Saturday, November 07, 2009

Liar’s Paradox

 

The following is NOT a Liar’s Paradox

stmt1: Following statement is false;
stmt2: Preceding statement is false;

Explanation:

It has the following possible solutions:

stmt1 stmt2
T F
F T

Take row 1: Stmt 2 is true, Stmt 1 is false. What Paradox?
Take row 2: Stmt 2 is false, Stmt 1 is true. What Paradox?

The following IS a Liar’s Paradox

stmt3: Following statement is true;
stmt4: Preceding statement is false;

Explanation:

Take row 1: stmt3 is true, therefore stmt4 is true, therefore stmt3 is false.
Now row 2: stmt3 is false, therefore stmt4 is false, therefore stmt3 is true.

Completely un-decidable.

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