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 and hyperintensional cognitivism and modal and hyperintensional expressivism. I also develop 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 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 interpretational and objective modalities and the 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 in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. I provide a counter-example to epistemic closure for reductio proofs. 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)

Two related claims have lately garnered currency: dispositional essentialism—the view that some or all properties, or some or all fundamental properties, are essentially dispositional; and the claim that laws of nature (or again, many or the fundamental ones) are metaphysically necessary. I have argued elsewhere (On the metaphysical contingency of laws of nature, Oxford University Press, Oxford, 2002) that the laws of nature do not have a mind-independent metaphysical necessity, but recent developments on dispositions have given these ideas a new (...) vibrancy and made them the topic of more focused discussion. So I would like to revisit this, arguing that the new work, as interesting and important as it is to our understanding of fundamental properties, powers and dispositions, should not change our minds about metaphysical necessity. One should still think necessity is conceptually or conventionally grounded. I do not argue that laws of nature are not necessary, nor that properties do not have dispositional essences, but only that if these are the case, then, like other de re or empirical necessities, they have no metaphysical weight and are based in our rules or decisions about how to talk about the world. We may have excellent reasons to talk and think in this way—but these reasons do not include, require or provide evidence of mind-independent metaphysical necessity or essences. (shrink)

This paper challenges the soundness of the two-dimensional conceivability argument against the derivation of phenomenal truths from physical truths in light of a hyperintensional, ground-theoretic regimentation of the ontology of consciousness. The regimentation demonstrates how ontological dependencies between truths about consciousness and about physics cannot be witnessed by epistemic constraints, when the latter are recorded by the conceivability—i.e., the epistemic possibility—thereof. Generalizations and other aspects of the philosophical significance of the hyperintensional regimentation are further examined.

I develop a new argument against Russellian Monism about consciousness.

In The Matter of Consciousness (TMOC), I defend Frank Jackson’s (1982, 1986, 1995) knowledge argument, which poses a significant challenge to physicalism. I also argue that the knowledge argument leads to Russellian monism.

Materialism is the view according to which a zombie world is metaphysically impossible. Assuming that zombies are conceivable in the sense that we cannot rule out a priori that our world is a zombie world, materialists must hold that a zombie world is metaphysically impossible despite being conceivable. There are no good reasons to think that this view (type-B materialism) is false, since there are no good reasons to think that the corresponding phenomenal and physical/functional concepts cannot be distinct concepts (...) of the same thing. Nonetheless, we cannot understand how type-B materialism can be true. We cannot understand this, because we cannot in principle explain how a zombie world could be impossible despite being conceivable. (shrink)

ABSTRACTType B, or a posteriori, physicalism is the view that phenomenal-physical identity statements can be necessarily true, even though they cannot be known a priori—and that the key to understanding their status is to understand the special features of our phenomenal concepts, those concepts of our experiential states acquired through introspection. This view was once regarded as a promising response to anti-physicalist arguments that maintain that an epistemic gap between phenomenal and physical concepts entails that phenomenal and physical properties are (...) distinct. More recently, however, many physicalists have lost confidence in the view, and have proposed less promising defences of physicalism—or have become outright sceptical about its prospects. I argue here that these physicalists have underestimated the resources of Type B physicalism and are thereby retreating too quickly—or fighting battles that have already been won. (shrink)