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Jan von Plato

    Chapters from Gödels Unfinished Book on Foundational Research in Mathematics
    Can Mathematics Be Proved Consistent?
    Portrait of Young Gödel
    • 2024

      Portrait of Young Gödel

      Education, First Steps in Logic, the Problem of Completeness

      • 320 Seiten
      • 12 Lesestunden

      Set against the backdrop of 1928, this book chronicles Kurt Gödel's groundbreaking journey in logic, highlighting his rapid rise to fame through his resolution of a pivotal problem in quantificational logic. By 1929, he extended his findings to arithmetic, leading to his renowned incompleteness theorem published in 1931. This theorem is celebrated as one of the 20th century's most significant scientific achievements, profoundly influencing formal language theories and algorithmic computability, which are foundational to the emergence of the information society.

      Portrait of Young Gödel
    • 2022

      The book features English translations of Gödel's significant works on logicism, antinomies, and the foundations of pure logic, along with outlines for a chapter on metamathematics. It includes a comprehensive collection of his reading notes, offering insights into his thought process and the development of his ideas in mathematical logic. This volume serves as a valuable resource for understanding Gödel's contributions to the field.

      Chapters from Gödels Unfinished Book on Foundational Research in Mathematics
    • 2020

      Can Mathematics Be Proved Consistent?

      Gödel's Shorthand Notes & Lectures on Incompleteness

      • 276 Seiten
      • 10 Lesestunden

      Kurt Gödel's groundbreaking work in 1931 revealed profound limitations in formal mathematical systems, particularly through his first incompleteness theorem. He demonstrated that in any sufficiently complex system containing elementary arithmetic, there exist true statements that cannot be proven within that system. This challenged the notion that all mathematical truths could be derived from a finite set of rules. Gödel's insights not only transformed mathematics but also raised critical questions about the consistency and completeness of mathematical proofs, leading to further exploration in the field.

      Can Mathematics Be Proved Consistent?