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Author: Rod Adams Publisher: Docent Press ISBN: 0983700400 Category : Mathematics Languages : en Pages : 312
Book Description
Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.
Author: Rod Adams Publisher: Docent Press ISBN: 0983700400 Category : Mathematics Languages : en Pages : 312
Book Description
Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.
Author: Roman Murawski Publisher: Springer Science & Business Media ISBN: 9401728666 Category : Philosophy Languages : en Pages : 416
Book Description
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
Author: Hans Hermes Publisher: Springer ISBN: 9783642461804 Category : Mathematics Languages : en Pages : 0
Book Description
Once we have accepted a precise replacement of the concept of algo rithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algo rithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathe matics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms.
Author: Rod Adams
Author: Rod Adams
Author: Hartley Rogers (Jr.)
Author: Roman Murawski
Author: Stephen Cole Kleene
Author: Hans Hermes
Author: R. G. Adams
Author: Nigel Cutland
Author: Rózsa Péter
Author: 
Author: Rózsa Péter