This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. 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 Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Dominance hierarchies are ubiquitous in the societies of human and non-human animals. Evidence from comparative, developmental, and cognitive psychological investigations is presented that show how social dominance hierarchies shaped the evolution of the human mind, and hence, human social institutions. It is argued that the pressures that arise from living in hierarchical social groups laid a foundation of fundamental concepts and cognitive strategies that are crucial to surviving in social dominance hierarchies. These include recognizing and reasoning transitively about dominance relations, (...) fast-track learning of social norms (permissions, prohibitions, and obligations), detecting violations of social norms (cheating), monitoring reciprocal obligations, and reading the intentions of others. (shrink)

My first paper on the Is/Ought issue. The young Arthur Prior endorsed the Autonomy of Ethics, in the form of Hume’s No-Ought-From-Is (NOFI) but the later Prior developed a seemingly devastating counter-argument. I defend Prior's earlier logical thesis (albeit in a modified form) against his later self. However it is important to distinguish between three versions of the Autonomy of Ethics: Ontological, Semantic and Ontological. Ontological Autonomy is the thesis that moral judgments, to be true, must answer to a realm (...) of sui generis non-natural PROPERTIES. Semantic autonomy insists on a realm of sui generis non-natural PREDICATES which do not mean the same as any natural counterparts. Logical Autonomy maintains that moral conclusions cannot be derived from non-moral premises.-moral premises with the aid of logic alone. Logical Autonomy does not entail Semantic Autonomy and Semantic Autonomy does not entail Ontological Autonomy. But, given some plausible assumptions Ontological Autonomy entails Semantic Autonomy and given the conservativeness of logic – the idea that in a valid argument you don’t get out what you haven’t put in – Semantic Autonomy entails Logical Autonomy. So if Logical Autonomy is false – as Prior appears to prove – then Semantic and Ontological Autonomy would appear to be false too! I develop a version of Logical Autonomy (or NOFI) and vindicate it against Prior’s counterexamples, which are also counterexamples to the conservativeness of logic as traditionally conceived. The key concept here is an idea derived in part from Quine - that of INFERENCE-RELATIVE VACUITY. I prove that you cannot derive conclusions in which the moral terms appear non-vacuously from premises from which they are absent. But this is because you cannot derive conclusions in which ANY (non-logical) terms appear non-vacuously from premises from which they are absent Thus NOFI or Logical Autonomy comes out as an instance of the conservativeness of logic. This means that the reverse entailment that I have suggested turns out to be a mistake. The falsehood of Logical Autonomy would not entail either the falsehood Semantic Autonomy or the falsehood of Ontological Autonomy, since Semantic Autonomy only entails Logical Autonomy with the aid of the conservativeness of logic of which Logical Autonomy is simply an instance. Thus NOFI or Logical Autonomy is vindicated, but it turns out to be a less world-shattering thesis than some have supposed. It provides no support for either non-cognitivism or non-naturalism. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. 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 Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

In this paper, I apply the "conceptual role semantics" approach that I have proposed elsewhere (according to which the meaning of normative terms is given by their role in practical reasoning or deliberation) to the meaning of the term 'ought'. I argue that this approach can do three things: It can give an adequate explanation of the special connection that normative judgments have to practical reasoning and motivation for action. It can give an adequate account of why the central principles (...) of deontic logic are correct. It can give an explanation of the precise ways in which the term 'ought' is systematically context-sensitive, so that the term expresses different (but systematically related) concepts in different contexts. (shrink)

Research from ethology and evolutionary biology indicates the following about the evolution of reasoning capacity. First, solving problems of social competition and cooperation have direct impact on survival rates and reproductive success. Second, the social structure that evolved from this pressure is the dominance hierarchy. Third, primates that live in large groups with complex dominance hierarchies also show greater neocortical development, and concomitantly greater cognitive capacity. These facts suggest that the necessity of reasoning effectively about dominance hierarchies left an indelible (...) mark on primate reasoning architectures, including that of humans. In order to survive in a dominance hierarchy, an individual must be capable of (a) making rank discriminations, (b) recognizing what is forbidden and what is permitted based one's rank, and (c) deciding whether to engage in or refriin from activities that will allow one to move up in rank. The first problem is closely tied to the capacity for transitive reasoning, while the second and third are intimately related to the capacity for deontic reasoning. I argue that the human capacity for these types of reasoning have evolutionary roots that reach deeper into our ancestral past than the emergence of the hominid line, and the operation of these evolutionarily primitive reasoning systems can be seen in the development of human reasoning and domain-specific effects in adult reasoning. (shrink)

This paper critically examines a formal argument against deducing ‘ought’-judgments from ‘is’-judgments, an argument suggested by a literal reading of a famous passage in Hume'sTreatise of Human Nature. According to this argument, judgments of the two kinds have different logical structures (i.e., their subjects are differently related to their predicates) and this difference disallows cross-categorical deductive inferences. I draw on Fregean accounts of the ‘is’- copula and on syntactical interpretations of ‘ought’-judgments that have become standard in deontic logic to argue (...) that twentieth century work in philosophical grammar and logic casts doubt on all three of the argument's premises. (shrink)

