I propose an account truthmaking that provides truthmakers for negative truths. The account replaces Truthmaker Necessitarianism with a "Duplication Principle", according to which a suitable entity T is a truthmaker for a proposition P just in case the existence of an appropriate counterpart of T entails the truth of P, where the counterpart relation is cashed out in terms of qualitative duplication. My account captures an intuitive notion of truthmakers as "things the way they are", validates two appealing (...) principles about entailment and containment proposed by David Armstrong, and invalidates the controversial Disjunction Thesis. (shrink)

According to the Truthmaker Principle: every truth has a truthmaker. Spelled out a bit more exactly: for every true proposition, there is some entity whose existence entails, or necessitates, the truth of the proposition. A counterpart theorist can accept the Truthmaker Principle after all without buying into unmereological composition and mysterious necessary connections. This chapter introduces the idea of truthmaking, and considers how much truthmaking can be done by things without making controversial assumptions in modal metaphysics. It (...) presents Armstrong's account of truthmaking and the states of affairs needed to play the role of truthmakers. A fortiori should not be taken to be a version of the correspondence theory of truth. The chapter presents David Lewis's critique of the Truthmaker Principle, and the ontology of states of affairs that (typically) goes with it. Lewis's claim that he can accept the Truthmaker Principle is also presented here. (shrink)

In this paper I examine two principles of orthodox truthmaker theory: truthmaker maximalism - the doctrine that every (contingent) truth has a truthmaker, and truthmaker necessitarianism - the doctrine that the existence of a truthmaker necessitates the truth of any proposition which it in fact makes true. I argue that maximalism should be rejected and that once it is we only have reason to hold a restricted form of necessitarianism.

Finding truthmakers for negative truths has been a problem in philosophy for a long time. I will present and discuss the solution to this problem offered by Bertrand Russell, Raphael Demos, D. M. Armstrong, and myself. I will argue that some negative truths do not require truthmakers and that truthmakers for the other negative truths are the entities that these negative truths imply exist. I will also argue that truthmakers for general truths of the form, only X, Y, Z, and (...) etc. are F's, are the sum of each X, Y, Z, and etc.'s being F, and hence that sometimes truthmakers do not necessitate truths. (shrink)

As concerns the explication of the intuitive notion of truthmaking, Barry Smith has an insight that deserves more attention. Basically, in his view, an object x makes a proposition true iff (i) x necessitates and (ii) is representationally closely tied with x. To be more specific, he suggests that (ii) is fulfilled only if x is among ’s ontological commitments. I appreciate his basic insight but reject his specific suggestion. I argue that we can make a more attractive proposal from (...) his basic insight if we take into consideration that the close tie can also be realized by ’s being about x. (shrink)

On the truthmaker view of ontological commitment [Heil (From an ontological point of view, 2003); Armstrong (Truth and truthmakers, 2004); Cameron (Philosophical Studies, 2008)], a theory is committed to the entities needed in the world for the theory to be made true. I argue that this view puts truthmaking to the wrong task. None of the leading accounts of truthmaking—via necessitation, supervenience, or grounding—can provide a viable measure of ontological commitment. But the grounding account does provide a needed (...) constraint on what is fundamental. So I conclude that truthmaker commitments are not a rival to quantifier commitments, but a needed complement. The quantifier commitments are what a theory says exists, while the truthmaker commitments are what a theory says is fundamental. (shrink)

The core of the truthmaker research program is that true propositions are made true by appropriate parts of the actual world. This idea seems to give realists their best shot at capturing a robust account of the dependence of truth on the world. For a part of the world to be a truthmaker for a particular it must suffice for, or necessitate, the truth of the proposition. There are two extreme and unsatisfactory truthmaker theories. At one extreme (...) any part of the world (up to and including the whole world) that suffices for a proposition is deemed to be a truthmaker for that proposition. At the other extreme there is only one truthmaker that can do the job, and that is the entire world, the whole show. Another possibility suggests itself, that a truthmaker be any minimal sufficer for a proposition. A truthmaker is minimal if it suffices but no proper part of it suffices. A minimal sufficer would be both sufficient for the truth of the proposition and, in one sense, necessary for it as well. A minimal sufficers would be commensurate with the proposition it makes true. Unfortunately not all propositions have minimal sufficers. But it does not follow that not every proposition has a commensurate sufficer. The problem, then, is to specify a coherent notion of commensurateness on which every truth has a commensurate sufficer. I argue that this problem may not be soluble. (shrink)

