Guises and Perspectives: An Intentional and Hyperintensional Sketch

TL;DR

This paper introduces a formal, hyperintensional logic for guises as bundles of properties with intentions, integrating semantics, modal operators, and analyzing hyperintensional phenomena.

Contribution

It develops a novel intensional logic framework for guises based on Leibnizian semantics, capturing internal relations and perspectives in a formal system.

Findings

Established soundness and completeness sketches for the logic.

Analyzed hyperintensional phenomena like substitution failure and de se reference.

Compared the framework with classical and hyperintensional semantics.

Abstract

This paper develops a formal logic for guises based on the work of H\'ector-Neri Casta\~neda, who understood relations from an internalist viewpoint, following Leibniz. We introduce a syntax, model theory, and proof theory for an intensional logic in which guises (taken as bundles of properties equipped with intention) serve as primary semantic objects. The system integrates (i) a Leibnizian containment semantics for singular truths, (ii) an intentional operator that captures internal relations among guises, and (iii) a modal layer for possibility and necessity modeled as maximally consistent closures. We establish core metatheoretic results (e.i. soundness and canonical-model completeness sketches) and analyze hyperintensional phenomena such as substitution failure in intentional contexts, quasi-indexicality, and de se reference. We compare the framework to classical intensional semantics (Montague), property theory (Bealer), hyperintensional logics (Fine), situation semantics (Barwise and Perry), and to the Leibniz program for a calculus of concepts. The result is a selfcontained formal framework that demonstrates that relations are not external causal links but intentional internal structures encoded in the guises through which agents and objects are conceived: i.e., they are perspectives.