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We present a series of proof systems for exact entailment (i.e., relevant truthmaker preservation from premises to conclusion) and prove soundness and completeness. Using the proof systems, we observe that exact entailment is hyperintensional not only in the sense of Cresswell, but also in the sense recently proposed by Odintsov and Wansing.
To be a truthmaker theorist is not to accept any particular metaphysical doctrine; nearly every thesis under discussion within truthmaker theory is contentious. Rather, it is to adopt a methodology, to confront metaphysical questions with the tools and resources of truthmaker theory. As a result, taking truthmaking seriously need not come with some of the more controversial commitments that have long been associated with it, such as the doctrine that all truths require truthmakers, or that entities such as facts or states of affairs exist. Those are positions that one may ultimately stake out, but they are not ones that are required from the outset. So what form should truthmaking arguments take? What kind of theory should truthmaker theorists endeavor to produce? What assumptions are truthmaker theorists allowed to hold when exploring their inquiries? This chapter presents a general framework for developing a theory of truthmakers, and highlights the various choice points that theorists must confront. It defends the view that to be is to be a truthmaker, and that “cheater catching” is an unhelpful way of understanding truthmaker theory.
The chapter begins by delineating the separate tasks of truthmaker theory and theories of truth. The two kinds of theories can be separated, and so are in principle distinct. However, history has not always treated them that way. It is proposed that one way of understanding the distinction between substantive and deflationary theories of truth is in terms of their contrasting relationship to truthmaking. It is then argued that truthmaking cannot be put to work in a theory of truth. Consequently, truthmaking motivates the rejection of substantive accounts of the property of truth. (It ultimately remains neutral regarding the substance of the concept of truth.) As a result, it is shown how correspondence theorists – traditional allies of the notion of truthmaking – are threatened by this book’s approach to truthmaking, whereas deflationists – who frequently see an opponent in the truthmaker theorist – have found a friend.
The concluding chapter summarizes the specific ontological claims defended in the latter part of the book, and demonstrates how thinking about truthmaking can help defend and articulate a variety of metaphysical views. The view on offer falls somewhere in the middle of the metaphysical spectrum: it is more thoroughly committed when it comes to properties and the past, but less so with respect to mathematics and fictional discourse. As a result, it is hoped to show that concern for truthmaking itself does not lead to across-the-board realism, and can be hospitable toward certain forms of nominalism or antirealism.
A common account of the distinction between analytic and synthetic truths is that while the former are true solely in virtue of meaning, the latter are true also in virtue of the way of the world. Quine famously disputed this characterization, and his skepticism over the analytic/synthetic distinction has cast a long shadow. Against this skepticism, it is argued that the common account comes close to the truth, and that truthmaker theory offers the resources for providing a compelling account of the distinction that preserves the basic ideas behind it, and avoids the standard criticisms (from Quine, Harman, and Boghossian) facing the distinction. The thesis is that we can formulate an analytic/synthetic distinction in terms of the distinction between truths that require no ontological accounting whatsoever versus those that do. The ontological accounting required for analytic truths is trivial – any set of books will suffice. What distinguishes the synthetic truths is that they require some form of substantive ontological accounting.
This chapter takes up the question of truthmakers for truths in and about fiction. After adopting a liberal attitude toward such truths, it surveys some of the basic positions and stances one might take regarding the alethic and metaphysical issues related to fiction. It then offers an (admittedly non-comprehensive) approach to the truthmakers for the truths related to fiction. Though the topic of truthmaking and fiction has only received minimal explicit attention, the view favoured here is most in line with Amie Thomasson’s artifactual theory that takes fictional characters to be dependently existing abstract beings. The chapter finishes by downplaying the ontological costs that accompany this view, and showing how views like Thomasson’s about fictional characters resonate with the trivialist view about mathematics.
Truth depends on reality. When something is true, its truth depends upon the world. Its truth is not some brute, inexplicable feature of reality. Truths are true in virtue of reality, and not vice versa. These ideas are the source of the philosophical enterprise known as truthmaker theory. Truthmaker theorists, accordingly, are philosophers who explore the domain of metaphysics by using the tools of truthmaker theory. Explaining what those tools are, and how they are best used, are the main goals of this monograph. The goal of this introduction is to defend the claim that truthmakers are worth caring about, and to identify some of the core motivations that drive the project. It shows how truthmaking ideas are already at work in many philosophical discussions and arguments.
A familiar view is that truthmaking is in tension with nominalism: to accept an ontology of truthmakers is to reject the austere metaphysical worldview of the nominalist. However, there is nothing inherently antinominalist in the idea of truthmaking. As has been argued, the notion of truthmaking is ontologically neutral, and so in principle compatible with any ontological worldview. Nevertheless, leading advocates of truthmaking (most notably Armstrong) have put their theories to the task of arguing against nominalism. This book is interested in exploring how strong a truthmaking-based defense the nominalist can wield. This chapter briefly presents an overview of the various theoretical options available when it comes to realism and nominalism in the context of truthmaking. In so doing, it introduces a particular distinction between hard road and easy road forms of nominalism. It aims to give the best possible defense of these different forms of nominalism, but raise its own own objections against them. Ultimately, it is suggested that truthmaker theory is best served by a realist commitment to properties, whether in terms of universals or tropes.