This paper is an argument against Truthmaker Necessitarianism—the doctrine that the existence of a truthmaker necessitates the truth of the proposition it makes true. Armstrong’s sufficiency argument for necessitarianism is examined and shown to be question begging. It is then argued in detail that truthmaking is a matter of grounding truth and that grounding is a dependency relation that neither entails nor reduces to necessitation.

This paper is an investigation in the use of truthmaker theory for exploring the relation of logic to world, and as a tool for metaphysics. A variant of truthmaker theory, which we call the simple theory, is defined and defended against objections. It is characterized formally, and its central features are derived. As part of this project, we give a formal metaphysics based on nondeterministic necessitation relations among possible entities. In what is called the fundamental theorem of (...) truthmaking, it is shown that, as long as a logic is sound and complete, its inferential structure will be isomorphic to the necessitation structure of our metaphysics. We thus arrive at a purely structural logic–world relationship which can be used for metaphysical investigations. Other products of our investigation are a sound and complete semantics for first-order logic with identity and a solution to a result of Restall which has threatened to make truthmaker theory trivial. (shrink)

A central tenet of truthmaker theory is that necessitation is necessary for truthmaking (NEC). This paper defends NEC in a novel, piecemeal way, namely by responding to a potential counterexample involving a changing past. If Carter won a race at t1 but is later disqualified at t2, then Carter no longer won at t1. A wholly past event seems to have changed in the future. The event makes ‘Carter won the race at t1’ (RACE) true between t1‐2 but (...) fails to make it true at t2. So, we have a potential counterexample to necessitation: a truthmaker of RACE fails in another context to make the same truthbearer RACE true. I argue that the best solution to this challenge is not that there are different truthbearers at t1‐2 and t2 (the semantic response), or that RACE was never true because of the future disqualification or will always be true despite the future disqualification. The best solution is to accept that the past can change: past events can change based on what happens in the future (e.g., via their effects). This paper's novel defence of necessitation will illustrate the importance of utilising explicitly ontological and commonsensical tools in accounting for truth. (shrink)

According to one tradition in realist philosophy, 'truthmaking' amounts to necessitation. That is, an object x is a truthmaker for the claim A if x exists, and the existence of x necessitates the truth of A. I argued in my paper "Truthmakers, Entailment and Necessity" [14], that if we wish to use this account of truthmaking, we ought understand the entailment connective "=>" in such a claim as a relevant entailment, in the tradition of Anderson and Belnap and (...) their co-workers [1, 2, 8, 11]. Furthermore, I proposed a number of theses about truthmaking as necessitation. The most controversial of these is the disjunction thesis: x makes a disjunction A v B true if and only if it makes one of the disjuncts (A or B) true. That paper left one important task unfinished. I did not explain how the theses about truthmaking could be true together. In this paper I give a consistency proof, by providing a model for the theses of truthmaking in my earlier paper. This result does two things. First, it shows that the theses of truthmaking are jointly consistent. Second, it provides an independently philosophically motivated formal model for relevant logics in the 'possible worlds' tradition of Routley and Meyer [8, 16, 17]. (shrink)

It is argued that, if Armstrong is correct and truthmakers necessitate the truths they make true, then the truthmakers must include facts about the meanings of the words used to express those truths, and nominalism apparently results. This conclusion, no doubt unpalatable to Armstrong, is, it is claimed, the result of his having failed to distinguish sufficiently the meanings of words and the properties of things.

