Re: The Liar Paradox is merely an ill-formed statement

From: George Greene (greeneg_at_greeneg-cs.cs.unc.edu)
Date: 06/01/04 

Date: 01 Jun 2004 10:59:35 -0400

 : > If UTM outputs ACCEPT in response to an input, we say
 : > that it has accepted the string.
 : >
 : > So, with this formulation, we don't have to worry about
 : > what UTM can say or not--there are only three possible
 : > things it can say.

"Peter Olcott" <olcott@worldnet.att.net> writes:
 : (1) Its a true statement
 : (2) Its a false statement
 : (3) Its not a statement
 : (a) Its incorrectly formed
 : (b) Its not intended to be a statement
 : 1) Its a question
 : 2) Its an exclamation

Peter, please, you are just LYING.

DARRYL DEFINED the machine. It behaves EXACTLY the way HE says
it behaves. PERIOD. NObody else is entitled to an opinion!
More to the point, even if the definition of this machine were a hole
instead of a peg, even if there could exist legitimate argument
(which there can't) about how it "ought" to be defined, about WHICH
peg should go in this hole, it would STILL be the case that THIS
PARTICULAR peg, this PARTICULAR definition, would STILL be a WELL-
defined option or choice!

THE ONLY outputs that THIS machine can have are accept, reject,
and ask-later. All of the possibilities in your (3) are SUBSUMED
under the REJECT alternative, i.e., the machine will just reject them.

Just by way of improving upon Darryl's definition, you don't need
"reject" as an outcome, either. In real life, the middle REALLY IS
excluded. On EVERY input, EVERY TM either halts or it doesn't.
There IS NO POSSIBLE third alternative. 

-- 
 --- The history of our nation has demonstrated that separate is seldom, if ever, equal.
 --- (Feb.3,2004) Supreme Judicial Court of Massachusetts (4-3), adv.Sen.#2175

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