Prologue

2017 ◽  
Author(s):  
Jan von Plato
Keyword(s):  
Information Society ◽  
Formal Languages ◽  
Foundations Of Mathematics ◽  
Direct Path ◽  
John Von Neumann ◽  
Von Neumann ◽  
Alan Turing ◽  
Kurt Gödel

It may sound paradoxical, but if around 1930 Kurt Gödel had not thought very deeply about the foundations of mathematics, there would be no information society in the form in which we have it today. Gödel’s solitary work was the single most important factor in the development of precise theories of formal languages, ones that through the coding he invented could be handled by a machine. Likewise, his work led to precise notions of algorithmic computability from which a direct path led to the first theoretical ideas of a computer, in the work of Alan Turing in 1936 and John von Neumann some years later....

Von Neumann, Gödel and Complexity Theory

2010 ◽  
Vol 16 (4) ◽  
pp. 516-530 ◽  
Author(s):  
Alasdair Urquhart
Keyword(s):  
Complexity Theory ◽  
Decision Procedure ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
John Von Neumann ◽  
Von Neumann ◽  
Complexity Of Algorithms ◽  
Kurt Gödel ◽  
The 1960S ◽  
Separate Discipline

AbstractAround 1989, a striking letter written in March 1956 from Kurt Gödel to John von Neumann came to light. It poses some problems about the complexity of algorithms; in particular, it asks a question that can be seen as the first formulation of the P = ? NP question. This paper discusses some of the background to this letter, including von Neumann's own ideas on complexity theory. Von Neumann had already raised explicit questions about the complexity of Tarski's decision procedure for elementary algebra and geometry in a letter of 1949 to J. C. C. McKinsey. The paper concludes with a discussion of why theoretical computer science did not emerge as a separate discipline until the 1960s.

scholarly journals Observações sobre a meta final do modo de fazer filosofia de Ludwig Wittgenstein

2019 ◽  
Vol 22 (3) ◽  
pp. 411-438
Author(s):  
Gustavo Augusto Fonseca
Keyword(s):  
Ludwig Wittgenstein ◽  
Basic Concept ◽  
Foundations Of Mathematics ◽  
Newtonian Physics ◽  
Alan Turing ◽  
Kurt Gödel ◽  
Perfect Model ◽  
Proposal A ◽  
Heinrich Hertz

In The Principles of Mechanics, physicist Heinrich Hertz argues that instead of replying to the question “what is force?” like physicists and philosophers had been doing unsuccessfully, Newtonian physics should be reformulated without considering “force” a basic concept. Decades after Hertz’s book, Ludwig Wittgenstein considered the physicist’s proposal a perfect model for how philosophical problems should be solved, to the point that he made it the foundation of his way of doing philosophy. This article addresses Wittgenstein’s way of doing philosophy, while it also proposes the reason why he failed in solving the philosophical problems — as did Hertz in his project on reformulating Newtonian physics without considering the concept “force”. And to illustrate Wittgenstein’s failure, it examines his disputes with mathematicians Kurt Gödel and Alan Turing on the foundations of mathematics.

scholarly journals A számítóközpontoktól a digitális esélyegyenlőségig. Az NJSZT első 50 éve

2019 ◽  
Vol 18 (3-4) ◽  
pp. 139
Author(s):  
Gábor Képes
Keyword(s):  
Information Society ◽  
Digital Inclusion ◽  
John Von Neumann ◽  
Non Profit ◽  
Von Neumann ◽  
Hungarian Society

Idén fél évszázada alakult meg a Neumann János Számítógép-tudományi Társaság (NJSZT). Mostani tanulmányunk azt mutatja be, hogyan nyílt ki az NJSZT és vált az információs társadalom kérdéseinek egyik legfontosabb nonprofit szereplőjévé – s közben hogyan hatott a magyar társadalomra, amely iránt felelős elkötelezettséget vállalt. --- From Computer Centres to Digital Inclusion: the First Fifty Years of the John von Neuamnn Computer Society The John von Neumann Computer Society (NJSZT) was founded half a century ago this year. This study shows how NJSZT has opened up and became one of the most important non-profit actors in information society issues – and at the same time how it has influenced the Hungarian society to which it committed itself. Keywords: NJSZT, Computer centres, history, digital inclusion

The Great Formal Machinery Works

2017 ◽  
Author(s):  
Jan von Plato
Keyword(s):  
Nineteenth Century ◽  
Programming Languages ◽  
Algebraic Logic ◽  
Formal Languages ◽  
Formal Proof ◽  
Boolean Logic ◽  
Digital Revolution ◽  
Von Neumann ◽  
Alan Turing ◽  
History Of

The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. This book draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. The book examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. The book shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. The book describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, this book is essential reading for students and researchers in logic, mathematics, and computer science.

scholarly journals ARTIFICIAL INTELLIGENCE AND NEURAL NETWORKS THE LEGACY OF ALAN TURING AND JOHN VON NEUMANN

2014 ◽  
pp. 10-20
Author(s):  
Heinz Muhlenbein
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Transfer Learning ◽  
State Of The Art ◽  
Machine Intelligence ◽  
Probabilistic Logic ◽  
John Von Neumann ◽  
Von Neumann ◽  
Alan Turing ◽  
Essential Components

The work of Alan Turing and John von Neumann on machine intelligence and artificial automata is reviewed. Turing's proposal to create a child machine with the ability to learn is discussed. Von Neumann had doubts that with teacher based learning it will be possible to create artificial intelligence. He concentrated his research on the issue of complication, probabilistic logic, and self-reproducing automata. The problem of creating artificial intelligence is far from being solved. In the last sections of the paper I review the state of the art in probabilistic logic, complexity research, and transfer learning. These topics have been identified as essential components of artificial intelligence by Turing and von Neumann.

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