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    The set of true arithmetical sentences cannot be defined ... — Carmelics
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    Supports→The set of provable sentences in arithmetic and the set of true arithmetical sentences cannot coincide

    The set of true arithmetical sentences cannot be defined in the language of arithmetic

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    The set of provable sentences in arithmetic and the set of true arithm...91%There must be true arithmetical sentences which are not provable89%The set of sentences provable in arithmetic can be defined in the lang...89%Arithmetical truth cannot be defined in arithmetic81%

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    SEP: goedel-incompleteness
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    Be that as it may, it seems that Gödel actually arrived at the first exact observations about incompleteness via a different route, during his attempts to contribute to Hilbert’s program, and not to undermine it (see Dawson 1997: Ch. IV). Namely, in 1930, Gödel made an effort to advance Hilbert’s program by attempting to prove the consistency of analysis (or, second-order arithmetic) with the resources of arithmetic, and thus reduce the consistency of the former to the consistency of the latter.

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