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Math Help - Curry's paradox

  1. #1
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    Curry's paradox

    Curry's paradox in natural language:
    "If this sentence is true, then Santa Claus exists."

    Proof (in natural language)
    Suppose the sentence is true. Then, since it is true, and it says that if it's true, Santa Claus exists, we can conclude that Santa Claus exists. This step follows from the technique of natural deduction known as conditional derivation.

    So if the sentence is true, then Santa Claus exists which is exactly what the sentence states. Therefore the sentence is true and Santa Claus must exist.


    I don't understand the 2nd paragraph. I know if we can show that the sentence is true, then we may conclude Santa Claus exists. But how do we show that the sentence is true in the first place????

    Thanks, for those who helped
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    Quote Originally Posted by acc100jt View Post
    Curry's paradox in natural language:
    "If this sentence is true, then Santa Claus exists."

    Proof (in natural language)
    Suppose the sentence is true. Then, since it is true, and it says that if it's true, Santa Claus exists, we can conclude that Santa Claus exists. This step follows from the technique of natural deduction known as conditional derivation.

    So if the sentence is true, then Santa Claus exists — which is exactly what the sentence states. Therefore the sentence is true and Santa Claus must exist.


    I don't understand the 2nd paragraph. I know if we can show that the sentence is true, then we may conclude Santa Claus exists. But how do we show that the sentence is true in the first place????

    Thanks, for those who helped
    It may help readers of this post to know the quotation is from Curry's paradox - Wikipedia, the free encyclopedia.
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    "How quaint the ways of paradox."
    W. S. GILBERT
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