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

CSLI Publications (1986)
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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

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Christopher Menzel
Texas A&M University

Citations of this work

Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
Ordinal Type Theory.Jan Plate - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
Qualitative properties and relations.Jan Plate - 2022 - Philosophical Studies 179 (4):1297-1322.
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.

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