It is generally thought that truthmaking has to be an internal relation because if it weren’t, then, as David Armstrong argues, “everything may be a truthmaker for any truth”. Depending on whether we take an internal relation to be one that is necessitated by the mere existence of its terms or one that supervenes on the intrinsic properties of its relata, the truthbearers involved in the truthmaking relation must either have their contents essentially or intrinsically. In this paper, I (...) examine Armstrong’s account, according to which what is made true at the fundamental level are mental state tokens. The conclusion is reached that such tokens have their contents neither essentially nor intrinsically, and so, are simply the wrong kind of entities to be made true internally. (shrink)

In this paper, I both propose and discuss a novel account of truthmaking. I begin by showing what truthmaking is not: it is not grounding and it is not correspondence. I then show what truthmaking is by offering an account that appeals both to grounding and what I call ‘deep correspondence’. After I present the account and show that it is an account that unifies, I put it to work by showing how it can overcome an objection to truthmaking, how (...) we can get truthmaking from correspondence, what it says about truthmaker necessitation, and how it can explain a connection between truthmaker maximalism and pluralism about truth. (shrink)

A truthmaker for a proposition P is exact if it contains nothing irrelevant to P. What are the exact truthmakers for necessitated propositions? This paper makes progress on this issue by showing how to extend Fine’s truthmaker semantics for intuitionistic logic to an exact truthmaker semantics for intuitionistic modal logic. The project is of interest also to the classical logician: while all distinctively classical theorems may be true, they differ from the intuitionistic ones in how they are (...) made true. This sheds new light on the status of the T and B axioms. (shrink)

Australasian Journal of Philosophy, Ahead of Print.

I will present and criticise the two theories of truthmaking David Armstrong offers us in Truth and Truthmakers (Armstrong 2004), show to what extent they are incompatible and identify troublemakers for both of them, a notorious – Factualism, the view that the world is a world of states of affairs – and a more recent one – the view that every predication is necessary. Factualism, combined with truthmaker necessitarianism – ‘truthmaking is necessitation’ – leads Armstrong to an all-embracing (...) totality state of affairs that necessitates not only everything that is the case but also everything else – that which is not the case, that which is merely possible or even impossible. All the things so dear to realists – rocks, natural properties, real persons – become mere abstractions from this ontological monster. The view that every predication is necessary does in some sense the opposite: it does away with totality states of affairs and, arguably, also with states of affairs. We have particulars and universals, partially identical and necessarily connected to everything else. Just by the existence of anything, everything is necessitated – the whole world mirrored in every monad. Faced with the choice between these two equally unappealing alternatives, I suggest returning to Armstrong’s more empiricist past: the world is not an all-inclusive One, nor necessitated by every single particular and every single universal, but a plurality of particulars and universals, interconnected by a contingent and internal relation of exemplification. While a close variant, truthmaker essentialism, can perhaps be saved, this means giving up on truthmaker necessitarianism. This, I think, what it takes to steer a clear empiricist course between the Scylla of Spinozist general factness and the Charybdis of a Leibnizian overdose of brute necessities. (shrink)

Truthmaker necessitarianism is the view that an object is a truthmaker for a truth-bearer only if it is impossible for the object to exist and the truth-bearer be false. While this thesis is widely regarded as truthmaking "orthodoxy", it is rarely explicitly defended. In this paper I offer an argument in favor of necessitarianism that raises the question of what the truthmakers are for the truths about truthmaking. The supposed advantages of non-necessitarianism dissolve once we take these truths (...) into account. (shrink)

We take as our starting point a thesis to the effect that, at least for true judgments of many varieties, there are parts of reality which make such judgments are true. We argue that two distinct components are involved in this truthmaker relation. On the one hand is the relation of necessitation, which holds between an object x and a judgment p when the existence of x entails the truth of p. On the other hand is the dual (...) notion of projection, which holds between a judgment p and an object x when the truth of p entails the existence of x. A truthmaker for a judgment p is then a necessitator for p which satisfies the further constraint that it is part of p’s projection. We offer a formal theory of the truthmaker relation thus defined, exploiting ontological tools of basic mereology and the theory of dependence. We then apply the theory to a range of problems connected with generic expressions, ellipsis, vagueness, and indexical and perceptual judgments. (shrink)