In this paper I argue that deontic modals are hyperintensional, i.e. logically equivalent contents cannot be substituted in their scope. I give two arguments, one deductive and the other abductive. First, I show that the contrary thesis leads to falsity; second, I argue that a hyperintensional theory of deontic modals fares better than its rivals in terms of elegance, theoretical simplicity and explanatory power. I then propose a philosophical analysis of this thesis and outline some consequences. In Section 1 I (...) introduce and define deontic modality and hyperintensionality. In Section 2 I give a reductio for the hyperintensionality of deontic modals. If the argument is sound, a useful corollary is that deontic modals are also non-intensional, and therefore possible-world semantics accounts are illfitted for them. I then show how the main result can be strengthened or weakened by varying the definition of logical validity. In Section 3 I give an abductive argument for the hyperintensionality of deontic modals, arguing that with a single move we are able to solve many paradoxes and puzzles traditionally troubling deontic logic. I present a version of a hyperintensional deontic logic in an appendix, which I prove is sound and complete with respect to a version of truthmaker semantics. (shrink)

This paper presents an Anscombian alternative to the traditional deontic conception of ought. According to the Anscombian conception of ought developed here, ought is general as opposed to ‘peculiarly moral’, norm-referring instead of law- or obligation-referring, and ‘heroic’ in the sense that it does not presuppose that individuals can do or be as they ought. Its connection to matters of fact can, moreover, be clearly stated. In the first part of the paper, I describe some significant logical characteristics of this (...) conception, and argue that it provides a more suitable account of the oughts of ethics as compared to the deontic conception. One particular strength of the Anscombian conception of ought is that it does justice to the possibility of tragedy in human life, where tragedy is understood as the possibility that a thoroughly well-intentioned individual might sometimes ensure her own moral imperfection, precisely by doing what is morally right or best at every step along the way. To motivate this feature of the view, I sketch a corresponding picture of responsibility for actions in terms of ownership of one’s deeds. This conception of responsibility allows that what one ought to do is not always constrained by what one can do, while saving the intuitions about fairness and the practical scope of moral norms that principally motivate ‘ought implies can’. To illustrate and motivate the overall account I discuss a number of cases, including the character Winston from George Orwell’s 1984. (shrink)

Dominance hierarchies are ubiquitous in the societies of human and non-human animals. Evidence from comparative, developmental, and cognitive psychological investigations is presented that show how social dominance hierarchies shaped the evolution of the human mind, and hence, human social institutions. It is argued that the pressures that arise from living in hierarchical social groups laid a foundation of fundamental concepts and cognitive strategies that are crucial to surviving in social dominance hierarchies. These include recognizing and reasoning transitively about dominance relations, (...) fast-track learning of social norms (permissions, prohibitions, and obligations), detecting violations of social norms (cheating), monitoring reciprocal obligations, and reading the intentions of others. (shrink)

Philosophers like G.H. von Wright and D. Makinson have pointed to serious challenges regarding the foundations of deontic logic. In this paper, I suggest that to deal successfully with these challenges a reconsideration of the research program of the discipline is useful. Some problems that have troubled this particular field of logical study for decades may disappear or appear more tractable if we view them from the perspective of a language game introduced by D. Lewis involving three characters: the Master, (...) the Slave and the Kibitzer. The adoption of this perspective opens a natural approach to a new layout of the domain of deontic studies. I propose dividing deontic logic into six sub-areas which are distinguished by their focus on the different idioms typical of the individual players, by conceiving the language game as either being static or as dynamic and by the aims of the logical inquiry. What kind of insights the proposed perspective provides is illustrated by an analysis of the so-called Ross paradox—a problem that has troubled deontic logic since its origins and, though it was many times pronounced solved, still keeps coming back ‘alive and kicking’. (shrink)

This article strives to provide an original conceptual frame- work that should open a way to clarification of general philosophical debates on rules and norms. It makes a clear distinction between rules understood as social facts grounded on specific relation- ships between social subjects and rules understood as linguistic entities. Norms are taken as specific social rules and divided into three different types: social constitutive norms, particular constitutive norms, and institutional norms. Attention is also devoted to relation between normality and (...) normativity, to the role of permissions and to specific features of technological ‘rules’. In the last part of the article the outlined conceptual apparatus is employed for analysis of two passages from Wittgenstein’s Investigations. (shrink)

In an earlier paper by the author, Åqvist , I presented an approach to the logic of historical necessity, or inevitability, in the sense of a “two-dimensional” combination of tense and modal logic for worlds, or histories, with the same time order, known as T × W logic. Distinctive features of that approach were, apart from its two-dimensionality, its being based on discrete and finite time, and its use of so-called systematic frame constants in order to enable us to indicate (...) longitudes and latitudes of any points in the co-ordinate systems under consideration. This led us to study and axiomatize an infinite hierarchy HTWxy of two-dimensional modal tense logics with the characteristic operators for historical necessity and possibility added to the original basic vocabulary. The main purpose of the present paper is then twofold: to extend the logics HTWxy to the interesting branch of philosophical logic constituted by deontic logic as combined with tense logic; and to deal with a curious puzzle known as the so-called epistemic obligation paradox – a well known stumbling-block in this area of research in philosophical logic. We argue for a solution to both these problems, which appeals to a new infinite hierarchy DHTWxym of extensions of the HTWxy in the sense of logics combining dyadic deontic modalities with temporal ones such as those for historical necessity and other two-dimensional modalities. (shrink)

A new deontic logic, Action Type Deontic Logic, is presented. To motivate this logic, a number of benchmark cases are shown, representing inferences a deontic logic should validate. Some of the benchmark cases are singled out for further comments and some formal approaches to deontic reasoning are evaluated with respect to the benchmark cases. After that follows an informal introduction to the ideas behind the formal semantics, focussing on the distinction between action types and action tokens. Then the syntax and (...) semantics of Action Type Deontic Logic is presented and it is shown to meet the benchmarks. Finally, possibilities for further research are indicated. In the appendix, decidability of the satisfiability of formulas is proved via a technique known from monadic First Order Logic. (shrink)