Substitutional Validity for Modal Logic

Notre Dame Journal of Formal Logic 64 (3):291-316 (2023)
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Abstract

In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.

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10.1215/00294527-2023-0007

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Marco Grossi
University of Oxford

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References found in this work

Everything.Timothy Williamson - 2003 - Philosophical Perspectives 17 (1):415–465.
Nominalist platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
Reflecting on incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.
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Toward a Theory of Second-Order Consequence.Augustín Rayo & Gabriel Uzquiano - 1999 - Notre Dame Journal of Formal Logic 40 (3):315-325.

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