Spiritual reading covers topics like God, ultimate truth, love, faith, and happiness.
They are metaphysical concepts which are in the world of infinity.

If the topic is for everyday life, natural languages will be good.
But natural languages are not proper for the infinity world.

This problem can be solved by formal languages which can manage infinities.
This book introduces some mathematical backgrounds to the formal languages and some key concepts in religions.

The Kingdom of God and the Heavenly Kingdom are the same and distinct.
If you cannot distinguish, you do not clearly understand Judaism or Christianity.

Nirvana and Tao are the same and distinct.
If you cannot distinguish, you do not clearly understand Buddhism or Taoism

인하대학교 공학사, KAIST 공학석사, Univ. of Ghent 공학박사, 인하대학교 명예교수

Preface ⅳ

1. Languages for Spiritual Reading 1
2. Modern Algebra 6
2.1 Why Modern Algebra? 6
2.2 Equivalence. Congruence 15
2.3 Group Homomorphism 23
3. Set Theory 32
3.1 Set. Axioms 32
3.2 Well-Ordered Sets. Ordinals 40
3.3 The Axiom of Choice. Cardinals 46
4. Mathematical Logic 49
4.1 Syntax. Semantics 49
4.2 First-Order Languages 59
4.3 Filters. Incompleteness 65
5. Religion. Ultimate Truths 72
5.1 Judaism 76
5.2 Christianity 82
5.3 Taoism 88
5.4 Buddhism 93
5.5 Discussions 100
6. Questions and Answers 103
6.1 Mathematical Background 103
6.2 Some Concepts in Religion 109

References 115