I argue that Traditional Christian Theism is inconsistent with Truthmaker Maximalism, the thesis that all truths have truthmakers. Though this original formulation requires extensive revision, the gist of the argument is as follows. Suppose for reductio Traditional Christian Theism and the sort of Truthmaker Theory that embraces Truthmaker Maximalism are both true. By Traditional Christian Theism, there is a world in which God, and only God, exists. There are no animals in such a world. Thus, it is (...) true in such a world that there are no zebras. That there are no zebras must have a truthmaker, given Truthmaker Maximalism. God is the only existing object in such a world, and so God must be the truthmaker for this truth, given that it has a truthmaker. But truthmakers necessitate the truths they make true. So, for any world, at any time at which God exists, God makes that there are no zebras true. According to Traditional Christian Theism, God exists in our world. In our world, then, it is true: there are no zebras. But there are zebras. Contradiction! Thus, the conjunction of Traditional Christian Theism with Truthmaker Necessitation and Truthmaker Maximalism is inconsistent. (shrink)

We take as our starting point a thesis to the effect that, at least for true judgments of many varieties, there are parts of reality which make such judgments are true. We argue that two distinct components are involved in this truthmaker relation. On the one hand is the relation of necessitation, which holds between an object x and a judgment p when the existence of x entails the truth of p. On the other hand is the dual (...) notion of projection, which holds between a judgment p and an object x when the truth of p entails the existence of x. A truthmaker for a judgment p is then a necessitator for p which satisfies the further constraint that it is part of p’s projection. We offer a formal theory of the truthmaker relation thus defined, exploiting ontological tools of basic mereology and the theory of dependence. We then apply the theory to a range of problems connected with generic expressions, ellipsis, vagueness, and indexical and perceptual judgments. (shrink)

In this paper, I first present an overview of Asay’s _A Theory of Truthmaking_, highlighting what I take to be some of its most attractive features, especially his re-invigoration of the ontological understanding of truthmaking and his defence of ontology-first truthmaking over explanation-first truthmaking. Then, I articulate what I take to be a puzzling potential inconsistency: (a) he appeals to considerations to do with aboutness in criticising how well ontological views account for truth while (b) ruling out aboutness from the (...) right account of truthmaking. He argues, instead, that necessitation is both necessary and sufficient for truthmaking (§3.3). I suggest that adding aboutness to one’s account in the right way is not just compatible with but important for ontology-first truthmaking. I do all this to invite Asay to clarify his position on these matters. Overall, Asay’s worldview displays the fruitfulness of an ontologically serious approach to metaphysics that puts truthmaking centre-stage. (shrink)

Mark Jago has presented a dilemma for truthmaker non-maximalism—the thesis that some but not all truths require truthmakers. The dilemma arises because some truths that do not require truthmakers by the non-maximalist’s lights (e.g., that Santa Claus does not exist) are necessitated by truths that do (e.g., that Barack Obama knows that Santa Claus does not exist). According to Jago, the non-maximalist can supply a truthmaker for such a truth only by conceding the primary motivation for the view: (...) that it allows one to avoid positing strange ‘negative’ entities without adopting a non-standard account of the necessary features of ordinary things. In this paper, I sketch out and defend two plausible non-maximalist proposals that evade Jago’s dilemma. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

In his "On the Metaphysics of Knowledge" (this volume), Sven Bernecker introduces and defends a novel account of knowledge that he calls ‘identificationism’. In fact, Bernecker’s account is a hybrid view that combines a modal tracking condition – some variation on safety and/or sensitivity – with his original identificationist condition. The reason for including a tracking condition is that some Gettier cases, like the famous fake barn case, are best accommodated in this way. In making this more familiar claim, Bernecker (...) follows epistemologists like Nozick, Sosa, or Pritchard. But he also adds the less familiar claim that there are ‘intractable’ Gettier cases that cannot be dealt with by a tracking condition alone. These intractable cases involve necessary or modally stable propositions, such as '2+2=4' or 'there is carbon on earth', which are either true in all possible worlds, or at least true in all possible worlds that are close to the actual world. In this paper, I will not directly address the epistemological adequacy of Bernecker’s identificationism. Rather, I want to focus on the substantial metaphysical commitments that it incurs, in particular on the problematic idea that our epistemic reasons identify the truthmaker of our respective belief when we know something. My conclusion will be that being a truthmaker for p is metaphysically more demanding than being an epistemic reason for p. A truthmaker for p must necessitate the truth of p, while an epistemic reason for p must merely indicate the truth of p. Thus, we should not expect that epistemic reasons identify the truthmakers of our knowledge-constituting beliefs in the way that Bernecker suggests. (shrink)

