CIFOL: Case-Intensional First Order Logic: Toward a Theory of Sorts

Journal of Philosophical Logic 43 (2-3):393-437 (2014)
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Abstract

This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, and lambda-predicates and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute properties, essential properties, de re vs. de dicto, and the results of possible tests.

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Author Profiles

Nuel Belnap
University of Pittsburgh
Thomas Muller
Universität Konstanz

Citations of this work

Modal Logic.James W. Garson - 2009 - Stanford Encyclopedia of Philosophy.
On the Humphrey Objection to Modal Realism.Michael De - 2018 - Grazer Philosophische Studien 95 (2):159-179.
Time and Determinism.Thomas Müller - 2015 - Journal of Philosophical Logic 44 (6):729-740.

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Reference and generality.P. T. Geach - 1962 - Ithaca, N.Y.,: Cornell University Press. Edited by Michael C. Rea.
Semantical Considerations on Modal Logic.Saul Kripke - 1963 - Acta Philosophica Fennica 16:83-94.

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