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From: hh5s@lucifer.acc.virginia.edu (Heiko Hecht)
Newsgroups: comp.ai
Subject: Re: Fun with the semantics of paradox
Message-ID: <1036@hudson.acc.virginia.edu>
Date: 22 Jan 89 04:36:31 GMT
References: <1883@buengc.BU.EDU> <2996@uhccux.uhcc.hawaii.edu> <905@ubu.warwick.UUCP> <479@aipna.ed.ac.uk>
Sender: news@hudson.acc.virginia.edu
Reply-To: hh5s@lucifer.psyc.Virginia.EDU.acc.Virginia.EDU (Heiko Hecht)
Organization: University of Virginia, Charlottesville
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It seems to me that the question whether we need more than two truth-values
(true - false) depends on the extent to wich we want to make logic
paradox-proof. To remove paradoxes we basically have three choices: 

   1. We declare logic as not applicable to certain sentences:
      e.g. "The king of France is bald" because it has no empirical reference,
           "This sentence is false" because it is self-referencing,
           "All people are liars" because it includes the person who writes it.

   2. We introduce "new" truth values like undecidable or meaningless. The
      question is whether this is a good idea, because it becomes very fuzzy.
      My favorite is "uncomfortable":
      e.g. "You are stupid" is not true, then again it may not be false and
           it is probably undecidable even though it may be very meaningful.

   3. Meta-logic to the rescue! If 1. and 2. don't work, we can always try to 
      claim that the sentence in question is actually (or includes) a 
      meta-logic sentence that refers to its own truth/falseness.

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"    ?
        

Heiko Hecht (hh5s@virgina.edu)       "Say yes to paradoxes"