. Together they provide a comprehensive account of modal reality—the realm of possible worlds—from a Humean perspective, with excursions into neighboring topics in metaphysics. Part 1 sketches an account of reality as a whole, both the mathematical and the modal, defending a form of plenitudinous realism: every consistent proposition is true of some portion of reality. (...) Part 2 presents and defends a realist theory of concrete possible worlds with an absolute ontological distinction between the actual and the merely possible. Part 3 presents and defends a Humean account of modal plenitude, formulating and endorsing principles of recombination, of plenitude of possible structures, and of plenitude of alien contents. Part 4 applies the Humean account to truthmaking, mereology, spacetime, and quantities. I argue that holding fast to Humean strictures leads to views that differ in radical ways from those put forth by contemporary metaphysicians. (shrink)

This article concerns the treatment of propositional quantification in a framework of labelled natural deduction for modal logic developed by Basin, Matthews and Viganò. We provide a detailed analysis of a basic calculus that can be used for a proof-theoretic rendering of minimal normal multimodal systems with quantification over stable domains of propositions. Furthermore, we consider variations of the basic calculus obtained via relational theories and domain theories allowing for quantification over possibly unstable domains of propositions. The main result (...) of the article is that fragments of the labelled calculi not exploiting reductio ad absurdum enjoy the Church–Rosser property and the strong normalization property; such result is obtained by combining Girard’s method of reducibility candidates and labelled languages of lambda calculus codifying the structure of modal proofs. (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 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)