• Alessandro Cecconi1,
• Fabrice Correia1 &
• Martin Glazier2

What is meaning? What is it for a statement to have a meaning? Given a particular statement, what meaning does it have? How does the meaning of a statement depend upon the meaning of its parts? These are among the central questions of semantics.

According to the truthmaker approach to semantics, these questions are to be answered in terms of the relation of exact verification. As a first approximation, the meaning or semantic content of a statement is taken to be the set of states which exactly verify it. What is a state? In one way, a state is like a possible world: both kinds of entity correspond to ways for things to be. But while a world is total, specifying a way for all of reality to be, a state may be merely partial, specifying a way for only some portion of reality to be; and while a possible world is possible, specifying a possible way for reality to be, a state may be impossible. A state is said to exactly verify a statement when (a) it necessitates the statement–that is, necessarily, if the state obtains, then the statement is true–and (b) it is wholly relevant to the statement. This latter requirement of whole relevance is what is most distinctive of truthmaker semantics, setting it apart from other state-based approaches to semantics such as Barwise and Perry (1983). For example, the presence of heat and sun will be an exact verifier for the statement ‘it is hot and sunny’ but not for the statement ‘it is sunny’, since heat is not relevant to the latter.

How does the meaning of a logically complex statement depend upon the meanings of its logical parts? Within the truthmaker framework, this question is answered by specifying how which states verify the whole depends upon which states verify the parts. For example, on the simplest proposal, a state will verify the disjunctive statement (:\text{A}\vee:\text{B}) just in case either it verifies (:\text{A}) or it verifies (:\text{B}). To handle the case of a conjunctive statement (:\text{A}\wedge:\text{B}), truthmaker semantics supposes that states are endowed with mereological structure. A state will verify (:\text{A}\wedge:\text{B}) just in case it is the fusion of a state which verifies (:\text{A}) and a state which verifies (:\text{B}).

The case of a negation statement (:\neg:\text{A}) is more difficult. A state cannot be taken to verify (:\neg:\text{A}) just in case it fails to verify (:\text{A}). For a state may fail to verify (:\text{A}) simply because it has nothing to do with whether or not (:\text{A}) is true, and clearly no such state should be taken to verify (:\neg:\text{A}). The standard response to this difficulty is take each statement to have not only verifying states but also falsifying states, states which both necessitate the statement’s falsity and are wholly relevant to it. A state will verify (:\neg:\text{A}) just in case it falsifies (:\text{A}) and a state will falsify (:\neg:\text{A}) just in case it verifies (:\text{A}). Given this assumption, the earlier specification of the verifiers of disjunctive and conjunctive statements must be supplemented with an additional specification of their falsifiers, and the claim that the meaning of a statement is the set of its verifying states must be revised. The meaning may instead be taken to be an ordered pair whose first member is the set of verifying states and whose second member is the set of falsifying states. For details, consult Fine (2017).

Although the basic outlines of truthmaker semantics have been known since van Fraassen (1969), the past decade or so has seen a surge of interest in the approach, spearheaded in large part by Kit Fine. The present issue features contributions from eight philosophers working at the forefront of truthmaker semantics. The first two papers investigate the foundations of the truthmaker approach, including the nature and mereology of states, while the subsequent five develop or extend applications of truthmaker semantics to topics as diverse as modality, ground, and scientific ‘level’. The remainder of this introduction offers a brief preview of the contributions that follow.

The states of truthmaker semantics stand in relations of part-whole. But what mereological principles govern these relations? In ‘The Mereological Basis of Truthmaker Semantics’, Daniele Porello and Giovanni Gonnella show how different answers to this question yield different truthmaker semantics capable of characterizing a range of logics. They adopt Fine’s (2010) approach to mereology, on which it is the operation of composition rather than the relation of part-whole which is taken as primitive.

In truthmaker semantics, the meaning of a statement is identified with a certain set whose urelements are states. But what is a state? In ‘What the States of Truthmaker Semantics Could (Not) Be’, Francisca Silva takes up this question, aiming to move beyond Fine’s (2017) highly general and abstract characterization of states. She proposes certain metaphysical and semantic desiderata for any account of states and considers three proposals: (i) that states are concrete particulars, (ii) that they are rigid embodiments, and (iii) that they are abstract constructions. Silva argues that both (i) and (ii) should be rejected, leaving (iii) as the only viable option.

