This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

Though the divide between reason-based and causal-explanatory approaches in psychiatry and psychopathology is old and deeply rooted, current trends involving multi-factorial explanatory models and evidence-based approaches to interpersonal psychotherapy, show that it has already been implicitly bridged. These trends require a philosophical reconsideration of how reasons can be causes. This paper contributes to that trajectory by arguing that Donald Davidson’s classic paradigm of 1963 is still a valid option.

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)

Neo-Fregeanism is a family of positions in the philosophy of mathematics that combines a certain type of platonism about mathematical abstracta with a certain type of logicism about the foundations and epistemology of mathematics. This paper addresses the following question: what sort of theory of reference can/should NF be committed to? The theory of reference I propose for NF comes in two parts. First, an alethic account of referential success: the fact that a term ‘a’ succeeds in referring to something (...) depends on facts about truth. Second, a deflationary account of referential specification: given that ‘a’ refers to something, the fact that ‘a’ refers to b specifically follows from the disquotational schema for reference together with the fact that b = a. In the first section of the paper I argue that NF should be committed to the first part of this theory. This a point on which there is already agreement. The bulk of the paper is therefore devoted to arguing that NF should be committed to the second part, given that it is committed to the first part. I close the paper by indicating some significant implications and a possible problem for this theory of reference. (shrink)

Oystein Linnebo's book Thin Objects is partly devoted to defending the view that some objects are “thin” in that their existence does not impose any substantive demands on the world. In this paper, I discuss the concern that the defense relies on there being entities that serve as the referents of predicates. Linnebo thus seems to assume the thinness of those entities. In the course of my discussion, I also discuss what Linnebo says about the role of criteria of identity (...) in his discussion of reference and existence. (shrink)