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- W1888409996 abstract "This chapter focuses on the Aristotle's modal syllogisms. McCall's purely syntactic system—Q–L–X–M—has some unAristotelian features that helped in the development of a modified system called “QLXM'” in the chapter. After examining McCall's L–X–M system and work related to it, the chapter examines the contingent syllogisms. Semantics for QLXM enables the chapter to provide formal countermodels for a large percentage of the assertoric, apodeictic, or contingent syllogisms that Aristotle explicitly considered to be invalid. Aristotle's syllogisms are “implicational” rather than “inferential.” The chapter describes the Lukasiewicz's assertoric system (LA). Given the assertion portion of the basis for LA, the chapter provides some assertion deductions that capture some Aristotelian principles involving conversions, subordinations, and oppositions. Lukasiewicz's system for the assertoric syllogistic has 100% Aristotelicity to use McCall's expression. The chapter presents McCall's L–X–M system. The basis for L–X–M includes that of LA together with primitive symbols, formation rules, definitions, axioms, and transformation rules. The chapter also examines valuable attempts by Thomason—Thomason models—to improve on the semantics." @default.
- W1888409996 created "2016-06-24" @default.
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- W1888409996 date "2004-01-01" @default.
- W1888409996 modified "2023-09-27" @default.
- W1888409996 title "Aristotle's Modal Syllogisms" @default.
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- W1888409996 doi "https://doi.org/10.1016/s1874-5857(04)80006-2" @default.
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