In ‘The Levels of Scientific Disciplines’, Samuel Elgin argues that the truthmaker framework makes possible an attractive account of disciplinary level. Scientists and philosophers of science alike often speak of the scientific disciplines as occupying different levels, with physics, perhaps, occupying a more fundamental level than chemistry, which in turn occupies a more fundamental level than biology. On Elgin’s account, one discipline occupies a more fundamental level than another just in case the truthmakers for predications of the second discipline are composed of truthmakers for predications of the first discipline and not vice versa. He argues that this account does justice to the connection between level and reduction, permits disciplines to overlap in subject matter, and allows for multiple realizability.

In ‘Approaches to the Impure Logic of Ground’, Kit Fine and Louis deRosset compare the semantics for their (2023) propositional logic of ground to the approaches of Correia (2017) and Krämer (2018; 2021). All these semantics approaches agree on the introduction and elimination rules for the truth-functional connectives laid down in Fine (2012), but there are many underlying points of similarity and difference between them that Fine and deRosset carefully discuss. Two important elements of comparison are the following: (i) Krämer’s semantical treatment of the truth-functional connectives is much closer to Fine and deRosset’s treatment than to Correia’s, and (ii) Correia and Krämer share a conception of weak ground that Fine and deRosset reject. Fine and deRosset conclude their paper by claiming that their semantics characterizes a minimal system of ground, one weaker than the systems targeted by Correia and Krämer.

A second paper by Fine and deRosset, ‘Truthmaker Semantics, Ground, and Generality’, extends their (2023) logic and its accompanying truthmaker semantics to handle quantification. They initially adopt the assumption of a fixed domain of individuals but go on to explore how this assumption may be dropped. The idea that which objects exist may vary has long posed problems for the grounding of quantified statements, and Fine and deRosset suggest two ways of dealing with these problems in the particular form in which they arise for their logic. The first appeals to the idea of a dependent content, the second to a distinction between ‘back-grounds’ and ‘fore-grounds’.

In ‘Web Consequence Untangled’, Stephan Krämer uses the truthmaker framework to shed light on Benjamin Schnieder’s (2021) intriguing notion of web consequence. A statement is a web consequence of some others just in case, roughly, the latter have a ground which contains a ground of the former. Part of the interest of the notion lies in its ability to avoid some of the counterintuitive aspects of the standard modal notion of consequence, such as that everything follows from a contradiction and that a tautology follows from everything. Krämer develops two alternative truthmaker-semantic characterizations (and a many-valued semantic characterization) of Schnieder’s logic and of some of its natural variations, situates these logics with respect to the subclassical logics FDE, K3 and LP, and provides sound and complete tableaux-based proof systems for each.

In ‘Truthmaker Semantics for Intuitionistic Modal Logic’, Jon Litland aims to make progress on the question of what makes necessitated propositions true, where a necessitated proposition is a proposition expressed by a statement of the form ‘necessarily, p’. To that end, Litland extends Fine’s (2014) truthmaker semantics for intuitionistic logic to a truthmaker semantics for modal intuitionistic logic. The semantics is a neighborhood semantics rather than a Kripke-style relational semantics. Litland argues that the neighborhood approach can model certain situations that the relational approach cannot, and so whatever the merits of the latter for the purpose of characterizing certain modal systems, it is the former which should ultimately be preferred.

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Authors and Affiliations

Department of Philosophy, University of Geneva, Geneva, Switzerland

Alessandro Cecconi & Fabrice Correia 1.

Scripps College, Claremont, California, USA

Martin Glazier

Authors

1. Alessandro Cecconi
2. Fabrice Correia
3. Martin Glazier

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Correspondence to Martin Glazier.

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Cecconi, A., Correia, F. & Glazier, M. Introduction: Truthmaker Semantics: What,*** What For***,*** and How?***. Topoi 44, 237–239 (2025). https://doi.org/10.1007/s11245-025-10201-8

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Published: 19 April 2025

Version of record: 19 April 2025

Issue date: May 2025

DOI: https://doi.org/10.1007/s11245-025-10201-8