Path: utzoo!attcan!uunet!mcvax!unido!uklirb!kerber
From: kerber@uklirb.UUCP (Manfred Kerber)
Newsgroups: comp.ai
Subject: Re: Fun with the semantics of paradox
Keywords: Types, Paradoxes
Message-ID: <3715@uklirb.UUCP>
Date: 24 Jan 89 18:52:39 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>
Reply-To: kerber@uklirb.UUCP (Manfred Kerber)
Organization: Universitaet Kaiserslautern, West Germany
Lines: 16

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"    ?

This can be excluded by Russell's "Theory of Types" as described in "Principia
Mathematica" or in the American Journal of Mathematics p.222 ff, Vol.XXX, 1908.
In order to avoid paradoxies Russell introduces a strict hierarchy of types.
The first sentence of the above example is of type "sentence about sentence".
Then the second must be of type "sentence". On the other hand in order to make
a statement about the first, the second must be of type "sentence about sentence
about sentence", both is impossible. So such a self-reference, direct or
indirect, is excluded.
Manfred Kerber