Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!tut.cis.ohio-state.edu!unmvax!pprg.unm.edu!hc!lll-winken!uunet!mcvax!ukc!s1!jrk
From: jrk@s1.sys.uea.ac.uk (Richard Kennaway CMP RA)
Newsgroups: comp.ai
Subject: Re: Fun with the semantics of paradox
Keywords: Types, Paradoxes
Message-ID: <415@s1.sys.uea.ac.uk>
Date: 27 Jan 89 18:58:17 GMT
References: <1883@buengc.BU.EDU> <2996@uhccux.uhcc.hawaii.edu> <905@ubu.warwick.UUCP> <479@aipna.ed.ac.uk> <1036@hudson.acc.virginia.edu> <3715@uklirb.UUCP> <48717@yale-celray.yale.UUCP>
Reply-To: jrk@uea-sys.UUCP (Richard Kennaway)
Organization: University of East Anglia, Norwich
Lines: 22

In article <48717@yale-celray.yale.UUCP> engelson@cs.yale.edu (Sean Philip Engelson) writes:
[refers to the paradox: "The following sentence is true"/"The preceding
sentence is false"]
>In article <3715@uklirb.UUCP>, Manfred Kerber resolves the paradox by
>introducing Russell's hierarchy of types, saying that the first is of
>types "Sentence about Sentence", thus the second must thus be of type
>"Sentence", but it's also "S about S".  However, if you allow infinite
>types, the paradox remains, as both sentences can be of type T, where
>T is defined as the fixed point of T', as follows:
>	T' = "Sentence" | "Sentence about T'"
>Each sentence is of type T and can thus refer to the other.  Is there
>any a priori reason to exclude infinite types?

You said it yourself: "the paradox remains".  (Well, an a posteriori
reason, I suppose...)  Ever since Russell showed that the system of
logic Frege had just published was self-contradictory, people have
been trying to find ways of avoiding the paradoxes of self-reference.
However, all the solutions so far seem (IMHO) pretty ad hoc.

-- 
Richard Kennaway                SYS, University of East Anglia, Norwich, U.K.
uucp:	...mcvax!ukc!uea-sys!jrk	Janet:	kennaway@uk.ac.uea.sys