Epsilon calculi

Internet Encyclopedia of Philosophy (2001)
  Copy   BIBTEX

Abstract

Epsilon Calculi are extended forms of the predicate calculus that incorporate epsilon terms. Epsilon terms are individual terms of the form ‘εxFx’, being defined for all predicates in the language. The epsilon term ‘εxFx’ denotes a chosen F, if there are any F’s, and has an arbitrary reference otherwise. Epsilon calculi were originally developed to study certain forms of Arithmetic, and Set Theory; also to prove some important meta-theorems about the predicate calculus. Later formal developments have included a variety of intensional epsilon calculi, of use in the study of necessity, and more general intensional notions, like belief. An epsilon term such as ‘ εxFx’ was originally read ‘the first F’, and in arithmetical contexts ‘the least F’. More generally it can be read as the demonstrative description ‘that F’, when arising either deictically, i.e. in a pragmatic context where some F is being pointed at, or in linguistic cross-reference situations, as with, for example, ‘There is a red haired man in the room. That red haired man is Caucasian’. The application of epsilon terms to natural language shares some features with the use of iota terms within the theory of descriptions given by Bertrand Russell, but differs in formalising aspects of a slightly different theory of reference, first given by Keith Donnellan. More recently epsilon terms have been used by a number of writers to formalise cross-sentential anaphora, which would arise if ‘that red haired man’ in the linguistic case above was replaced with a pronoun such as ‘he’. There is then also the similar application in intensional cases, like ‘There is a red haired man in the room. Celia believed he was a woman.’

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Seneca’s ninetieth letter. [REVIEW]Costas Panayotakis - 2004 - The Classical Review 54 (01):103-.
Epsilon Substitution Method for $\Pi _{2}^{0}$ -FIX.Toshiyasu Arai - 2006 - Journal of Symbolic Logic 71 (4):1155 - 1188.

Analytics

Added to PP
2009-01-28

Downloads
50 (#282,559)

6 months
6 (#202,901)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Hartley Slater
University of Western Australia

Citations of this work

Logic and grammar.Hartley Slater - 2007 - Ratio 20 (2):206–218.

Add more citations

References found in this work

No references found.

Add more references