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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
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The true reason for the incompleteness of formal systems
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The true source of the incompleteness attaching to all formal systems of mathematics, is to be found — as will be shown in Part II of this essay — in the fa …