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Truthmaker theory

Truthmaker theory is a metaphysical asserting that for every true , there exists an in —known as a truthmaker—that necessitates its truth, grounding truth in the structure of the world rather than treating it as a or inexplicable feature. This view posits that truths depend on , with the truthmaking being one of metaphysical where the existence of the truthmaker entails the truth of the . Central to the theory is the Truthmaker Principle (TM), which states: "Necessarily, if ⟨p⟩ is true, then there is some in virtue of which it is true." The theory emerged in through the work of key figures such as Kevin Mulligan, Peter Simons, and Barry Smith, who in their 1984 paper introduced truthmakers as entities—often "moments" or dependent particulars—that account for the truth of sentences about the real world, challenging traditional assumptions about the alignment between and ontological structure. David M. Armstrong further developed the framework in his 2004 monograph Truth and Truthmakers, arguing that truth is a relational property determined by states of affairs in the world, with propositions serving as primary truth-bearers. Gonzalo Rodriguez-Pereyra has also contributed significantly, emphasizing truthmakers' role in supporting a robust by linking propositions to worldly entities like facts or tropes. Truthmaker theory addresses fundamental issues in and semantics, including the need for truthmakers for negative existentials (e.g., "There are no penguins at the "), modal truths, and general statements, often requiring commitments to additional entities such as totality states of affairs or absences. It contrasts with deflationary or minimalist theories of truth by insisting on ontological grounding, influencing debates on , universals, and the nature of facts, while raising challenges like truthmaker (every truth has a truthmaker) versus more restricted applications.

Introduction

Core Definition

Truthmaker theory is a metaphysical in that asserts every truth-bearer, such as a or , requires a corresponding in —termed a truthmaker—whose guarantees or necessitates the truth of that bearer. This view posits that truths are not merely abstract or linguistic phenomena but are ontologically grounded, meaning that for a to be true, there must be something about the world that makes it so, rather than allowing for "bare truths" that lack any existential foundation. The core intuition behind truthmaker theory emphasizes a robust about truth, where the semantic evaluation of truth is tied directly to ontological commitments, distinguishing it from theories that treat truth as merely truth-apt without requiring worldly backing. Unlike deflationary or coherence-based accounts, which may analyze truth in terms of assertibility or among beliefs, truthmaker theory demands that truth involves a substantive to existent entities, ensuring that truths reflect the structure of itself. A classic illustration of this framework is the "The cat is on the mat," whose truth is necessitated by the actual state of affairs consisting of the cat's position relative to the mat in the world; without such a existing, the could not be true. This truthmaking relation underscores the theory's commitment to explaining truth through rather than mere or .

Historical Origins

The roots of truthmaker theory trace back to , particularly 's account in the Metaphysics and Categories, where he posits that truth corresponds to states of affairs in the world, such that a is true because the relevant entities or conditions exist. For instance, suggests that the is true because the man exists, rather than the man existing because the is true—a paraphrase of his emphasis that reality grounds truth. This idea serves as a precursor to the correspondence theory of truth, laying foundational groundwork for later developments in truthmaker semantics. In the medieval period, built upon Aristotelian themes with his definition of truth as adaequatio rei et intellectus (the adequation of thing and intellect), articulated in the Summa Theologiae. Aquinas holds that truth resides primarily in the intellect but secondarily in things insofar as they conform to the divine intellect, implying that entities themselves ground the truth of judgments about them. This entity-grounding notion influenced scholastic metaphysics, bridging ancient correspondence ideas with later ontological concerns about what makes propositions true. The modern emergence of truthmaker theory occurred in early 20th-century , with advancing this in his 1918 lectures on "The Philosophy of ," where he proposed that atomic facts act as truthmakers for elementary propositions, such as the fact of an object's greenness making "X is green" true. The 1920s saw analytic debates intensify around , with figures like Wittgenstein in the Tractatus Logico-Philosophicus (1921) exploring atomic facts as truthmakers, though controversies over negative facts persisted. A post-1950s revival in metaphysics solidified truthmaker theory, with the concept revitalized in the 1984 paper "Truth-Makers" by Kevin Mulligan, Peter Simons, and Barry Smith, which formalized truthmakers as entities in virtue of which sentences are true. This culminated in David Armstrong's 1997 book A World of States of Affairs, which established it as a systematic framework using states of affairs to ground all contingent truths. Armstrong's maximalist principle—that every truth has a truthmaker—drew from earlier analytic traditions while addressing gaps in correspondence theories. This work marked the theory's contemporary formulation, influencing ongoing discussions in .

