Recent years have seen a growing body of work using higher-order formal languages for metaphysical theorizing. This literature differs from earlier work using second-order logic in the philosophy of mathematics (e.g. Wright 1983, Boolos 1984, Shapiro 1991, Lewis 1991) in that it tends to adopt a non-extensional interpretation of higher-order quantification, so that higher-order quantification is closer to quantification over properties and relations than it is to quantification over sets and classes; see Skiba (Phil Compass, 2021) for a review. Topics in this literature include:

* On a non-extensional interpretation of higher-order quantification, what principles formulated using higher-order quantification are true? Many of the natural questions here have to do with fineness of grain, with traditional questions about structural or other individuating aspects of propositions, properties, and relations being reformulated in higher-order terms. See especially Dorr "To be F is to be G" (2016); Fritz "How fine-grained is reality?" (2017) is a gentle introduction.

* Applying higher-order languages to systematically investigate questions about time and modality (Fine 1977, Williamson 2013, Bacon 2018), fundamentality (Bacon 2020), grounding (Fritz 2021, Goodman 2022), semantics (Williamson 2003, Linnebo & Rayo 2011), propositional attitude puzzles (Bacon & Russell 2018, Caie, Goodman & Lederman 2020), and other topics in philosophical logic.

* Foundational questions about the status of higher-order languages. (Are these languages legitimate tools for metaphysical theorizing? Are they an alternative to theories that posit an ontology of properties and relations? If so, what is their intended interpretation? Is higher-order logic logic? What is the appropriate methodology for higher-order metaphysics?)

* Historical questions about the role of higher-order quantification in the metaphysical views of Frege, Russell, Prior, Church, etc.

We invite submissions on any of the above topics for a two-day workshop on higher-order metaphysics hosted by the USC School of Philosophy. The workshop will take place immediately following NASSLLI2022 from June 18-24. NASSLLI participants are encouraged to stay for the workshop. Two bootcamps on June 18-19 (by Peter Fritz, on propositional quantification, and by Cian Dorr and Harvey Lederman, on non-extensional higher-order logic and propositional attitudes) will provide excellent background for the workshop. Confirmed speakers are:

Andrew Bacon (USC)
Michael Caie (Toronto)

Submissions should be anonymized and take the form of either a full paper or an extended abstract. The deadline for submissions has been extended to March 23th. Decisions will be announced by the first week of April. Accepted speakers will have 60-90 minutes for presentations and Q&A. First-order questions can be addressed to goodman.jeremy[at]gmail[dot]com.