In recent work on truth and truthmaking, D. M. Armstrong has defended a version of 'truthmaker necessitarianism', the doctrine that truths necessitate truthmakers. Truthmaker necessitarianism, he contends, requires the postulation of 'totality facts', which serve as ingredients of truthmakers for general truths and negative truths, and propositions, which function as the fundamental truth bearers. I argue that neither totality facts nor propositions need figure in an account of truthmaking, and suggest that both are artifacts stemming, albeit in different (...) ways, from an ontologically shady 'linguisticizing' tendency to conflate features of descriptions and features of what is described. (shrink)

Milne [2005] argued that a sentence saying of itself that it does not have a truthmaker is true but does not have a truthmaker. López de Sa and Zardini [2006] worried that, by parity of reasoning, one should conclude that a sentence saying of itself that it is not both true and short is true but not short. Recently, Milne [2013] and Gołosz [2015] have replied to López de Sa and Zardini’s worry, arguing in different ways that the (...) worry is illfounded. In this paper, I’ll address these replies and argue that they fail to dispel López de Sa and Zardini’s worry, bringing out in the process some broader points concerning the use of self-referential sentences in arguments in philosophy of logic. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Revenant sur la question des vérifacteurs, D. Armstrong demande ici d'abord comment concilier le maximalisme et la relation de nécessitation. L'A. examine quel sens métaphysique donner à la notion d'implication, et s'il y a un sens à admettre une contingence de re. Il traite à ce niveau des possibilités pures, examine le cas des aliens chez David Lewis, puis pose la question de savoir s'il est contingent de dire qu'il y a de l'être plutôt que rien. L'exposé le conduit à (...) traiter du cas des vérifacteurs pour les vérités nécessaires, mais adopte une thèse possibiliste pour les sujets de la science démonstrative. Il se clôt par un examen du genre de nécessité transcatégorielle qui est implicite à la généralisation des vérifacteurs. The A. wants to reconcile maximalisme about truthmakers and the relation of necessitation. He investigates the metaphysical sense of the implication and whether one can admit de re contingency. He examines the pure possibilities and the case of alien properties according with David Lewis and studies whether it is contingent that there is something rather than nothing. He analyses the truthmakers of necessary truths and adopts a possibilist thesis for matters of demonstrative science. He concludes with the transcategorial necessity which is implicit in the generalization of truthmakers. (shrink)

This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal profile of rational intuition; and (...) to the types of intention, when the latter is interpreted as a modal mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. Chapter 3 provides an abstraction principle for epistemic intensions. Chapter 4 advances a two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states, by contrast to availing of modal axiom 4. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's "criterial" identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The epistemic two-dimensional truthmaker semantics developed in chapter 4 is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapter 8 examines the modal commitments of abstractionism, in particular necessitism, and epistemic modality and the epistemology of abstraction. Chapter 9 examines the modal profile of $\Omega$-logic in set theory. Chapter 10 examines the interaction between epistemic two-dimensional semantics and absolute decidability. Chapter 11 avails of modal coalgebraic automata to interpret the defining properties of indefinite extensibility, and avails of epistemic two-dimensional semantics in order to account for the interaction of the interpretational and objective modalities thereof. The hyperintensional, epistemic two-dimensional truthmaker semantics developed in chapter 4 is applied in chapters 8, 10, and 11. Chapter 12 provides a modal logic for rational intuition. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