Fundamental Concepts

Truthmakers

In truthmaker theory, truthmakers are entities that ground or necessitate the truth of propositions, existing independently of , thought, or . These entities are posited to provide an ontological basis for truth, ensuring that truths correspond to something real in the world rather than being merely linguistic or conceptual constructs. The primary candidates for truthmakers include states of affairs, which are complex structures composed of particulars (such as objects) and universals (such as properties or relations) that obtain in the world. For instance, the truth of the proposition " is " is grounded by the state of affairs consisting of and the particularized quality of instantiated in him. Alternative proposals include tropes, which are individual instances of properties or relations (e.g., this particular redness of an apple), or even concrete particulars themselves in simpler cases. David Armstrong, a key proponent, emphasizes that truthmakers must be non-propositional entities to avoid circularity, such as the particularized relation in a proposition like "aRb," where the state of affairs of a standing in relation R to b serves as the truthmaker without involving any proposition-like structure. Truthmakers are generally divided into positive and negative types, though the latter remain a point of contention. Positive truthmakers account for or truths, such as the of a specific grounding the truth of "there is a in the room," where the itself or the state of affairs involving it suffices. Negative truthmakers, intended to ground truths of absence like "there is no in the room," are debated; while some theorists accept absences or non-existents as truthmakers, others reject this on grounds of ontological parsimony, proposing instead that positive entities—such as totality facts encompassing all that exists—indirectly necessitate such negatives. George Molnar argued that negative truths require positive truthmakers, like the relevant positive features of the world that exclude the absent entity, to maintain consistency with the theory's realist commitments. By demanding that every truth be backed by an existing , truthmakers impose ontological commitments, enforcing a form of metaphysical where the truth of a claim requires the actual of its grounding , rather than mere possibility or . This approach ties truth directly to the furniture of the , compelling philosophers to inventory what must exist to support our assertions about it.

Truthmaking Relation

The truthmaking relation is a necessitating link between a truth and its truthmaker, wherein the existence of the truthmaker entails the truth of the . This relation posits that for every true T, there exists an TM (the truthmaker) such that the existence of TM guarantees the truth of T, often formalized as TM \models T, where \models denotes necessitation or strict entailment. In this framework, truthmakers serve as the ontological ground for truths, ensuring that truth depends on reality rather than vice versa. Philosophers have characterized the truthmaking relation through various axiomatic approaches, emphasizing its role in linking worldly entities to representational content. For instance, one influential schema requires that truthmakers entail the truths they support, while also incorporating principles like factivity (truthmakers exist only for true propositions) to avoid overgeneration. This formalization underscores the relation's : the truthmaker grounds or necessitates the truth, but the truth does not similarly ground the truthmaker, preserving the independence of the ontological from the propositional. Debates surrounding the of the truthmaking center on whether it involves strict logical entailment or a broader form of explanatory grounding. Proponents of strict entailment argue that the truthmaker's existence logically implies the truth, avoiding weaker dependencies that might dilute . favor grounding as a non-causal, metaphysical dependence, where the truthmaker explains the truth without requiring full logical , thus accommodating variations. This distinction highlights the 's non-symmetry, as the direction of dependence flows unilaterally from truthmaker to truth, preventing circularity in explanation. A representative example illustrates the relation's dynamics: the state of affairs consisting in the sun's rising serves as a truthmaker for the proposition "The sun is rising," necessitating its truth through direct worldly instantiation, yet the proposition does not necessitate the state of affairs in return. This asymmetry ensures that the truthmaking relation anchors truths in concrete existence without implying reciprocal dependence.

