Mathematics and the Divine seem to correspond to opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable? The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to be intimately related. Religious activities such as the building of temples, the telling of ritual stories, or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism, and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history.
Key Features
· Mathematics and man's quest for the Absolute
· A selective history highlighting key figures, schools, and trains of thought
· An international team of historians presenting specific new findings as well as general overviews
· Confronting and uniting otherwise compartmentalized information

lgli/Mathematics and the Divine - 2005 - Koetsier & Bergmans (Editors).pdf

lgrsnf/Mathematics and the Divine - 2005 - Koetsier & Bergmans (Editors).pdf

edited by T. Koetsier, L. Bergmans

Koetsier, Teun; Bergmans, Luc

Teun Koetsier; Luc Bergmans

Wolters Kluwer Legal & Regulatory U.S.

Aspen Publishers

United States, United States of America

Amsterdam, Oxford, Netherlands, 2005

Elsevier Ltd., Amsterdam, 2005

Ist ed, Amsterdam, 2005

December 30, 2004

https://lccn.loc.gov/2009659127

{"edition":"1","isbns":["0444503285","9780444503282"],"last_page":701,"publisher":"Elsevier","source":"libgen_rs"}

Bibliogr.
1

Cover
Half-title Page
Title Page
Copyright c Page
Dedicatory
Preface
List of Contributors
Contents
Introduction
The divine and mathematics
Three periods: The pre-Greek period, the Pythagorean-Platonic period and the period of the Scientific Revolution and its aftermath
The pre-Greek period and the ritual origin of mathematics
The Pythagorean-Platonic period
The Scientific Revolution and its aftermath
References
Chinese Number Mysticism
Introduction
The Hetu Diagram and the Luoshu Chart
The system of the Yijing (Book of Changes)
Daoist liturgy
Mysticism in the Chinese magic square
Popular beliefs in number mysticism and conclusions
Bibliographical comments
References
Derivation and Revelation: The Legitimacy of Mathematical Models in Indian Cosmology
Indian science, Indian religion: ``Orientalist'' and ``post-Orientalist'' views
The Puranas
The siddhantas
Contradiction and concession
The quest for non-contradiction
The status of siddhantas in the nineteenth century
Mathematical models in siddhantas
Conclusion
Bibliographical notes
References
The Pythagoreans
Introduction
Pythagoreanism in Plato and Aristotle
Pythagoreanism: some evidence from the Pythagoreans
Mathematics and the divine in the Pythagoreans: a suggestion
Notice for further reading
References
Mathematics and the Divine in Plato
Preliminary remarks
Introduction
The Timaeus
The Republic
Conclusion
Appendix A. The division of the stuff of the world soul (Timaeus 35b-36b)
References
Nicomachus of Gerasa and the Arithmetic Scale of the Divine
Introduction
Theologoumena Arithmetica
References
Geometry and the Divine in Proclus
Philosophy as divinisation
Mathematics in the divinisation of human nature
The nature of mathematical science
The metaphysics of geometry
St. Sophia: a geometry of the divine?
Bibliographical note
Religious Architecture and Mathematics During the Late Antiquity
Introduction
Religious architecture and heavenly measurements
Religious architecture and geometrical measurements
The building in its Earth-Heaven dialectic, or the circle above the square
References
The Sacred Geography of Islam
Introduction
The dichotomy of science in Islamic civilisation
The sacred geography of the legal scholars
The sacred geography of the scientists
The orientation of mosques and Islamic cities
Concluding remarks
References
``Number Mystique'' in Early Medieval Computus Texts
Introduction
The shape and scope of computus
Computus as ratio numerorum: the Irish computus of ca. 658
Computus as ratio temporum: Bede's revision of computistical ``number mystique''
Byrhtferth's choices
Is the Universe of the Divine Dividable?
The sefirotic concept of Divinity developed in response to philosophy and rational theology
Eyn-sof, the perfectly unknowable origin of the sefirot
The struggle between mat]PlotinusPlotinus' God and the God of the Bible
Thought and Will in zoharic and pre-zoharic literature
The relations between Eyn-sof and the sefirot; the One and the multiple; otherness and immanence
The origin of the term sefirot. A presentation of the nomenclature
Lights and colours
The unbreakable dynamic unity governing the sefirot and respected in prayer
References
Mathematics and the Divine: Ramon Lull
Introduction
The arbor elementalis
Lull's dynamic understanding of reality
The disciplines as productive arts
Geometry as an ``art''
Conclusion
References
Odd Numbers and their Theological Potential. Exploring and Redescribing the Arithmetical Poetics of the Paintings on the Ceiling of St. Martin's Church in Zillis
Introduction: displaying the method
An anatomical description of the ceiling
