Abstract: The aim of this talk is to compare truthmaker semantics and inquisitive semantics from the perspective of hyperintensional logic.
Following Cresswell (1975), we call an operator, , hyperintensional just in case doesn’t respect logical equivalence, meaning that O(ϕ) and O(ψ) can differ in truth-value even when and are logically equivalent. The research of the last decades has shown that a wide range of philosophically significant operators are, in fact, hyperintensional—including (but not limited to) knowledge and belief operators, question and explanation operators, imperative and permission operators, and many others.
From a logical perspective, the thing about hyperintensional operators is that they force us to banish from our logical models of propositions an incredibly useful assumption, namely that (logically) equivalent formulas are synonymous (express the same proposition). But what, if anything, replaces the assumption? This question, also known as the Problem of Grain, is sometimes put as: How hyperintensional does our model of propositions have to be?
Truthmaker semantics and inquisitive semantics provide competing (?) models of propositions that have proven independently fruitful for the logical study of hyperintensional logic (Fine 2017, Jago 2017, Ciardelli, Groenendijk, and Roelofsen 2018). In this sense, they provide different answers to the Problem of Grain. But is any of them right? Are there logical reasons to prefer one model of propositions over another?
In this talk, I’ll sketch a framework for answering questions of grain from a logical perspective, and I’ll apply the framework by comparing the truthmaker model of propositions to the inquisitive model.
References
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Ciardelli, Ivano; Groenendijk, Jeroen & Roelofsen, Floris. 2018. Inquisitive Semantics. Oxford, England: Oxford University Press.
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Cresswell, M. J. 1975. “Hyperintensional logic.” Studia Logica 34(1): 25-38.
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Fine, Kit. 2017. “A Theory of Truthmaker Content I: Conjunction, Disjunction and Negation.” Journal of Philosophical Logic 46(6): 625-674.