Core Principles

Maximalism

Maximalism in truthmaker theory posits that every truth, whether contingent or necessary, requires a corresponding —an whose necessitates the truth of the in question. This principle rejects any exceptions, ensuring that no truth lacks ontological grounding and thereby avoiding the notion of truthmaker gaps where certain truths might float free of . The rationale for lies in its commitment to a comprehensive metaphysical foundation for truth, anchoring all propositions in mind-independent entities to uphold a robust about truth. By demanding truthmakers for every truth, maximalism prevents the proliferation of ungrounded assertions and aligns with the broader truthmaker that what is true must be made true by something in the world. This approach contrasts with more permissive views by insisting on universal applicability, thereby providing a testable for metaphysical theories. David Armstrong, a primary advocate of , extends its scope to all categories of truths, including negative existentials and statements, which he argues demand positive entities as truthmakers rather than mere absences or possibilities. For negative truths, such as "there are no ," Armstrong proposes totality states of affairs—facts about what exists in the world—that collectively make such propositions true without invoking negative facts. Similarly, for truths, he relies on combinatorial structures involving universals and to ground possibilities and necessities. Armstrong's framework thus demands that truthmakers be "totally necessitating," entailing the truth in question. A key challenge for arises in handling necessary truths, such as mathematical propositions like "2 + 2 = 4," which appear true in all possible worlds and thus risk overgeneration if everyday entities serve as their truthmakers. Armstrong addresses this by positing abstract entities, such as universals or perhaps the overall structure of , as potential truthmakers that necessitate these truths without . However, this invites over the ontological status of such abstracta and whether they adequately ground truths independent of empirical .

Truthmaker Gaps

Truthmaker gaps refer to truths that lack corresponding truthmakers, posing a direct challenge to the principle of in truthmaker theory, which holds that every truth must be grounded by some entity. These gaps arise particularly for certain types of propositions where no obvious existent in the world can account for their truth, leading proponents of non-maximalism or optimalism to argue that not all truths require ontological grounding. A primary argument for allowing truthmaker gaps centers on negative existentials, such as the proposition "No unicorns exist." Unlike positive existentials like "Unicorns exist," which could be made true by the presence of unicorns, negative existentials appear to be true due to the absence of such entities, yet absences themselves are not typically considered existent truthmakers. This creates an apparent gap, as positing negative facts or totality states of affairs to ground these truths risks ontological extravagance, prompting some theorists to accept the truths as ungrounded. Modal truths provide another key example, including statements of possibility like "It is possible that exist" or necessity like "All bachelors are unmarried." For modal truths, identifying truthmakers is complicated by their dependence on non-actual scenarios or necessities, which may not correspond to entities in the actual world. Advocates for gaps argue that requiring truthmakers here would overcommit to possibilia or , whereas accepting gaps preserves a leaner metaphysics without necessitating such posits. Gonzalo Rodriguez-Pereyra endorses a moderate form of truthmaker maximalism, applying the principle primarily to synthetic truths while allowing gaps for certain logical or analytic truths, such as tautologies or necessary identities, which he views as not grounded in contingent reality. In this approach, logical truths like "All bachelors are unmarried" do not demand worldly entities as truthmakers, as their truth derives from conceptual or formal relations rather than existential dependence. If truthmaker gaps proliferate beyond isolated cases, the theory risks undermining its explanatory power, potentially leading to a retreat toward deflationary accounts of truth, where truth is not substantially grounded in ontology but treated as a minimal semantic property without requiring worldly makers for all propositions. This implication highlights the tension between maximalist ambitions and the intuitive resistance to inflating ontology for problematic truths.

