The Epsilon Calculus

In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University (2008)

Richard Zach
University of Calgary
Jeremy Avigad
Carnegie Mellon University
The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term εx A denotes some x satisfying A(x), if there is one. In Hilbert's Program, the epsilon terms play the role of ideal elements; the aim of Hilbert's finitistic consistency proofs is to give a procedure which removes such terms from a formal proof. The procedures by which this is to be carried out are based on Hilbert's epsilon substitution method. The epsilon calculus, however, has applications in other contexts as well. The first general application of the epsilon calculus was in Hilbert's epsilon theorems, which in turn provide the basis for the first correct proof of Herbrand's theorem. More recently, variants of the epsilon operator have been applied in linguistics and linguistic philosophy to deal with anaphoric pronouns.
Keywords epsilon calculus  indefinite description  proof theory
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References found in this work BETA

Epsilon Substitution Method for ID1.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 121 (2-3):163-208.
Mathematical Logic and Hilbert's & Symbol.A. C. Leisenring - 1969 - London: Macdonald Technical & Scientific.
Update Procedures and the 1-Consistency of Arithmetic.Jeremy Avigad - 2002 - Mathematical Logic Quarterly 48 (1):3-13.

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Citations of this work BETA

Notions of Invariance for Abstraction Principles.G. A. Antonelli - 2010 - Philosophia Mathematica 18 (3):276-292.
Hilbert’s Program.Richard Zach - 2003 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University.

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