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This thesis develops the philosophical and formal foundations for a logic of essence and ground which aim to regiment the informal locutions 'necessary for' and 'sufficient for', respectively.

Metaphysical necessity is one of contemporary philosophy's widely-used tools for theorising. Since the 1970s, it has played central roles in metaphysics, epistemology, philosophy of language, philosophy of science, and beyond. Throughout philosophy, it is used to formulate important theories and hypotheses, and features pivotally in various influential arguments. Due to its wide use, metaphysical necessity has a multifarious theoretical role. To take a few examples, it is expected to be the broadest objective necessity, license paradigm essentialist claims, and obey liberal principles of recombination. Nevertheless, there has never been an attempt to investigate whether the many postulates of this role and applications of metaphysical necessity are compatible, in the sense that they can all be satisfied by a single notion of necessity. The aim of this thesis is to provide such an investigation. The Introduction outlines the themes of the thesis, and provides an overview of each individual essay. Essay One addresses certain foundational issues by criticising a popular form of scepticism towards metaphysical necessity. Essay Two investigates whether a family of natural principles of recombination can be integrated with the thesis that metaphysical necessity is the broadest objective necessity. Similarly, Essay Three studies whether paradigm portions of essentialist discourse can also be integrated with the same thesis. Essay Four draws on material from the previous essays to answer Timothy Williamson's notorious expressive challenge to contingentist theories of modality. Finally, Essay Five provides a formal characterisation of so-called relative necessities which supports various claims and arguments made elsewhere in the thesis. Together, the essays constitute an investigation into the role and status of metaphysical necessity.

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.