According to presentism, everything that exists is present. According to the truthmaker principle, for every true proposition there is a truthmaker – an entity that suffices for the truth of that proposition. According to realism about the past, there are true propositions about the past. Together these claims necessitate presently existing truthmakers for truths about the past (presentist truthmakers). Cameron (2010) argues that temporal distributional properties (TDPs) can play the role of presentist truthmakers. Corkum (2014) argues that they (...) cannot. I argue against Corkum’s objections. In §2, I introduce and outline the motivation for TDPs. In §3, I show that unless TDPs are stipulated to be fundamental, as Cameron does, they can be reduced to temporal non–distributional properties, which are unable to play the role of presentist truthmakers. In §4, I argue against Corkum’s two objections to Cameron’s stipulation. Corkum’s first objection is that Cameron has no grounds on which to stipulate that TDPs are fundamental, and that the reducibility of TDPs to temporal non–distributional properties (as discussed in §3) shows that they are not. I argue that the burden of proof is not on Cameron to argue that TDPs are fundamental, but on Corkum to argue that they are not, and that to argue from the reducibility of TDPs to their non–fundamentality is to beg the question against Cameron: the reduction is only possible once their non–fundamentality is assumed. Corkum’s second objection is that if Cameron is allowed to stipulate that TDPs are fundamental in order to escape objections, then Bigelow's (1996) account is allowed to make the same move, rendering Cameron’s account redundant. I argue that the cases are asymmetric: the alternative account faces a legitimate objection whilst Cameron’s account does not. (shrink)

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

According to the Truthmaker Principle: every truth has a truthmaker. Attempts to come to grips with the Truthmaker Principle played a prominent role in Lewis’s metaphysical writings over the last fifteen years of his career. Although Lewis agreed that the truth of propositions must somehow be ontologically grounded, the Truthmaker Principle was too strong: it conflicted with two of Lewis’s most fundamental metaphysical assumptions, the uniqueness of composition and the Humean denial of necessary connections. Lewis endorsed (...) instead a weaker principle: Truth Supervenes on Being. But towards the end of his career, he changed course, noting that his critique of the Truthmaker Principle rested on essentialist assumptions that he, as a counterpart theorist, does not accept. Once freed from those assumptions, a counterpart theorist can accept the Truthmaker Principle after all without buying into unmereological composition and mysterious necessary connections. (shrink)

Creeping minimalism threatens to cloud the distinction between realist and anti-realist metaethical views. When anti-realist views equip themselves with minimalist theories of truth and other semantic notions, they are able to take on more and more of the doctrines of realism (such as the existence of moral truths, facts, and beliefs). But then they start to look suspiciously like realist views. I suggest that creeping minimalism is a problem only if moral realism is understood primarily as a semantic doctrine. I (...) argue that moral realism is better understood instead as a metaphysical doctrine. As a result, we can usefully regiment the metaethical debate into one about moral truthmakers: in virtue of what are moral judgments true? I show how the notion of truthmaking has been simmering just below the surface of the metaethical debate, and how it reveals one metaethical view (quasi-realism) to be a stronger contender than the others. (shrink)

In this paper I examine the objection to truthmaker theory, forcibly made by David Lewis and endorsed by many, that it violates the Humean denial of necessary connections between distinct existences. In Sect. 1 I present the argument that acceptance of truthmakers commits us to necessary connections. In Sect. 2 I examine Lewis’ ‘Things-qua-truthmakers’ theory which attempts to give truthmakers without such a commitment, and find it wanting. In Sects. 3–5 I discuss various formulations of the denial of necessary (...) connections and argue that each of them is either false or compatible with truthmaker theory. In Sect. 6 I show how the truthmaker theorist can resist the charge that they are committed to necessary exclusions between possible existents. I conclude that there is no good objection to truthmaker theory on the grounds that it violates the Humean dictum. (shrink)

Truthmaker theorists hold that propositions about higher-level entities (e.g. the proposition that there is a heap of sand) are often made true by lower-level entities (e.g. by facts about the configuration of fundamental particles). This generates a problem: what should we say about these higher-level entities? On the one hand, they must exist (since there are true propositions about them), on the other hand, it seems that they are completely superfluous and should be banished for reasons of ontological parsimony. (...) Some truthmaker theorists—most prominently David Armstrong—have tried to solve this puzzle by arguing that these entities are ‘an ontological free lunch’, i.e. real existents that are still ‘no addition of being’. This answer is prima facie attractive, but I argue in this paper that the standard approaches to truthmaking—modal theories and grounding theories—are unable to vindicate the doctrine of the ontological free lunch, and thus fail to solve the problem of higher-level entities. Fortunately, there is a non-standard account of truthmaking available, the reductive explanation account, which succeeds where the standard approaches fail. (shrink)

