Individual km#application_of_techniques_of_formal_logic_to_mathematics
  >part:  logicism  pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to logic. The various attempts to carry this out met with a series of failures, from the crippling of Frege's project in his Grundgesetze by Russell's Paradox, to the defeat of Hilbert's Program by Gödel's incompleteness theorems; however, every rigorously defined mathematical theory can be exactly captured by a first-order logical theory; Frege's proof calculus is enough to describe the whole of mathematics, though not equivalent to it
  >part of:  mathematical_logic__symbolic_logic__metamathematics__metamathematic
     >part of:  formal_logic
        >part of:  logic.philosophy  the branch of philosophy that analyzes inference
           >part of:  philosophy  the rational investigation of questions about existence and knowledge and ethics
     >part of:  abstract_algebra

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