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Summer 1997 Cumulative versus Noncumulative Ramified Types
Anthony F. Peressini
Notre Dame J. Formal Logic 38(3): 385-397 (Summer 1997). DOI: 10.1305/ndjfl/1039700745


In this paper I examine the nature of Russell's ramified type theory resolution of paradoxes. In particular, I consider the effect of construing the types in Church's cumulative sense, that is, the range of a variable of a given type includes the range of every variable of directly lower type. Contrary to what seems to be generally assumed, I show that the decision to make the levels cumulative and allow this to be reflected in the semantics is not neutral with respect to the solution of the paradoxes. I introduce a distinction between syntactical and semantical cumulativeness. It turns out that noncumulative type theories (in either sense) are equally capable of dealing with the paradoxes. Furthermore, whether cumulativeness is appropriate appears to be context dependent.


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Anthony F. Peressini. "Cumulative versus Noncumulative Ramified Types." Notre Dame J. Formal Logic 38 (3) 385 - 397, Summer 1997.


Published: Summer 1997
First available in Project Euclid: 12 December 2002

zbMATH: 0910.03002
MathSciNet: MR1624954
Digital Object Identifier: 10.1305/ndjfl/1039700745

Primary: 03B15

Rights: Copyright © 1997 University of Notre Dame


Vol.38 • No. 3 • Summer 1997
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