Abstract
Ambiguity is a property of syntactic expressions which is ubiquitous in all informal languages–natural, scientific and mathematical; the efficient use of language depends to an exceptional extent on this feature. Disambiguation is the process of separating out the possible meanings of ambiguous expressions. Ambiguity is typical if the process of disambiguation can be carried out in some systematic way. Russell made use of typical ambiguity in the theory of types in order to combine the assurance of its (apparent) consistency (“having the cake”) with the freedom of the informal untyped theory of classes and relations (“eating it too”). The paper begins with a brief tour of Russell’s uses of typical ambiguity, including his treatment of the statement Cls ∈ Cls. This is generalized to a treatment in simple type theory of statements of the form A ∈ B where A and B are class expressions for which A is prima facie of the same or higher type than B. In order to treat mathematically more interesting statements of self membership we then formulate a version of typical ambiguity for such statements in an extension of Zermelo-Fraenkel set theory. Specific attention is given to how the“naive” theory of categories can thereby be accounted for.
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References found in this work BETA

Principia Mathematica.A. N. Whitehead & B. Russell - 1931 - Erkenntnis 2 (1):73-75.
Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
Non-Well-Founded Sets.J. L. Bell - 1989 - Journal of Symbolic Logic 54 (3):1111-1112.

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Citations of this work BETA

Category Theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.
Generality of Logical Types.Brice Halimi - 2011 - Russell: The Journal of Bertrand Russell Studies 31 (1).

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