A Complete, Type-free "Second-order" Logic and Its Philosophical Foundations

CSLI Publications (1986)
Abstract
In this report I motivate and develop a type-free logic with predicate quantifiers within the general ontological framework of (nonextensional) properties, relations, and propositions. In Part I, I present the major ideas of the system informally and discuss its philosophical significance, especially with regard to Russell's paradox. In Part II, I prove the soundness, consistency, and completeness of the logic.
Keywords property theory  Russell's paradox  structured propositions
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Jeffrey Barrett (2007). Stability and Paradox in Algorithmic Logic. Journal of Philosophical Logic 36 (1):61 - 95.
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