Self-reference in Arithmetic∗
نویسندگان
چکیده
AGödel sentence is oen described as a sentence saying about itself that it is not provable and a Henkin sentence as a sentence stating its own provability. We discuss what it couldmean for a sentence to ascribe to itself a property such as provability or unprovability. e starting point will be the answer Kreisel gave to Henkin’s problem. We describe how the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing the properties and the way a xed point for the formula is obtained. Some further examples of self-referential sentences are considered such as sentences that ‘say of themselves’ that they are Σn-true (or Πn-true) and their formal properties are investigated. Volker Halbach’s work was supported by the Arts & Humanities Research Council ah/h039791/1. He thanks Christopher von Bülow, Cezary Cieśliński, Kentaro Fujimoto, Graham Leigh, Dan Isaacson, Arthur Merin and Lavinia Picollo for valuable comments and suggestions.
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تاریخ انتشار 2013