Realism – as its name suggests – ought to be thought of primarily as a metaphysical thesis. Realism is a commitment to reality, and reality is the domain of metaphysical study. Though realism is connected to matters both epistemological and semantic, it is suggested that realism, at its core, be construed as fundamentally a metaphysical view. Hence it is suggested that, when we contemplate the thorny question of what realism is, we employ the notion of truthmaking. Truthmaker theory, which falls squarely within the domain of metaphysics, is perfectly suited to articulate what realism is all about. It therefore enjoys an advantage over attempts to define realism in terms of truth, reference, or any semantic notion. This chapter presents a truthmaker-based conception of the debate between realism and antirealism, and showcase its virtues in helping us to understand a perennial metaphysical topic. It first shows how truthmaking is a more useful tool than truth in defining realism. Then the book’s account of realism, which is applied to the realism debates in metaethics and the philosophy of science, is defended. Along the way, a projectivist attitude toward truthmaking for quasirealists is motivated.
This chapter defends the unorthodox view that metaphysical necessitation is both necessary and sufficient for truthmaking. For x to be a truthmaker for y is for it to be metaphysically necessary that if x exists, then y is true. The necessity of necessitation is defended by considering the truthmakers for truths about truthmaking: facts of the form ‘x is a truthmaker for y’. The sufficiency of necessitation is defended by addressing the many counterexamples that been offered against it (notably those involving necessary truths), and showing how they pose no problem for truthmaking when understood as the task of ontological accounting. It is also shown how this view avoids the triviality challenge posed by Greg Restall.
This chapter distinguishes two broad conceptions of what the truthmaker project is all about. On the one hand, it might be thought of as a project of alethic explanation, that is, of offering systematic explanations as to why true truth-bearers are true (and why false truth-bearers are false). On the other hand, it might be a project of ontological accounting, of properly coordinating our beliefs and ontological inventories. The chapter adopts the latter approach, and defends it against the explanatory paradigm. This conception of truthmaking as ontological accounting then informs the conception of how we should think about the relation of truthmaking. The chapter begins by articulating the two perspectives on truthmaking, and defends the accounting approach over the explanatory conception. The accounting focus then enables an explaination of the relationship between truthmaking and ontological commitment, which is where the chapter ends.
Do all truths have truthmakers, or just a proper subset? The chapter adopts the latter answer, and uses the ontological accounting paradigm to defend it. The primary goal in this chapter is to defend nonmaximalism, that is, to defend the existence of legitimate truthmaker gaps: truths without a truthmaker. The goal is not to offer a precise statement of which truths have, and which truths lack truthmakers. Doing so goes against this book’s preferred methodological approach to truthmaking, according to which truths must be treated on a case by case basis. The main ambition, then, is to defend the tenability of truthmaker gaps in general; where exactly they are found is a topic that will surface frequently in the rest of the book, as truthmaker theorists have reasonable disagreements about it. For now, a general defense of non-maximalism is undertaken. A large part of the defense is concerned with meeting the objections that maximalists have offered against their opponents. As it is argued, those objections frequently turn on presupposing an explanatory approach to truthmaking, or on conflating truthmaker gaps with supervenience gaps: truths whose truth does not supervene on being.
This chapter demonstrates how thinking about truthmakers can bring some clarity to the ongoing debate concerning the ontological status of mathematical entities, and advances one position on the topic. It begins with what is nowadays the most familiar argument in the ontology of mathematics: the indispensability argument. Close inspection of it reveals that the notion of truthmaking is indeed playing a role, and that by thinking about indispensability and truthmaking in tandem, both ideas emerge with greater clarity. Focusing on indispensability will shed light on what the ontological stakes are in the overall debate, so the second section presents what is seen to be the most tenable ontological positions. It then offers a personal (rather deflationary) contribution to the truthmaking question about mathematics, and concludes by comparing and contrasting that view with a recent brand of mathematical trivialism.
It has long been thought that presentists face a difficulty squaring their ontological view with respectable truthmaker theory. Presentists either fall foul of the requirements of truthmaking or must commit to unfortunate ontological posits in order to satisfy them, thereby spoiling the supposed advantages of their view. Given the enormity of responses that have been generated to this objection, one could be forgiven for thinking that there must be some palatable response available to presentists. This book inclines toward the view that presentists, as compared to eternalists, have only inferior options available to them when it comes to the accounting of truths involving the past. The available replies to legitimate questions about truthmaking favor eternalism over presentism. What is offered in this chapter is a perspective on the presentism debate that applies a conception of truthmaking as ontological accounting. It poses a dilemma to presentism. Either the view fails to do justice to the task of ontological accountability, or – if it succeeds – it results in a view that is less ontologically satisfying than eternalism.
This chapter meets several of the objections that have been offered against truthmaker theory being a worthy metaphysical enterprise. It counters the charges that truthmaker theory is maximalist or nothing, and that it requires up-front contentious ontological posits. It also rebuts challenges from Timothy Williamson and Kit Fine that truthmaker theory is an inferior if not pointless endeavor. It identifies and argues against “truthmaker deflationists” who believe that the point of truthmaker theory can be accomplished without resort to any ontological investigation whatsoever. Finally, it considers challenges from those who might take the relation of grounding to be a competing and superior metaphysical notion.
The theory of truthmaking has long aroused skepticism from philosophers who believe it to be tangled up in contentious ontological commitments and unnecessary theoretical baggage. In this book, Jamin Asay shows why that suspicion is unfounded. Challenging the current orthodoxy that truthmaking's fundamental purpose is to be a tool for explaining why truths are true, Asay revives the conception of truthmaking as fundamentally an exercise in ontology: a means for coordinating one's beliefs about what is true and one's ontological commitments. He goes on to show how truthmaking connects to analyticity, truth, and realism, and how it contributes to debates over nominalism, presentism, mathematical objects, and fictional characters. His book is the most comprehensive exploration to date into what truthmaking is and how it contributes to metaphysical debates across philosophy, and will interest a wide range of readers in metaphysics and beyond.
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