Gödel's Mistake: The Role of Meaning in Mathematics

Gödel's Mistake: The Role of Meaning in Mathematics
ISBN-10
1453811354
ISBN-13
9781453811351
Category
Mathematics
Pages
184
Language
English
Published
2010-09-14
Publisher
Createspace Independent Pub
Author
Ashish K. Dalela

Description

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.

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