Theoretical Relations

Correspondence Theory

Truthmaker theory aligns closely with the correspondence theory of truth, offering a metaphysical elaboration by positing truthmakers as the specific entities in that serve as the "correspondents" for true s. In this view, a is true it corresponds to a truthmaker that necessitates its truth, thereby grounding the semantic relation in . David Armstrong articulates this connection by arguing that the correspondence theory inherently requires truthmakers, stating that "the Correspondence theory tells us that, since truths require a truthmaker, there is something in the world that corresponds to a true . The and the truthmaker are the same thing." This integration transforms the abstract notion of correspondence into a concrete demand for existent entities that entail truth. A key distinction lies in their scopes: the correspondence theory operates primarily at a semantic level, emphasizing a bipartite matching between or thought and the world without detailing the ontological structure of that world. Truthmaker theory, by contrast, introduces an , requiring that for every truth, there exists something—a truthmaker—that makes it the case, often through an asymmetrical "in virtue of" relation where the truthmaker entails the but not . This addition addresses potential in correspondence by enforcing a of : no truth can "float free" without an ontological anchor. Armstrong emphasizes this ontological depth as essential for a robust , distinguishing truthmaker theory as a more precise realization of correspondence rather than a mere . Historically, Armstrong positioned truthmaker theory as a means to substantiate theory, particularly for propositions that describe simple states of affairs, ensuring that truth reflects the structure of rather than idealist or nominalist alternatives. He drew on earlier realist traditions to argue that truthmakers realize correspondence by providing the worldly entities that truths track. For example, the "Snow is white" corresponds to through the state of affairs consisting of particular snow instantiating the of whiteness, which acts as its truthmaker and thereby makes the true. This example illustrates how truthmakers fulfill the correspondent role, preventing truth from being an empty relation.

Coherence and Deflationary Theories

Truthmaker theory contrasts sharply with coherence theories of truth, which hold that a proposition's truth consists in its coherence or mutual support within a comprehensive system of beliefs or propositions, rather than in any direct relation to independent entities in the world. This holistic view, associated with idealists like F. H. Bradley and H. H. Joachim, treats truth as an internal property of a belief network, potentially allowing multiple coherent systems without regard for external reality. In opposition, truthmaker theory demands ontological grounding through existent entities that necessitate the truth of propositions, rejecting such internalism as insufficient for explaining why truths track the world independently of human cognition. A key critique of coherence theories from the truthmaker perspective is that they permit truths without worldly anchoring, as a fully coherent but mistaken belief set—such as an idealized —could qualify as true without corresponding to actual states of affairs. Truthmaker advocates, emphasizing , argue this undermines the intuitive link between truth and , insisting instead on independent truthmakers like facts or objects to ensure truths are not merely epistemically consistent but metaphysically necessitated. Unlike the theory, which shares truthmaker theory's realist commitments but focuses on a general matching , coherence theories prioritize systemic harmony over any such worldly . Similarly, truthmaker theory opposes deflationary theories of truth, which treat truth as a minimal or disquotational device without substantive metaphysical content, encapsulated in the schema "'P' is true P." Deflationists like Paul Horwich view truth as merely a tool for semantic generalization, imposing no ontological requirements on what makes propositions true and avoiding commitments to robust entities or properties. Truthmaker theory counters this minimalism by requiring that every truth be grounded in existent truthmakers, thereby imposing significant ontological demands that deflationism evades. Without truthmakers, deflationary approaches allow truths to obtain without explanatory worldly grounding, as the disquotational schema explains truth's application but not its source—for instance, it states "'Snow is white' is true if and only if snow is white," yet fails to identify what or necessitates snow's whiteness. This lack of depth renders deflationism incompatible with truthmaker theory's substantive view of truth as ontologically dependent on , potentially leading to anemic accounts of how truths connect to the world. Critics like Fraser MacBride argue that aligning truthmaking with deflationism undermines the principle's intuitive force, as instances like "cats purr" lose their grounding without a robust truth property.

