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Robert Boyle's self-flowing flask fills itself in this picture, but perpetual motion machines cannot exist.
The Pinocchio paradox is a variant of the Liar paradox

A paradox is a sentence in logic that cannot be true but also cannot be false. It is self-contradictory. Many famous problems of this kind exist.

Liar's paradox[change | change source]

A famous paradox is called the liar's paradox. It is the simple sentence "This sentence is a lie", or equivalently, "This statement is false."[1]

If the sentence is true, then it is a lie as it says. But if it is a lie, it cannot be true. A lie cannot also be a truth. So the sentence being true makes it a lie.

On the other hand, if the sentence is a lie, then it is not as it says: it is true. But that is just what the sentence says, which makes the content of the sentence true. So the sentence being a lie makes it true.

This paradox is not just in English, but in any language. It is true of mathematics as well. Paradox can never be removed from any symbol system that makes claims about itself.

Other examples[change | change source]

Another example is the statement that "there is no cabal". Only a cabal can know if there is no cabal, so this is either a guess, or, it is a cabal trying to pretend it does not exist.

Not all paradoxes are true logical paradoxes, since they can also be common-sense-defying statements that appear true.[2] Some famous examples of this kind of paradox include:

Quine's classification[change | change source]

Willard Van Orman Quine did a classification of paradoxes. He found three different types:[3][4]

Informal uses of "paradox"[change | change source]

A paradox can also arise in ethics. Assuming power over others may sometimes be required to protect them while diminishing their right to autonomy. This is an ethical dilemma but not a logical paradox.

Related pages[change | change source]

References[change | change source]

  1. "The Definitive Glossary of Higher Mathematical Jargon". Math Vault. 2019-08-01. Retrieved 2020-10-08.
  2. "Definition of PARADOX". Retrieved 2020-10-08.
  3. Quine, W.V. (1966). "The ways of paradox". The Ways of Paradox, and other essays. New York: Random House. ISBN 9780674948358.
  4. W.V. Quine (1976). The Ways of Paradox and Other Essays (REVISED AND ENLARGED ed.). Cambridge, Massachusetts and London, England: Harvard University Press.