Type-free property theory, exemplification and Russell's paradox

Notre Dame Journal of Formal Logic 32 (3):432-447 (1991)
This paper presents a type-free property-theoretic system in the spirit of a framework proposed by Menzel and then supplements it with a theory of truth and exemplification. The notions of a truth-relevantly complex (simple) sentence and of a truth-relevant subsentence are introduced and then used in order to motivate the proposed theory. Finally, it is shown how the theory avoids Russell's paradox and similar problems. Some potential applications to the foundations of mathematics and to natural language semantics are sketched in the introduction.
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DOI 10.1305/ndjfl/1093635839
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