Godel´s Mistake: The Role of Meaning in Mathematics
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What makes humans intelligent? Can machines be intelligent like humans? These questions are central to an emerging interdisciplinary science positioned at the cross roads of physics, mathematics, psychology, neuroscience and computing. While neuroscience aims to reduce the mind to the brain (and ultimately to physics and mathematical laws), two key mathematical results - Gödel's incompleteness and Turing's Halting Problem - are often cited reasons for why machines cannot emulate the human mind. The key thing that separates minds from machines is the meaning processing capacity in the minds that does not exist in machines. But what is meaning in the mind? How do material minds get meanings? Gödel's Mistake connects Gödel's and Turing's theorems to the question of meaning. It shows that human cognition distinguishes between being, knowing and doing as three ways of counting although mathematics only uses one way. Gödel's proof results from confusion between a thing and its knowledge, or being and knowing. Turing's proof comes from confusion between a thing and its effects, or being and doing. The distinction between being, doing and knowing exists in ordinary language, although not in mathematics. Minds that use ordinary language are therefore free of incompleteness and incomputability whereas machines that use mathematics aren't. If machines could be programmed in ordinary language - meaning if they could distinguish between being, knowing and doing - then they would be intelligent like humans. The distinctions will also make mathematics consistent, complete and computable. Paperback, Label: CreateSpace Independent Publishing Platform, CreateSpace Independent Publishing Platform, Product group: Book, Published: 2010-09-14, Studio: CreateSpace Independent Publishing Platform, Sales rank: 7420235.

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Gödel's incompleteness theorem is a foundational result in mathematics that proves that any axiomatic theory of numbers will be either inconsistent or incomplete. Turing's Halting problem is a foundational result in computing proving that computers cannot know if a program will halt. Gödel's Mistake connects these theorems to the question of meaning. The book shows that the proofs arise due to category confusions between names, concepts, things, programs, algorithms, problems, etc. The book argues that these problems can be solved by introducing ordinary language categories in mathematics. WHERE THE SOLUTION LIES The solution to the problem, the author argues, requires a new approach to numbers where numbers are treated as types rather than quantities. To view numbers as types requires a foundational shift in which objects are constructed from sets rather than sets from objects. Since sets denote concepts, this shift implies that objects are created from concepts. This also changes our view of space-time from linear and open to hierarchical and closed. In this hierarchical description, objects are symbols of meaning, rather than physical things. The author calls this theory the Type Number Theory (TNT) and shows that the type view of numbers is free of Gödel's Incompleteness and Turing's Halting Problem. HOW THIS BOOK IS STRUCTURED Chapter 1: Mechanizing Thought-provides an overview of mathematical, philosophical, linguistic and logical issues that preceded Gödel's and Turing's results and shows that the problems encountered in mathematics have a wider undercurrent extending into other areas of science. Chapter 2: Gödel's Mistrick-discusses Gödel's Incompleteness Theorem and Turing's Halting problem and shows how their proofs rest on category mistakes. The chapter also connects the theorems to the issues of sentence and program meaning, with implications for fields such as artificial intelligence and others. This sets up the motivation for alternative views about nu.

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Godel's Mistake: Paperback: Shabda Press: 9788193052310: 17 Nov 2014.

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Godels-Mistake~~Ashish-Dalela, Godel's Mistake: The Role of Meaning in Mathematics, Paperback.

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CreateSpace, 2010-09-14. Paperback. Good.

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Von Händler/Antiquariat, ExtremelyReliable, TX, Richmond, [RE:3].
Paperback.