In contemporary formal theory of truth, model-theoretic and non-classical approaches have been dominant. I rather pursue the so-called classical axiomatic approaches toward truth and my dissertation begins by arguing for the classical axiomatic approach and against the others. The classical axiomatic approach inevitably leads to abandonment of the nave conception of truth and revision of the basic principles of truth derived from that nave conception such as the full T-schema. In the absence of the general guiding principles based on that nave conception, we need to conduct tedious but down-to-earth eld works' of various theories of truth by examining and comparing them from various points of view in searching for satisfactory theories of truth. As such attempt, I raise two new criteria for comparison of truth theories, make a proof-theoretic study of them in connection to the foundation of mathematics.

This thesis comprises three main chapters-each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate 'true' either expresses distinct concepts or expresses distinct properties. In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic and semantics that shows how they can answer central conceptual and logical challenges for their view. In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. In Chapter 3, I propose that 'true' is polysemous. I suggest that 'true' is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes.

The historical development of Morris’ tripartite distinction between syntax, semantics and pragmatics does not follow a smooth path. Examining definitions of the terms ‘semantic’ and ‘pragmatic’ and the phenomena they have been used to describe, provides insight into alternative approaches to the semantics/pragmatics distinction. Paul Grice’s work receives particular attention and taxonomy of philosophical positions, roughly divisible into content minimalist and maximalist groups, is set up. Grice’s often neglected theory of conventional implicature is defended from objections, various tests for the presence of conventional implicature are assessed and the linguistic properties of conventional implicature defined. Once rehabilitated, the theoretical utility of conventional implicature is demonstrated via a case study of the semantic import of the gender and number of pronouns in English. The better-known theory of conversational implicature is also examined and refined. New linguistic tests for such implicatures are devised and the refined theory is applied to scalar terms. A pragmatic approach to scalar implicatures is proposed and shown to fare better than alternatives presented by Uli Sauerland, Stephen Levinson and Gennaro Chierchia. With the details of the theory conversational implicature established, the use made of Grice’s tool in the work of several philosophers is critically evaluated. Kent Bach’s minimalist approach to quantifier domain restriction is examined and criticised. Also, the linguistic evidence for semantic minimalism provided by Herman Cappelen and Ernie Lepore is found wanting. Finally, a content maximalist approach to quantifier domain restriction is proposed. The approach differs from other context maximalist theories, such as Jason Stanley’s, in relying on semantically unarticulated constituents. Stanley’s arguments against such theories are examined. Further applications of the approach are briefly surveyed.

According to orthodoxy the study of the Soritical and semantical paradoxes belongs to the domain of the philosophy of language. To solve these paradoxes we need to investigate the nature of words like `heap' and `true.' In this thesis I criticise linguistic explanations of the state of ignorance we find ourselves in when confronted with indeterminate cases and develop a classical non-linguistic theory of indeterminacy in its stead. The view places the study of vagueness and indeterminacy squarely in epistemological terms, situating it within a theory of rational propositional attitudes. The resulting view is applied to a number of problems in the philosophy of vagueness and the semantic paradoxes.

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This thesis is concerned with the debate between absolutists and relativists about generality. Absolutists about quantification contend that we can quantify over absolutely everything; relativists deny this. The introduction motivates and elucidates the dispute. More familiar, restrictionist versions of relativism, according to which the range of quantifiers is always subject to restriction, are distinguished from the view defended in this thesis, an expansionist version of relativism, according to which the range of quantifiers is always open to expansion. The remainder of the thesis is split into three parts. Part I focuses on generality. Chapter 2 is concerned with the semantics of quantifiers. Unlike the restrictionist, the expansionist need not disagree with the absolutist about the semantics of quantifier domain restriction. It is argued that the threat of a certain form of semantic pessimism, used as an objection against restrictionism, also arises, in some cases, for absolutism, but is avoided by expansionism. Chapter 3 is primarily engaged in a defensive project, responding to a number of objections in the literature: the objection that the relativist is unable to coherently state her view, the objection that absolute generality is needed in logic and philosophy, and the objection that relativism is unable to accommodate ‘kind generalisations’. To meet these objections, suitable schematic and modal resources are introduced and relativism is given a precise formulation. Part II concerns issues in the philosophy of mathematics pertinent to the absolutism/relativism debate. Chapter 4 draws on the modal and schematic resources introduced in the previous chapter to regiment and generalise the key argument for relativism based on the set-theoretic paradoxes. Chapter 5 argues that relativism permits a natural motivation for Zermelo-Fraenkel set theory. A new, bi-modal axiomatisation of the iterative conception of set is presented. It is argued that such a theory improves on both its non-modal and modal rivals. Part III aims to meet a thus far unfulfilled explanatory burden facing expansionist relativism. The final chapter draws on principles from metasemantics to offer a positive account of how universes of discourse may be expanded, and assesses the prospects for a novel argument for relativism on this basis.

This thesis focuses on the ancient reception of the Categories of Aristotle, a work which served continuously, from late antiquity into the early modern period (Frede 1987), as the student’s introduction to philosophy.  There had previously been no comprehensive study of the reception of the Categories during the age of the first philosophical commentaries (c. 80 BC to AD 220). In this study, I have collected, assigned, and analyzed the relevant fragments of commentary belonging to this period, including some that were previously undocumented or inexplicit in the source texts, and sought to establish and characterize the influence of the early commentators’ activity on the subsequent Peripatetic tradition. In particular, I trace the early evolution of criticism and defense of the text through competing accounts of its aim (skopos), which would ultimately lead Stoic and Platonic philosophers to a partial acceptance of the Categories and frame its role in the later Neo-Platonic curriculum.