Liar’s Paradox

Consider the Liar sentence ‘This very sentence is false’. Is it true, false, neither or both?

From Wikipedia: Liar’s Paradox

This video is part of a series of work by High Tech High Media Arts 12th grade students in the curated exhibition, “Illuminated Mathematics.” Students were ask to produce a creative digital media piece about math in history, culture and the applied arts to heighten awareness of the beauty of math in our world.

IN POPULAR CULTURE : Star Trek

In the episode “I, Mudd” (Episode #41) of the original Star Trek series, Captain Kirk and Harry Mudd use the liar paradox to confuse and thus incapacitate an android who is holding the landing party captive.

One imagines a multiple choice questionnaire, with the following curious entry:

* This sentence is false.
The starred sentence is
a) True
b) False
c) All of the above
d) None of the above

* This sentence is not true.
The starred sentence is
a) True
b) False
c) All of the above
d) None of the above

Problems become yet more acute with a third questionnaire:

* This sentence is not true.
The starred sentence is
a) True
b) Not True
c) All of the above
d) None of the above.

The conclusions may surprise you. Find out more at “Two Versions of the Liar Paradox”

But I still have a problem with this presentation/explanation of the Liar’s Paradox problem.

Do you see it?

About benvitalis

math grad - Interest: Number theory
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