There are two main theories of ontological commitment: the quantifier view, and the truthmaker view. Since there are some truths that apparently commit us to certain entities, but actually do not, any ontological commitment theory must also contain an ontological reduction theory. Advocates of the quantifier view propose the paraphrasing method of reduction, while advocates of the truthmaker view propose the supervenience method. In this paper, after a brief discussion of the quantifier view, I propose a modified version (...) of truthmaker-based ontology, and show that a plausible account of the supervenience method can be deduced from my version. I then show that the supervenience method could explain why the paraphrasing method is successful, albeit that there are some cases in which the supervenience method works but the paraphrasing method does not, or so it seems prime facie. I also argue that according to the truthmaker view we must accept composite objects as something over and above the particles which constitute them. (shrink)

Beginning with Zagzebski (The Philosophical Quarterly 44:65–73, 1994), some philosophers have argued that there can be no solution to the Gettier counterexamples within the framework of a fallibilist theory of knowledge. If true, this would be devastating, since it is believed on good grounds that infallibilism leads to scepticism. But I argue here that these purported proofs are mistaken and that the truthmaker solution to the Gettier problems is both cogent and fallibilist in nature. To show this I develop (...) the notion of evidence of a state of affairs, a crucial concept in the truthmaker theory. I also argue that a common principle of the transmission of evidence through entailment is false, and the cause of much of the trouble. (shrink)

The paper criticizes the truthmaker principle that every truth is made true by something. If we interpret ‘something’ as quantifying into sentence position, we can interpret the principle as a harmless logical truth, but that is not what advocates of the principle intend. They interpret ‘something’ as quantifying into name position, and the principle as requiring the existence of truthmaking individuals. The paper argues that we have no reason to believe the principle on this interpretation. Moreover, the converse Barcan (...) formula is inconsistent with the existence of truthmaking individuals for contingent truths. Considerations about our ability to count possible truthmaking individuals are used to argue that we should prefer the converse Barcan formula. (shrink)

Consider a certain red rose. The proposition that the rose is red is true because the rose is red. One might say as well that the proposition that the rose is red is made true by the rose’s being red. This, it has been thought, does not commit one to a truthmaker of the proposition that the rose is red. For there is no entity that makes the proposition true. What makes it true is how the rose is, and (...) how the rose is is not an entity over and above the rose. It is against this view that I shall argue in this paper. I shall argue that a significant class of true propositions, including inessential predications like the proposition that the rose is red, are made true by entities. "No truthmaking without truthmakers" is my slogan. Although I have my view about what kinds of entities are truthmakers, I shall not argue for or presuppose that view here. All I shall argue for here is that if a proposition is made true by something, it is made true by some thing, but my argument will leave it open what kind of thing that thing is: it could be a fact or state of affairs, a trope, or any other sort of entity. (shrink)

The first way that a discussion of truth gets one going in metaphysics is via its connection to propositions. Philosophers have taken a number of views about the true nature of propositions. The early part of the twentieth century saw a strong reaction against holism, led prominently by Bertrand Russell and Ludwig Wittgenstein. This chapter considers why we should believe in Classical Truthmaker Theory in the first place, as well as a fundamental challenge to the very foundation of (...) class='Hi'>truthmaker theory: the deflationary theory of truth. The simplest, most natural understanding of Truthmaker Theory is the view that every truth has a truthmaker. This is 'Truthmaker Maximalism'. One of the fundamental motivations for truthmaker theory of any form is, as we have seen, the Correspondence Theory of Truth. Importantly, deflationists are anti‐realists only about one thing: the existence of a real property of truth. (shrink)

In this paper I undermine the Entailment Principle according to which if an entity is a truthmaker for a certain proposition and this proposition entails another, then the entity in question is a truthmaker for the latter proposition. I argue that the two most promising versions of the principle entail the popular but false Conjunction Thesis, namely that a truthmaker for a conjunction is a truthmaker for its conjuncts. One promising version of the principle understands entailment (...) as strict implication but restricts the field of application of the principle to purely contingent truths (i.e. those that contain no necessary proposition at any level of analysis). But a conjunction of purely contingent truths strictly implies its conjuncts. So this version of the principle is committed to the Conjunction Thesis. The same is true of the version of the principle where entailment is understood in the sense of systems T, R, and E of relevant logic, since in these systems conjunctions entail their conjuncts. I argue that the Conjunction Thesis is false because a truthmaker is that in virtue of what a certain proposition is true and it is false that, for example, what the proposition that Peter is a man is true in virtue of is the conjunctive fact that Peter is man and Saturn is a planet (or the facts that Peter is a man and that Saturn is a planet taken together). I also argue against other versions of the principle. (shrink)

