Natural Necessity and the Logic of Sortals
Two intensional logics for sortal concepts are characterized in this chapter. One is a modal-temporal bidimensional logic, with a constant domain interpretation of the second-order quantificatiers. The other is also a bidimensional logic but with a varying domain interpretation of second-order quantification. Both logics shared the same formal language and differ in their formal semantics. Soundness and completeness theorems are proved for their formal systems with respect to their corresponding semantics. Natural necessity is the modal notion represented in the logics in question. Its content and connection to conceptualism is presented.
KeywordsSortal concept Natural necessity Temporal-modal logic Constant domain quantification Varying domain quantification
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