Modelling Afthairetic Modality

Despite their controversial ontological status, the discussion on arbitrary objects has been reignited in recent years. According to the supporting views, they present interesting and unique qualities. Among those, two define their nature: their assuming of values, and the way in which they present...

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Bibliographic Details
Published in:Journal of philosophical logic 2024-08, Vol.53 (4), p.1027-1065
Main Authors: Venturi, Giorgio, Yago, Pedro
Format: Article
Language:English
Subjects:
Education
Inference
Language
Logic
Ontology
Philosophy
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Summary:Despite their controversial ontological status, the discussion on arbitrary objects has been reignited in recent years. According to the supporting views, they present interesting and unique qualities. Among those, two define their nature: their assuming of values, and the way in which they present properties. Leon Horsten has advanced a particular view on arbitrary objects which thoroughly describes the earlier, arguing they assume values according to a sui generis modality, which he calls afthairetic . In this paper, we offer a general method for defining the minimal system of this modality for any given first-order theory, and possible extensions of it that incorporate further aspects of Horsten’s account. The minimal system presents an unconventional inference rule, which deals with two different notions of derivability. For this reason and the failure of the Necessitation rule, in its full generality, the resulting system is non-normal. Then, we provide conditional soundness and completeness results for the minimal system and its extensions.
ISSN:0022-3611
1573-0433
DOI:10.1007/s10992-024-09757-4