This volume represents one of the final output of the collaborative project funded by the ANR and directed by Gabriella Crocco on Kurt Gödel's Nachlass.It is intended as the beginning of a new stage ...of research in interpreting Kurt Gödel's philosophy in relation to his scientific work. It is more than a collection of essays on Gödel. It is in fact the product of a long enduring international collaboration on Kurt Gödel's Philosophical Notebooks. New and significant material has made accessible to a group of experts, on which they rely for their article.
Kurt Gödel, el matemático del teorema de completez, de los teoremas de incompletez y de la prueba de la consistencia del axioma de elección y la hipótesis generalizada del continuo, fue lector de ...Edmund Husserl. ¿Este hecho se explica por un interés esporádico?, ¿Husserl, antes que Gödel, había concentrado esfuerzos en un proyecto filosófico de fundamentación?, ¿estuvo Husserl tan cerca de una tal fundamentación universal del conocimiento como para haber motivado el interés de Gödel? En este trabajo se evidencia que la primera pregunta queda descartada y es sobre las respuestas a la segunda y tercera interrogación sobre las que versa la comprensión de un Kurt Gödel como estudiante de la Fenomenología de Edmund Husserl. Palabras clave: Edmund Husserl, Kurt Gödel, Matemáticas, Fenomenología. Kurt Godel, the mathematician of the completeness theorem, of the incompleteness theorems and of the consistency test of the axiom of choice and the generalized hypothesis of the continuum, was a reader of Edmund Husserl. ?Is this fact explained by sporadic interest? Husserl, before Godel, had concentrated efforts on a philosophical project of foundation? Was Husserl so close to such a universal foundation of knowledge as to have motivated the interest of Godel? In this work it is evident that the first question is discarded and it is about the answers to the second and third questions about the understanding of a Kurt Godel as a student of the phenomenology of Edmund Husserl. Keywords: Edmund Husserl, Kurt Godel, Mathematics, Phenomenology.
This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number ...theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.
Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims ...arising from Gödel's arguments.Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chaptersDiscusses interpretations of the Theorem made by celebrated contemporary thinkersSheds light on the wider extra-mathematical and philosophical implications of Gödel's theoriesWritten in an accessible, non-technical style.
Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I ...contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincaré and Frege.
Kurt Gödel Feferman, Solomon; Parsons, Charles; Simpson, Stephen G
04/2010, Letnik:
v.Series Number 33
eBook
Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized ...arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.
The P=NP question is one of the great problems of science, which has intrigued computer scientists and mathematicians for decades. Despite the abundant research in theoretical computer science ...regarding the P=NP question, it has not been solved. The P=NP Question and Gödel`s Lost Letter covers historical developments (including the Gödel`s Lost letter), the importance of P=NP and the future of P=NP. This guide is also based on a new blog by the author, located at http://rjlipton.wordpress.com. Jin-Yi Cai, an Associate Professor in computer science at the University of Wisconsin remarks `I think it is the single most interesting web blog I have seen on related topics. He has a great insight and wit and beautiful way to see things and explain them.` Richard DeMillo, a professor in computer science at Georgia Tech remarks, `This is a much needed treatment of great open problem computing.` The P=NP Question and Gödel`s Lost Letter is designed for advanced level students and researchers in computer science, and mathematics as a secondary text and reference book. Computer programmers, software developers and IT professionals working in the related industry of computer science theory, will also find this guide a valuable asset. TOC:Part I A Prologue.- A Walk In the Snow.- Part II On the P=NP Question.- Algorithms: Tiny Yet Powerful.- Is P=NP Well Posed?.- What Would You Bet?.- What Happens What P=NP Is Resolved?.- NP Too Big or P Too Small?.- How To Solve P=NP?.- Why Believe P Not Equal To NP?.- A Nightmare About SAT.- Bait and Switch.- Who`s Afraid of Natural Proofs?.- An Approach To P=NP.- Is SAT Easy?.- SAT is Not Too Easy.- Ramsey`s Theorem and NP.- Can They Do That?.- Rabin Flips a Coin.- A Proof We All Missed.- Barrington Gets Simple.- Exponential Algorithms.- An EXPSPACE Lower Bound.- Randomness has Unbounded Power.- Counting Cycles and Logspace.- Ron Graham Gives a Talk.- An Approximate Counting Method.- Easy and Hard Sums.- How To Avoid O-Abuse.- How Good is The Worst Case Model?.- Savitch`s Theorem.- Adaptive Sampling and Timed Adversaries.- On The Intersection of Finite Automata.- Where are the Movies?.- Part III On Integer Factoring.- Factoring and Factorials.- BDD`s.- Factoring and Fermat.- Part IV On Mathematics.- A Curious Algorithm.- Edit Distance.- Protocols.- Erdõs and the Quantum Method.- Amplifiers.- Amplifying on the PCR Amplifier.- Mathematical Embarrassments.- Mathematical Diseases.- Mathematical Surprises.- A Gödel Lost Letter.- Index.
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