Jan von Plato Bücher

Focusing on Gerhard Gentzen's groundbreaking contributions to logic and proof theory, this volume explores his development of natural deduction and sequent calculus, as well as his resolution of Gödel's incompleteness results. It also highlights his dedication to Hilbert's proof theory before his tragic demise in a Prague prison. Jan von Plato provides a comprehensive overview of Gentzen's life and work, enriched by previously lost shorthand manuscripts, showcasing the evolution of his key ideas and insights into his intellectual brilliance.

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.

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.

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.

Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.