Guises and Perspectives: An Intentional and Hyperintensional Sketch
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910222413463552 |
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| author | Colomina-Alminana, Juan J. |
| author_facet | Colomina-Alminana, Juan J. |
| contents | This paper develops a formal logic for guises based on the work of Héctor-Neri Castañeda, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15144 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Guises and Perspectives: An Intentional and Hyperintensional Sketch Colomina-Alminana, Juan J. Logic in Computer Science History and Overview Logic 03A05, 01A60 This paper develops a formal logic for guises based on the work of Héctor-Neri Castañeda, 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. |
| title | Guises and Perspectives: An Intentional and Hyperintensional Sketch |
| topic | Logic in Computer Science History and Overview Logic 03A05, 01A60 |
| url | https://arxiv.org/abs/2605.15144 |