Thursday, 17 September 2015

Logic in Epimenides Paradox

The Epimenides paradox reveals a problem with self-reference in logic1.

Epimenides was a Cretan who made one immortal statement:
“All Cretans are liars.”
Now then, there are two statements that are part of the paradox:
  • Epimenides was a Cretan.
  • All Cretans are liars.

If we assume that Epimenides said "All Cretans are liars.", there are exactly four possible outcomes:
Epimenides was a CretanAll Cretans are liars
The Paradox is only visible if both statements be true. In all other cases, there is no paradox, and things go merrily on their way.

Thomas Fowler (1869) made a major mistake in determining the logic negation of the statement "All Cretans are liars.".

He assumed that the opposite of "All Cretans are liars." is "All Cretans speak the truth.". We, hardcore software designers, of course, do not fall for this trap.

The logical negation of "All Cretans are liars." is "Not all Cretans are liars." This, consequently, can be rewritten as "There is at least one Cretan who speaks the truth."


[1] Wikipedia - Epimenides Paradox

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