Conrad Kuck - Intuitionistic Set Theory
or How to construct semi-rings. Part IV
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The logical problem is an old problem. Leibniz developed a „mathesis universalis“, which he estimated to be the Logic of sciences. His approach was rational calculable. Frege took Leibniz‘s ideas and prepared a logic, which was composed by nitions.
In Frege‘s Logic the calculation with numbers plays an essential role. Frege thought that the arithmetic, which was known in his time, is a basis for a logic.
Finally David Hilbert continued the work by Leibniz-Frege. He tried to prove the consistency of mathematics by his predicate calculus. Hilbert worked with finite, decidable, mathematical procedures, as the author does.
Between the first and second volume of Hilbert‘s predicate calculus Kurt Gödel published his two incomplete propositions. He showed that the formalistic proofs by Hilbert cannot solve the consistency problem on principle; Gödel‘s result caused the crisis of the foundations of mathematics, which has done away with the Intuitionistic Set Theory.
Intuitionistic Set Theory, Part I: ISBN 3-86064-616-8 Intuitionistic Set Theory, Part II: ISBN 3-86064-617-6 Intuitionistic Set Theory, Part III: ISBN 3-8300-0378-1 [...]Schlagworte
Informatik
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SchriftenreiheForschungsergebnisse zur Informatik
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ISSN1435-6260
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Band61