Truthmakers, truth conditions, and analyses are closely related, but distinct in rather important ways. A failure to properly appreciate their differences has led to some confusion regarding the role that possible worlds ought to play with respect to modality. Those philosophers who initially proposed the existence of possible worlds were understood as providing an analysis of modality. More recently, many have interpreted them as providing modal truthmakers. But, possible worlds are only suited to serve as truth conditions for modal truths. (...) My goals are as follows: First, to dispel this confusion by detailing the differences between these three concepts. Second, to apply the lesson learned to the famous Humphrey objection against possible worlds. While this objection, if successful, does undermine Lewisian modal realism, it only partially undermines ersatzism, and leaves available a route by which ersatzers may avoid the objection altogether. (shrink)

Truthmaker theory has become immensely popular in recent years. So, it is not surprising that we are beginning to see it put to work in other areas of philosophy. Recently, several philosophers have proposed that truthmaker theory is the key to solving the Gettier problem. Edmund Gettier demonstrated that the traditional analysis of knowledge (as justified, true belief) was unsatisfactory. The truthmaker solution proposes that knowledge is a justified, true belief, where the source of one's justification is (...) either identical to, or else causally related to, the state of affairs which makes the believed proposition true. This amendment of the traditional analysis of knowledge purportedly escapes the problems identified by Gettier cases. In this paper, I will examine two particular recent endorsements of this solution – those from Sven Bernecker and Adrian Heathcote – and argue that truthmaker theory is not the key to solving the Gettier problem. (shrink)

I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant implication. I (...) then investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics. (shrink)

Charles Hermes argues that the Direct Argument for the incompatibility of determinism and moral responsibility fails because one of the inference rules on which it relies, Rule A, is invalid. Rule A states that if a proposition p is broadly logically necessary, then p is true and no one is, or ever has been, even partly morally responsible for the fact that p. Hermes purports to offer a counterexample to Rule A which focuses on agents’ moral responsibility for disjunctions. Hermes’s (...) objection is motivated by the idea that the logic of moral responsibility ought to be based on the logic of truthmakers rather than the logic of propositions. I show that the logic of moral responsibility does not track the logic of truthmakers and defend the validity of Rule A against Hermes’s objection. (shrink)

This chapter explains the basic framework of truthmaker or 'exact' semantics, an approach to semantics that has recently received a growing amount of interest, and discusses a number of different applications within philosophy and linguistics. The idea of truthmaking is the idea of something on the side of the world ‐ a fact, perhaps, or a state of affairs ‐ verifying, or making true, something on the side of language or thought ‐ a statement, perhaps, or a proposition. The (...) chapter focuses on the ultimate truthmakers, on what in the world ultimately makes something true, and the question of how the truthmakers make the statements of our language true is of no great concern. It also focuses on the immediate truthmakers, and the question of how they make the statements of the language true will be of greatest concern. (shrink)

A minimal truthmaker for a given proposition is the smallest portion of reality which makes this proposition true. Minimal truthmakers are frequently mentioned in the literature, but there has been no systematic account of what they are or of their importance. In this article we shall clarify the notion of a minimal truthmaker and argue that there is reason to think that at least some propositions have minimal truthmakers. We shall then argue that the notion can play a (...) useful role in truthmaker theory, by helping to explain the truth of certain propositions as precisely as possible. (shrink)

Jago argues that truthmaker non-maximalism, the view that some but not all truths require truthmakers, is vulnerable to a challenge from truths which ascribe knowledge of propositions about things which don't exist. Such truths, Jago argues, can only be dealt with using maximalist resources. I argue that Jago's point relies on the claim that the relevant truths require truthmakers, a point that non-maximalists can coherently and plausibly deny. Moreover, I argue that by making use of a safety account of (...) knowledge, non-maximalists can fully answer Jago's challenge. (shrink)