Substitution Structures

Journal of Philosophical Logic 48 (6):1017-1075 (2019)
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Abstract

An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion of a substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets.

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Andrew Bacon
University of Southern California

Citations of this work

A Theory of Structured Propositions.Andrew Bacon - 2023 - Philosophical Review 132 (2):173-238.
Ordinal Type Theory.Jan Plate - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
Logical Combinatorialism.Andrew Bacon - 2020 - Philosophical Review 129 (4):537-589.
Qualitative properties and relations.Jan Plate - 2022 - Philosophical Studies 179 (4):1297-1322.

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References found in this work

The identity of indiscernibles.Max Black - 1952 - Mind 61 (242):153-164.
Hyperintensional metaphysics.Daniel Nolan - 2014 - Philosophical Studies 171 (1):149-160.
Vagueness and Thought.Andrew Bacon - 2018 - Oxford, England: Oxford University Press.
Reality is not structured.Jeremy Goodman - 2017 - Analysis 77 (1):43–53.

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