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CIFOL: Case-intensional first order logic. (I) Toward a theory of sorts

Belnap, Nuel and Müller, Thomas (2012) CIFOL: Case-intensional first order logic. (I) Toward a theory of sorts. [Preprint]

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Abstract

This is Part I of a two-part essay introducing case-intensional first-order logic (CIFOL), 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 (Yale University Press 1972). 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 (whether the property applies, depends only on an extension in one case) 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 (substance) properties, essential properties, de re vs. de dicto, and the results of possible tests.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Belnap, Nuelbelnap@pitt.edu
Müller, ThomasThomas.Mueller@phil.uu.nl
Additional Information: Forthcoming in Journal of Philosophical Logic
Keywords: modal logic; extension/intension; intensional predication and quantification; sortal; tracing; substance
Subjects: General Issues > Determinism/Indeterminism
General Issues > Logical Positivism/Logical Empiricism
Depositing User: Dr. Thomas Müller
Date Deposited: 17 Oct 2012 18:30
Last Modified: 17 Oct 2012 18:30
Item ID: 9375
URI: http://philsci-archive.pitt.edu/id/eprint/9375

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