Metaphysical Applications

Presentism

Presentism is the metaphysical view that only present entities exist, with past and future objects and events having no ontological status whatsoever. This position, defended by philosophers such as Arthur Prior and more recently by Dean Zimmerman, contrasts with by denying the reality of non-present times. Truthmaker theory poses a significant challenge to presentism, particularly regarding truths about the past. For instance, the proposition " crossed the in 49 BCE" is true, yet under presentism, Caesar and the associated events no longer exist to serve as truthmakers. This issue arises because truthmaker maximalism—the principle that every truth requires an existent entity to ground it—demands that past truths be ontologically supported by something currently existing, which presentism appears unable to provide. David Armstrong, a key proponent of truthmaker theory, explicitly rejects presentism on these grounds, arguing that it fails to account for the truthmaking of historical facts without invoking implausible or ad hoc entities. In his view, the absence of past entities undermines the realist commitment central to truthmaking, leading him to favor an eternalist ontology where all times are equally real and available as truthmakers. To address this challenge, some philosophers propose alternatives that modify or abandon strict presentism. The "moving spotlight" theory, a tensed variant, posits that while all times exist, only the present is illuminated or privileged, potentially allowing past entities to ground truths without full presentist elimination. , by contrast, fully embraces the existence of past and future, resolving the truthmaker gap by treating temporal locations as on par with spatial ones. These approaches aim to preserve a dynamic sense of time while accommodating truthmaker requirements. The implications for presentists are profound: to uphold their view, they must either posit abstract entities—such as propositions, tropes, or distributional properties—as truthmakers for past truths, or relax the strict truthmaking demand for tensed propositions by allowing truthmaker gaps. Such concessions, however, risk diluting the intuitive appeal of presentism or conflicting with the austerity of its .

Actualism

Actualism is a metaphysical position asserting that only actual entities exist and that there are no non-actual possibilia, such that everything that exists does so in the actual world. This view contrasts with possibilism, which posits the existence of merely possible entities beyond the actual. Within truthmaker theory, actualism faces the challenge of accounting for the truthmakers of modal truths, such as the proposition "There could be talking donkeys," which appears to require grounding in non-actual entities like possible talking donkeys. Without possibilia, actualists must identify existing actual entities that necessitate such modal claims, avoiding truthmaker gaps for modal statements. One prominent solution is David Armstrong's combinatorial actualism, which posits that truthmakers for possibilities are recombinations of actual constituents, such as the actual properties of donkeys and the capacity for speech in other animals, allowing for the metaphysical possibility of their conjunction without invoking unreal entities. Armstrong argues that these actual parts—universals and —serve as the basis for all possible worlds as mereological fusions or fictions derived from real combinations, ensuring a sparse where arises from the actual alone. Possibilists, such as , critique this approach for failing to provide non-circular truth conditions for complex modal truths, arguing that without concrete possibilia or a robust definition of truth-in-recombined-worlds, cannot adequately ground macro-level possibilities like talking donkeys using only sparse actual universals. contends that the reliance on fictional recombinations undermines the reductive aims of combinatorialism, as it lacks a primitive analysis of the truthmaking relation for non-actual scenarios. The implications of actualist truthmaker commitments restrict to permutations of actual entities, promoting an that avoids ontological excess by aligning possible truths with the sparse structure of reality, though at the cost of explanatory power for alien possibilities.

