Path: utzoo!attcan!uunet!lll-winken!ames!ucsd!rutgers!cmcl2!yale!engelson
From: engelson@cs.yale.edu (Sean Philip Engelson)
Newsgroups: comp.ai
Subject: Re: Fun with the semantics of paradox
Keywords: Types, Paradoxes
Message-ID: <48717@yale-celray.yale.UUCP>
Date: 26 Jan 89 14:49:14 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>
Sender: root@yale.UUCP
Reply-To: engelson@cs.yale.edu (Sean Philip Engelson)
Organization: Computer Science, Yale University, New Haven, CT 06520-2158
Lines: 28
In-reply-to: kerber@uklirb.UUCP (Manfred Kerber)

>Heiko Hecht writes:
>>> But what if choices 1. to 3. don't seem to work, does anyone have suggestions
>>> as to how to resolve the following paradox:
>>>    
>>>       "The following sentence is true"
>>>       "The preceeding 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?

	-Sean-
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Sean Philip Engelson, Gradual Student	Who is he that desires life,
Yale Department of Computer Science	Wishing many happy days?
Box 2158 Yale Station			Curb your tongue from evil,
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(203) 432-0677				   falsehood.
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