Matt Leonard

In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality.

According to orthodoxy the study of vagueness belongs to the domain of the philosophy of language. On that view, to solve the paradoxes of vagueness we need to investigate the nature of words like ‘heap’ and ‘bald’. This book criticizes linguistic explanations of the state of ignorance we find ourselves in when confronted with borderline cases and develops, within the framework of classical logic, a theory of propositional vagueness in its stead. The view places the study of vagueness squarely in epistemological terms, situating it within a theory of rational propositional attitudes. Once one has accepted vague propositions, a number of questions about their role in thought become conspicuous. Can one’s total evidence be vague? What sort of support does vague evidence lend to precise matters and conversely? Can rational people agree about the precise whilst disagreeing about the vague? Is it rational to care intrinsically about vague matters? Can one’s attitudes towards vague propositions be relevant in decision making? The book develops a set of positions on these matters, and exploits them in expounding a novel theory of vagueness in which vagueness is defined in terms of its role in thought. The resulting view is applied to a number of problems in the philosophy of vagueness.