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Trail: paradox




An absurd truth. Hence, the derivation of an unacceptable conclusion from apparently unquestionable premises by an apparently valid inference. Resolution of a paradox requires that we abandon at least one of the premises, refute the process of inference, or somehow learn to live with the unpalatable result. Zeno used paradoxes to demonstrate the impossibility of motion. Modern semantic paradoxes (such as the liar and the term “heterological”) arise from difficulties inherent in self-reference.

The Liar Paradox is an argument that arrives at a contradiction by reasoning about a Liar Sentence. The classical Liar Sentence is the following self-referential sentence:

(1) This sentence is false.

Part One
The Paradox of Self-Amendment
The St. Petersburg Paradox

The St. Petersburg game is played by flipping a fair coin until it comes up tails, and the total number of flips, n, determines the prize, which equals $2n. Thus if the coin comes up tails the first time, the prize is $21 = $2, and the game ends. If the coin comes up heads the first time, it is flipped again. If it comes up tails the second time, the prize is $22, = $4, and the game ends. If it comes up heads the second time, it is flipped again. And so on.