Second-Order Modal Logic

Dissertation, University of Connecticut (2017)
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Abstract

This dissertation develops an inferentialist theory of meaning. It takes as a starting point that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. From this starting point the dissertation develops a theory of quantification as marking coherent ways a language can be expanded and modality as the means by which we can reflect on the norms governing the assertion and denial conditions of our language. If the view of quantification that is argued for is correct, then there is no tension between second-order quantification and nominalism. In particular, the ontological commitments one can incur through the use of a quantifier depend wholly on the ontological commitments one can incur through the use of atomic sentences. The dissertation concludes by applying the developed theory of meaning to the metaphysical issue of necessitism and contingentism. Two objections to a logic of contingentism are raised and addressed. The resulting logic is shown to meet all the requirement that the dissertation lays out for a theory of meaning for quantifiers and modal operators.

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Andrew Parisi
University of Connecticut

Citations of this work

One-step Modal Logics, Intuitionistic and Classical, Part 1.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):837-872.

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References found in this work

Multiple Conclusions.Greg Restall - 2005 - In Petr Hájek, Luis Valdés-Villanueva & Dag Westerståhl, Logic, Methodology, and Philosophy of Science. College Publications.
Sequent-systems for modal logic.Kosta Došen - 1985 - Journal of Symbolic Logic 50 (1):149-168.
More free logic.Scott Lehmann - 2002 - In D. M. Gabbay & F. Guenthner, Handbook of Philosophical Logic Vol. 5. Kluwer Academic Publishers. pp. 197-259.

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