The Baffling Pinocchio Paradox

Missing square paradox

What is a Paradox?

 

 

A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition. The term is also used for an apparent contradiction that actually expresses a non-dual truth such as two true sentences which put together seem incompatible as both being true . Typically however, quoted paradoxical statements do not imply a real contradiction and the puzzling results can be rectified by demonstrating that one or more of the premises themselves are not really true, a play on words, faulty and/or cannot all be true together. But many paradoxes, such as Curry’s paradox, do not yet have universally accepted resolutions. The word paradox is often used interchangeably with contradiction. Literary and other artistic uses of paradoxes imply no contradiction and may be used to describe situations that are ironic. Sometimes the term paradox is used for situations that are merely surprising.

The Liar Paradox

The following version is the version which we refer to as the liar paradox.

Consider the statement in the following box:

THIS SENTENCE IS FALSE

Is that sentence true or false? If it is false then it is true, and if it is true then it is false…

The following version of the liar paradox was first proposed by the English mathematician P E B Jourdain in 1913. It is sometimes referred to as “Jourdain’s Card Paradox”. We have a card on one side of which is written:

(1) THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE

Then you turn the card over, and on the other side is written:

(2) THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE

… Another popular version of the liar paradox is given by the following three sentences written on a card.

(1) THIS SENTENCE CONTAINS FIVE WORDS (2) THIS SENTENCE CONTAINS EIGHT WORDS (3) EXACTLY ONE SENTENCE ON THIS CARD IS TRUE

What is Logic?

Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science.It examines general forms which arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic figures in most major areas: epistemology, ethics, metaphysics. In mathematics, it is the study of valid inferences within some formal language.

[WIKIPEDIA]