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How do we explain the truth of true propositions? Truthmaker theory is the branch of metaphysics that explores the relationships between what is true and what exists. It plays an important role in contemporary debates about the nature of metaphysics and metaphysical enquiry. In this book Jonathan Tallant argues, controversially, that we should reject truthmaker theory. In its place he argues for an 'explanationist' approach. Drawing on a deflationary theory of truth he shows that it allows us to explain the truth of true propositions and respond to recent arguments that purport to show otherwise. He augments this with a distinction between internally and externally quantified claims: externally quantified claims are claims that quantify over elements of our ontology that play an indispensable explanatory role; internally quantified claims do not. He deploys this union of deflationism and a distinction between kinds of quantification to pursue metaphysical inquiry, sketching the implications for a number of first-order debates, including those in the philosophy of time, modality and mathematics, and also shows how this explanationist model can be used to solve the key problems that afflicted truthmaker theory. Truth and the World is an important contribution to debates about truth and truthmaker theory as well as metametaphysics, the metaphysics of time and the metaphysics of mathematics, and is essential reading for students and scholars engaged in the study of these topics.