Chaotic Liar The Chaotic Liar is a graphical exploration of the sematics of the following dualistic paradox in the context of infinite valued logic:

• X: X is true to the extent that Y is true
• Y: Y is true to the extent that X is false

These sentences can be viewed as a dynamic system:

• x_n+1=1-abs(y_n-x_n)
• y_n+1=1-abs((1-x_n)-y_n)

We can draw a standard escape-time diagram (bail-out value: 1.0609) from these equations which yields a quite beautiful picture. You can either play with the Java Applet or download the source code.

References

1

Ian Stewart. Mathematical Recreations. Scientific Americanpp 85-87, February 1993.

2

Gary Mor and patrick Grim. Pattern and Chaos: New Images in the Semantics of Paradox. Nous, 25(1991), 659-693

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