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Invertible definitions

By Timothy Williamson

Abstract

A concept of informational equivalence between relations is explicated to generalize some suggestions by Geach. It is shown that two relations are informationally equivalent if and only if each can be defined in terms of the other without the use of quantifiers. It is shown that there is a general method for listing the ./-place relations informationally equivalent to an arbitrary given /-place relation if and only if i<j. The equivalence classes of the relation of informational equivalence are characterized as the invariants of the group of invertible quantifier-free definitions, for / =j. Quantifier-free definition is contrasted with general first-order definition by means of an example of two first-order interdefinable relations which are not interdefined by any pair of mutually inverse first-order definitions.N.B. Prof Williamson is now based at the Faculty of Philosophy, University of Oxford

Topics: Philosophy, logic
Year: 1987
DOI identifier: 10.1305/ndjfl
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