A Complete, Type-Free "Second-Order" Logic and its Philosophical Foundations

CSLI Publications (1986)

Authors
Christopher Menzel
Texas A&M University
Abstract
In this report I motivate and develop a type-free logic with predicate quantifiers within the general ontological framework of 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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Abstract Objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
Property Theories.George Bealer & Uwe Monnich - 2003 - In Dov Gabbay & Frans Guenthner (eds.), Handbook of Philosophical Logic, Volume 10. Kluwer Academic Publishers. pp. 143-248.
Property Theories.George Bealer & Uwe Mönnich - 1989 - In Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, Volume IV. Kluwer Academic Publishers. pp. 133-251.
The Fundamental Theorem of World Theory.Christopher Menzel & Edward N. Zalta - 2013 - Journal of Philosophical Logic (2-3):1-31.
Property Theory: The Type-Free Approach V. The Church Approach.George Bealer - 1994 - Journal of Philosophical Logic 23 (2):139 - 171.

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