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Philosophy and Logic of Predication

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Edited By Piotr Stalmaszczyk

This book investigates philosophical and formal approaches to predication. The topics discussed include Aristotelian predication, a conceptualist approach to predication, possible formalizations of the notion, Fregean predicates and concepts, and Meinongian predication. The contributions discuss the approaches proposed by Aristotle and Frege, as well as the division of classes into a hierarchy of orders. They reanalyze the traditional notions, and offer new insights into predication theory. This book contributes to contemporary debates on predication and predicates in the philosophy of language.

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Meinongian Predication. An Algebraic Approach (Jacek Paśniczek)

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Jacek Paśniczek

Maria Curie-Skłodowska University, Lublin, Poland

Meinongian Predication. An Algebraic Approach

Abstract: Alexius Meinong, an Austrian philosopher, is particularly famous for his abundant ontology embracing various types of non-existent objects. The most distinguished formal-ontological feature of his theory of objects is that it allows for impossible and incomplete objects like the round square. Recently there have appeared several logical interpretations of Meinong’s theory of objects rendering it consistent. Generally, in order to render such a theory consistent we have to modify the classical concept of predication according to which it is a relation holding between objects and properties, i.e. basic formulas of respective formal languages are subject-predicate ones. In the present paper we are going to develop an unorthodox view of Meinongian predication based on a calculus of names. The calculus is semantically interpreted in an algebraic structure which is an extension of De Morgan lattice (the De Morgan negation as basically weaker than the Boolean negation enable us to interpret impossible objects in a consistent way). Roughly speaking, the idea is that predication is expressed by a formula ‘a is b’ where a and b are of the same syntactic category, i.e. the name category. This means that the roles of properties in the predication are played by objects of Meinongian kind. Within the proposed algebraic setting various ontological notions pertaining Meinong’s theory of objects are studied. Let us mention here notions of contradictory and complementary...

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