Truthmaker semantics is a novel formal semantic framework that in the last decade has attracted an ever growing amount of interest, mainly due to the fact that, unlike standard possible worlds semantics, it allows one to assign distinct semantic contents to sentences provably equivalent in classical logic. This renders truthmaker semantics capable of handling some of the paradoxes that affect possible-worlds semantic analysis of modal claims (such as the paradox of logical omniscience and the paradoxes of standard deontic logic). Despite these successes, however, the study of modal logics supported by the TMS framework is still underdeveloped. In particular, we still lack a completely satisfactory and fully general account of how to extend the standard TMS for propositional logic to the language of propositional modal logic.
In this talk, I try to address this situation by presenting a truthmaker semantics for the language of propositional modal logic that is powerful enough to interpret Kripke’s possible worlds semantics and more general than the other truthmaker semantics approaches to modal logic extant in the literature (such as those of Kim 2024 and Litland 2024). To do so, I build upon an idea already introduced by Fine 2023 and Kim 2024, that of augmenting standard modalized state spaces with two relations that behave as modal counterparts of exact verification and falsification: exact exclusion and exact allowance. After having developed a semantics based on this idea, I show that the weakest normal modal logic K is both sound and complete with respect to a particular class of truthmaker models. Additionally, I establish that the present truthmaker semantics developed interprets standard possible worlds semantics, in the sense that given any class of Kripke frames CK there is a corresponding class of modal state spaces CTMS such that logical consequence in CKis identical to loose consequence in CTMS . After having presented these metalogical results, I compare my framework to one of the most developed truthmaker semantics approaches to modal logic, that of Kim 2024. Specifically, I argue that my framework is preferable to Kim’s since (i) unlike his, it allows for state spaces in which there are no possible worlds (which are needed to represent metaphysical views according to which modal reality is essentially open and incompletable), and (ii) it extends naturally to the semantics of non-normal and non-classical modal logics. I conclude by presenting an overview of the main results and briefly sketching some directions for future work.
This talk presents a novel approach to modals and conditionals by integrating two independently well-known frameworks: variably strict semantics and truthmaker semantics. I demonstrate how this combination preserves the insights of the original variably strict framework for modals and conditionals due to Angelika Kratzer while combining it with the advantages of truthmaker semantics known from Kit Fine's work. This combination overcomes problems concerning the interaction of conditionals and disjunctions. It furthermore provides a natural home for implementing the popular idea that modalized statements are grounded in modal anchors (entities in the world), as argued by Hacquard, Moltmann, and recently Kratzer. This talk is based on joint work with Timothée Bernard (Université Paris Cité).
In the last few decades, truthmaker semantics has attracted the attention of scholars from various areas, arguably due to its philosophical underpinning and its flexibility in addressing a number of problems that are difficult to solve using alternative semantic frameworks. Attention is now focused on developing truthmaker semantics for modal logic; this paper contributes to that direction. The basic idea we introduce is that truthmakers of modal sentences are norms. This allows us to derive two interesting results: first, we introduce a new modal semantics for minimal monotonic logics; second, we provide a truthmaker semantics for every modal logic characterized by a class of Kripke frames.
In his 2012 paper, “Counterfactuals without Possible Worlds,” Kit Fine proposes a truthmaker semantical analysis of counterfactual conditionals. According to Fine’s analysis, a counterfactual conditional A > C is true at a possible world w if and only if every outcome of imposing an exact truthmaker for A on w is an inexact truthmaker for C. When viewed from the perspective of exact truthmaker semantics, however, Fine’s analysis faces two limitations. First, it gives only the truth conditions for counterfactual conditionals without specifying their exact truthmakers. Second, the analysis still depends, in a crucial sense, on the notion of a possible world.
To overcome these limitations, the present paper offers a bilateralist exactification of Fine’s analysis. According to the present approach, an exact truthmaker for A > C is a state that rules out as impossible any outcome of imposing an exact truthmaker for A which fails to be an inexact truthmaker for C; and an exact falsemaker for A > C is a state that countenances as possible some outcome of imposing an exact truthmaker for A that is an inexact falsemaker for C. This exact analysis will be developed into a formal semantics using the formal framework proposed by Kim (2024). It will be shown that the proposed analysis validates the same axioms as Fine’s, when given the same conditions on the outcome relation. Additionally, preliminary results will be given to illustrate how the present semantics can be extended to a unified formal framework for exact truthmaker semantical analysis of counterfactual conditionals, modal statements, and their interactions.
There is a clear sense in which causal claims—such as sentences containing “cause”, “because” or “reason”—imply that the cause is in some sense sufficient for the effect. To illustrate, consider:
(1) Ali has an Irish passport because he was born in Europe.
(2) Being born in Europe caused Ali to get an Irish passport.
(3) The/a reason why Ali got an Irish passport is that he was born in Europe.
These are unacceptable, intuitively because when we interpret them we consider the various ways for Ali to be born in Europe (being born in Hungary, Ukraine, …), and in some of these cases Ali would not have an Irish passport.
Sufficiency is not logical entailment: we hold plenty of facts fixed when we interpret causal claims. We judge, for example, that the light turned on because Ali flicked the switch, even though strictly speaking more was required for that to happen: the electricity in the building, the wiring, and so on. So there are worlds where Ali flicks the switch and the light does not turn on.
This suggests that C is sufficient for E just in case every relevant C-case is an E-case, where, for instance, the relevant cases where Ali is born in Europe include the various ways for him to be born in Europe, beyond merely the actual one. But how do we decide which cases are relevant?
Inspired by the similarity approach to conditionals, one may propose that the relevant cases are those most similar cases to the actual one where C holds. However, the logic (and spirit) of similarity approaches validates conjunctive sufficiency, predicting that “A and C” entails “if A, would C” (Stalnaker 1968, Lewis 1973). Moreover, Walters & Williams (2013) show that conjunctive sufficiency follows from mild assumptions, even in the absence of strong centring. But this rule does not hold for sufficiency: Ali was born in Europe and received an Irish passport, but being born in Europe was not sufficient for him to receive an Irish passport.
Hence the need for a new framework. In particular, I show that Fine's truthmaker semantics and McHugh's aboutness semantics of conditionals both account for the contrasts above. The required notion of aboutness may itself make use of truthmaker semantics. I argue that accounting for sufficiency requires a fundamental shift in how we think about modality and the nature of hypothetical reasoning, away from using orders (as in Kratzer's theory of modality). Along the way, we will see that this new framework resolves some longstanding issues in the semantics of conditionals.
In my previous work, I developed a version of truthmaker semantics (‘object-based truthmaker semantics’) which is centered on modal and attitudinal objects as entities that act as bearers of truthmaking (or satisfaction) conditions. Attitudinal objects are entities like beliefs, claim, intentions, desires, promises; modal objects include needs, obligations, permissions, abilities, and essences. One motivation for object-based truthmaker semantics is the way it converges with an emerging general interest in ‘localized modality’: modal truths, to a great extent, are grounded in particular conditions often pertaining to particular entities or actions, rather than be just relations among possible worlds. In this spirit, I will extend object-based truthmaker semantics to certain intensional transitive verbs, foremost what I call completion-related verbs of absence, such a 'lack' and 'be missing'.