This dissertation 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 dissertation demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...) epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the apriori-aposteriori distinction; to the modal profile of rational propositional intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Examining the nature of epistemic logic itself, I develop a novel approach to conditions of self-knowledge in the setting of the modal μ-calculus, as well as novel epistemicist solutions to Curry's, the liar, and the knowability paradoxes. Solutions to previously intransigent issues concerning the first-person concept; the distinction between fundamental and derivative truths; and the unity of intention and its role in decision theory, are developed along the way. (shrink)

Quantum logic understood as a reconstruction program had real successes and genuine limitations. This paper offers a synopsis of both and suggests a way of seeing quantum logic in a larger, still thriving context.

This essay presents an alternative to contemporary substantivalist and relationist interpretations of quantum gravity hypotheses by means of an historical comparison with the ontology of space in the seventeenth century. Utilizing differences in the spatial geometry between the foundational theory and the theory derived from the foundational, in conjunction with nominalism and platonism, it will be argued that there are crucial similarities between seventeenth century and contemporary theories of space, and that these similarities reveal a host of underlying conceptual issues (...) that the substantival/relational dichotomy fails to distinguish. (shrink)

This paper examines the interaction between the philosophy and psychology of concepts and the modal characterization of the deductive concept of logical validity. The concept of logical consequence on which I focus is model-theoretic, where the concept records the property of necessary truth-preservation from the premise of an argument to its conclusion, as well as the condition that, in the class of all possible worlds in which a premise is true, a consequent formula or succedent class of formulas is true, (...) as well. Focusing on the case of logical necessity, I argue that the ability to account for the modal properties of concepts places a desideratum on the explanatory adequacy of theories of mental representation. I outline, then, five approaches to the nature of concepts pursued in philosophy and cognitive science, and argue that the above desideratum does not appear to be satisfiable by the candidate proposals. Given the limits of the foregoing, I appeal to a sixth approach -- namely, cognitivism about epistemic modality, according to which epistemic intensions are semantically imbued functions in the language of thought -- and endeavor to demonstrate how the proposal can sufficiently account for the modal profile of the concept of logical consequence. (shrink)

The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In the first (...) part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)