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Mathematics and Religion

Our Languages of Sign and Symbol

Javier Leach

Mathematics and Religion: Our Languages of Sign and Symbol is the sixth title published in the Templeton Science and Religion Series, in which scientists from a wide range of fields distill their experience and knowledge into brief tours of their respective specialties. In this volume, Javier Leach, a mathematician and Jesuit priest, leads a fascinating study of the historical development of mathematical language and its influence on the evolution of metaphysical and theological languages.

Leach traces three historical moments of change in this evolution: the introduction of the deductive method in Greece, the use of mathematics as a language of science in modern times, and the formalization of mathematical languages in the nineteenth and twentieth centuries. As he unfolds this fascinating history, Leach notes the striking differences and interrelations between the two languages of science and religion. Until now there has been little reflection on these similarities and differences, or about how both languages can complement and enrich each other.

So long as scientists and theologians use different languages, they will continue to experience difficulties in understanding one another. Mathematics and Religion will help bridge these gaps in understanding and elevate the dialogue to new, mutually enriching heights.

Preface            / vii

Chapter 1: Mathematics and Natural Sciences / 3

Chapter 2: Metaphysical Language / 16

Chapter 3: Origins of Mathematics / 35

Chapter 4: Euclid and Beyond / 44

Chapter 5: Dawn of Science / 55

Chapter 6: Mathematics Formalized / 67

Chapter 7: Propositional Logic / 93

Chapter 8: Language and Meaning / 106

Chapter 9: Science, Language, and Religion / 120

Appendix 1: Syntax of Propositional Logic / 133

Appendix 2: Semantics of Propositional Logic / 136

Appendix 3: Syntax of First-Order Logic / 139

Appendix 4: Semantics of First-Order Logic / 143

Appendix 5: Numerical Systems: Their Role in First-Order Logic / 147

Appendix 6: The Paradox of Russell / 154

Appendix 7: The Completeness of First-Order Logic / 156

Appendix 8: Jack’s Formula / 158

Appendix 9: Maria’s Formula / 160

Appendix 10: Example of an L1 Formalization / 161

Glossary / 163

Essay on Sources / 173

Index / 179