
Godel's Mistake: The Role of Meaning in Mathematics, Paperback/Ashish Dalela
✔ În stoc la elefant.ro
Vezi oferta la elefant.ro
✔ În stoc la elefant.ro
Vezi oferta la elefant.roDescription Why Is Mathematics Incomplete? Godel'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. Godel'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 Godel's Incompleteness and Turing's Halting Problem. How This Book Is Structured Chapter 1: Mechanizing Thought --provides an overview of mathematical, philosophical, linguistic and lo











