David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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.
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Ebbe Groes, Hans Jørgen Jacobsen, Birgitte Sloth & Torben Tranaes (1998). Nash Equilibrium with Lower Probabilities. Theory and Decision 44 (1):37-66.
W. Kip Viscusi & Harrell Chesson (1999). Hopes and Fears: The Conflicting Effects of Risk Ambiguity. Theory and Decision 47 (2):157-184.
Marcel Crabbé (1984). Typical Ambiguity and the Axiom of Choice. Journal of Symbolic Logic 49 (4):1074-1078.
Ernst P. Specker (1962). Typical Ambiguity. In Ernst Nagel (ed.), Logic, Methodology and Philosophy of Science. Stanford University Press. 116--23.
Brendan S. Gillon (1990). Ambiguity, Generality, and Indeterminacy: Tests and Definitions. [REVIEW] Synthese 85 (3):391 - 416.
Ludwik Borkowski (1958). Reduction of Arithmetic to Logic Based on the Theory of Types Without the Axiom of Infinity and the Typical Ambiguity of Arithmetical Constants. Studia Logica 8 (1):283 - 297.
Jan Albert van Laar (2011). Ambiguity in Argument. Argument and Computation 1 (2):125-146.
Richard Kaye (1991). A Generalization of Specker's Theorem on Typical Ambiguity. Journal of Symbolic Logic 56 (2):458-466.
Added to index2009-01-28
Total downloads21 ( #83,253 of 1,102,631 )
Recent downloads (6 months)3 ( #121,188 of 1,102,631 )
How can I increase my downloads?