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Mathematics is often taught in a way that is boring and unnecessarily difficult. Like most people my mind goes blank when I face a page full of equations. Formal mathematics is important because people understand it and connect it with every day life but it is usually taught as if such connections were irrelevant.

By using English language explanations and connecting the mathematics to properties of computers it is hoped that this chapter and the next will be of interest to a wide audience. Parts require experience with mathematical expressions and the idea of a function at the level of high school algebra. It will be helpful but not essential to have had some computer programming experience.

Mathematics is taught as absolute truth. It is seen as fixed and immutable for all time. Yet Gödel proved in the 1930's that Mathematics cannot be captured in any finite system. Gödel's result suggests that mathematics is an inherently creative endeavor albeit one that can create absolute truth. This chapter and the next explain how this is possible. Gödel's result may be a key to understanding the creative evolution of consciousness.

Computer programs are used as a surrogate for logically determined process. The focus on them is not to suggest there is anything special about computers. Rather it is the nature of the universe that logic allows us to predict future events to a limited degree. It is that aspect of mathematics that has practical importance and computers are an accurate metaphor for a logically determined sequence of events in a potentially infinite universe.

- Mathematics and consciousness
- Logically determined unsolvable problems
- Formal logic
- Formal mathematics
- Axioms of Set Theory
- Axiom of extensionality
- Axiom of the empty set
- Axiom of unordered pairs
- Axiom of union
- Axiom of infinity

- Infinity
- Cardinal numbers
- Gödel's Incompleteness Theorem
- The Halting Problem

Completed
second draft of this book

PDF version
of this book

**Next:** Mathematics and consciousness **Up:** whatth
**Previous:** Extensions of consciousness **Contents**

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