A bilateral truthmaker semantics for a fragment of English

Reinhard Muskens (University of Amsterdam)

Possible worlds semantics is often considered the tool of choice for analysing natural language meaning. But the framework has a tendency to identify semantic values that should be distinguished and comes with a relation of entailment that seems far too strong. Truthmaker semantics is a subtler tool---a lancet, not a kitchen knife. While it can be viewed as a generalisation of possible worlds semantics and therefore is capable to emulate previous analyses, it also offers a wealth of semantic relations (exact and inexact entailment, part of, analytic containment, etc.) that cannot, or cannot straightforwardly, be obtained in the competing paradigm.   This is good news for linguistic semantics, as subtler formal tools may also lead to better analyses. But in order to show that truthmaker based analyses outcompete existing work two things must be done. It should be made clear that interesting formal fragments of natural languages can be provided with a truthmaker semantics, but also of course that the new analyses resulting from interpreting these fragments have an empirical edge over existing ones.   Two recent papers by Champollion and Bernard make important headway to meeting these goals. But in their work the unilateral variant of truthmaker semantics is chosen as a basis for natural language semantics. This choice comes at a price---negation cannot be modelled as a simple switch between verification and falsification, as can be done in the bilateral approach. As a result, the notion receives an interesting but rather complex analysis. It may be worthwile to also explore the alternative, and take the bilateral route.   In this talk I will develop a bilateral semantics for a toy fragment of English. The result will not be a fully-fledged truthmaker-based theory of natural language meaning, but may serve as a basis for further development with the aim of obtaining one. Like Champollion and Bernard, I will use Church's simple theory of types to talk about truthmakers. The general plan of the talk is for me to 1) say a few words about type-logical semantics for natural language, 2) give a simple general technique for embedding logics with a bilateral semantics in the theory of types, 3) develop a modest truthmaker-based fragment, and 4) say something about the remaining tasks ahead.