Philosophers and linguistics have recently shown a growing interest in truthmaker semantics (van Fraassen 1969; Fine 2013, 2016, 2017; Yablo 2014, 2016, 2017; Moltmann 2020, 2021), a new family of approaches to logical semantics oriented around the notion of 'exact' verification with a broad range of applications in philosophical logic and formal linguistics, including the study of subject matter, partial and common content, logical subtraction, ground, confirmation, verisimilitude, conditionals, exceptives, imperatives, 'case' constructions, attitude verbs, and modals. In this project, I develop a compositional generalization of the standard theory of "recursive" truthmaking (as opposed to the "reductive" truthmaking in Yablo 2014), which allows for a unified cross-categorial treatment of negation, conjunction, disjunction, and quantification in a pluralized partial setting.
The resulting theory has a number of attractive features. Among other things, it offers a new perspective on homogeneity effects in natural language (Lobner 1987, 2000; Schwarzschild 1993-1994; Gajewski 2005; Schmitt 2013, 2019; Kriz 2015, 2016; Kriz & Spector 2020), which arise from the bilateral nature of predication for NP conjunctions, plural definite descriptions, and other non-distributive plural NPs in the truthmaker framework combined with the mereological properties of distributive and certain collective predicates. The theory also predicts the availability of cumulative readings for sentences involving plural definites and singular distributive quantifiers (Schein 1993; Kratzer 2002; Champollion 2010; Chatain forthcoming). In compositional TMS, certain coordinated NPs involving non-upward entailing quantifiers can also be analyzed as denoting "mixed polarity" pluralities with both positive and negative parts, and I can thereby deal with the main challenges for the collective treatment of conjunction as fusion raised in Champollion (2015).