Criticisms and Developments

Objections to

One major objection to truthmaker is that it leads to ontological overcommitment, or "bloat," by requiring the positing of an excessive number of entities to serve as truthmakers for every true . For instance, to negative existential truths such as "There are no ," must introduce special entities like negative facts or absences, which critics argue inflate the ontology unnecessarily and violate principles of . This concern is exacerbated by the need for truthmakers for disjunctive or conjunctive truths, potentially demanding a vast array of additional states of affairs or totality facts that mirror the logical structure of all truths, thereby complicating metaphysics without clear explanatory gain. A related problem arises with vague truths, where appears to force the acceptance of vague as truthmakers. Consider a borderline case like "John is bald," which is true but vaguely so; its truthmaker cannot be a precise (as that would render the truth precise), nor can it lack a truthmaker without violating . Thus, maximalists must endorse vague truthmakers, yet this conflicts with views that fundamental is precise and determinate, leading to metaphysical awkwardness or the need for a multi-level with vagueness emerging only at higher levels. Critics contend this undermines the theory's appeal as a grounding principle, as it either imports vagueness into the basic furniture of the world or fails to account for indeterminate truths without adjustments. The challenge of necessary truths, such as logical statements like "2 + 2 = 4," poses another difficulty for . These truths hold in every , so no contingent entity can serve as their exclusive truthmaker without necessitating all other necessary truths as well, which seems arbitrary or overly broad. Some philosophers, emphasizing ontological sparseness, argue that the world contains only a limited repertoire of fundamental entities and properties, insufficient to ground the full range of logical and mathematical truths without invoking abstracta like propositions or —commitments that many sparse ontologists, including van Inwagen, reject in favor of a minimal inventory that does not mirror every truth. Van Inwagen's advocacy for such sparseness implies that overreaches by demanding truthmakers where none are ontologically required, as necessary truths supervene on alone rather than worldly entities. Finally, truthmaker maximalism suffers from empirical underdetermination, as there is no direct observational or experimental for the existence of truthmakers beyond philosophical from the nature of truth and . Proponents infer truthmakers from the that truths must be grounded, but alternative theories (such as deflationary accounts of truth) explain truth equally well without positing such entities, leaving the commitment empirically untestable and thus underdetermined by available data. This lack of evidential support renders maximalism vulnerable to charges of being a speculative metaphysical addition rather than a necessary explanatory framework. One common response to these objections involves allowing truthmaker gaps for certain classes of truths, such as necessary or vague ones, thereby moderating maximalism without abandoning the core principle.

Recent Extensions

In the early 2000s, truthmaker theory began integrating with metaphysical grounding, positing truthmaking as a specific instance of the broader grounding relation, whereby truths are grounded in existent entities that necessitate their truth. Kit Fine's seminal work argued that metaphysical reality consists of what is factual, with grounding providing the explanatory link between being and truth, allowing truthmakers to be understood as grounders of propositions without requiring additional ontological commitments beyond facts. This integration expanded truthmaker theory by embedding it within a more general framework of metaphysical dependence, influencing subsequent debates on how grounds truth without invoking superfluous states of affairs. Non-factualist variants emerged as alternatives to traditional truthmaker approaches reliant on states of affairs, with D. H. Mellor's success semantics offering a key adaptation. Mellor proposed that truth arises from the successful satisfaction of a proposition's conditions through and predication, rather than to abstract facts, thereby preserving the intuitive demand for ontological support while avoiding commitment to controversial entities like states of affairs. This approach reframes truthmakers in terms of practical success in semantic relations, applying particularly to causal and temporal truths, and has been defended as compatible with a realist metaphysics that prioritizes events and objects over reified facts. Applications of truthmaker theory to fictional truths have gained traction in post-2010 debates, addressing how statements about fictional entities can be true without corresponding real-world existents. One strategy employs pretense theories, where fictional truths are made true by acts of imaginative pretense that ground assertions within a fictional context, such as Walton's framework adapted to truthmaking. Alternatively, modal operators have been invoked to treat fictional truths as necessarily true relative to possible worlds or abstract story structures, ensuring ontological parsimony by linking truth to modal necessities rather than nonexistent objects. These developments resolve paradoxes in fiction by distinguishing levels of , with truthmakers drawn from the real-world origins of stories or interpretive conventions. Key anthologies and monographs from the mid-2000s consolidated these extensions, notably Beebee and Dodd's edited volume, which assembled essays exploring truthmakers' implications for , causation, and , fostering interdisciplinary dialogue. Complementing this, Stephen Mumford's trope-based approach posited particularized properties () as minimal truthmakers, arguing that they provide exact ontological support for truths without the inflation of universals or complex facts, particularly effective for handling negative and dispositional truths. This trope ontology aligns truthmaking with a , emphasizing concrete instances over abstract structures. In the 2020s, truthmaker theory has increasingly incorporated into formal semantics, developing truthmaker semantics as a hyperintensional alternative to possible-worlds models. This framework, advanced by and others, defines truth in terms of exact truthmakers—entities that verify propositions without excess content—enabling precise handling of , , and conditionals through exact verification and falsification conditions. Applications extend to semantics, where truthmaker structures model entailment and compositionality more finely than truth-conditional approaches, including recent work on modals and the nature of truthmaker states as of 2024-2025.

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