A theological imagination of odd numbers
A zoomorphic and soteriological arithmetic
The cross as cosmic sign and structure
The celestial cross and its function as odd-number Eon
Swester Katrei and Gregory of Rimini: Angels, God, and Mathematics in the Fourteenth Century
How many angels can dance on the point of a needle?
The place of angels: Gregory of Rimini
God and the continuum: Gregory of Rimini
Bibliography Swester Katrei and Gregory of Rimini
Mathematics and the Divine in Nicholas of Cusa
Introduction
The place of mathematics in human knowledge and its symbolic value
The problem of squaring the circle
References
Michael Stifel and his Numerology
Introduction
The end of the world and the Antichrist
The autumn of the Middle Ages
Stifel's numerology in 1532
Stifel's mathematics
Concluding remarks
References
Between Rosicrucians and Cabbala-Johannes Faulhaber's Mathematics of Biblical Numbers
Introduction
Pyramidal numbers and the Bible
Gog and Magog
Word calculus and signs
The Rosicrucian movement
The comet of 1618
Pyrgoidal numbers
Mathematics and the Divine: Athanasius Kircher
Biographical introduction
God and the rational foundation of music
The rules of the divine, combinatorial art
The world as God's organ
Universal science as an imitation of God's art
Mystical arithmetic
Mathematical theology
References
Galileo, God and Mathematics
Introduction
The mathematical sciences in early modern Europe
Galileo, God and mathematics
God and mathematics around Galileo
Concluding remarks
Selected bibliography
The Mathematical Model of Creation According to Kepler
Harmony and mathesis: the originality of Kepler
Mathematical ideas in God and creation
The limits of univocity
Colour Figures
The Mathematical Analogy in the Proof of God's Existence by Descartes
Introduction: Descartes' plan
Mathematical truth as an example
The ontological proof of God's existence
Arnauld's criticism: Descartes proof is circular
Truth and existence
Conclusion: Descartes' God and Pascal's God
References
Pascal's Views on Mathematics and the Divine
Introduction
Characteristics of God
God's Salvation-Plan
Heart and reason
The Wager argument (418)
Mathematical aspects of presentation
Conclusion
References
Spinoza and the Geometrical Way of Proof
Spinoza's time
The Jews in the Netherlands
Descent and youth
Influences
Interpretation
The mathematical way of reasoning
Social philosophy
Living nature
Summum bonum
References
John Wallis (1616-1703): Mathematician and Divine
The controversy with Thomas Hobbes
Wallis' defence of the Trinity
Mathematics and calendar reform
An Ocean of Truth
In search of ultimate truth
Natural philosophy and mathematical principles
Anticartesianism: passive matter and active principles
Prisca theologia and prisca sapientia
Prophecy and comets
Prisca geometria and fluxions
References
God and Mathematics in Leibniz's Thought
Introduction
The best of all possible worlds
The binary system and creation
A staircase leading to God
The existence of God
Concluding remark
References
Berkeley's Defence of the Infinite GodGod in Contrast to the InfiniteInfinite in Mathematics
Berkeley's intent
God and infinity
Mathematical exactitude
The astounding results of modern mathematics
Bibliography
Leonhard Euler
Historical background
Life
Euler on religion
Physico-theological arguments in Euler
References
Georg Cantor
The mathematician Cantor
Short vita of Cantor
Mathematics and metaphysics
Mathematics and religion
Paradoxes and truth
Religious denomination
References
Gerrit Mannoury and his Fellow Significians on Mathematics and Mysticism
The search for unifying explanations
Convictions and ideologies
Does 2+2 = 4 and is there a God to an all-levelling relativist?
Frederik van Eeden on the foundational status of uncertainty
Gerrit Mannoury on the foundational status of uncertainty
Beyond psychological foundations of mathematics: the unobjectifiable subject and the idea of the unreligious separation of subject and object
Uncertainty and docta ignorantia. The role of negation in significs, intuitionism and theology
Johan J. de Iongh. Shared longing as the religious meaning of mathematical dialogue
References
Arthur Schopenhauer and L.E.J. Brouwer: A Comparison
Introduction
From Kant to Schopenhauer
Brouwer, the prophet
Life, art and mysticism
Schopenhauer and Brouwer: A comparison
The turn to mathematics
Brouwer compared to Gödel
Final remarks
Acknowledgement
References
On the Road to a Unified World View: Priest Pavel Florensky-Theologian, Philosopher and Scientist
Early years
Moscow University
Theological Academy
The pillar and ground of the truth
Concrete metaphysics
Church and revolution
Religious and scientific work
Enemy of the people
Conclusion
References
Husserl and Impossible Numbers: A Sceptical Experience
Introduction
Beyond Hume
Prelogical use of signs
Husserl's philosophical quest
Impossible concepts
Natural selection
Structural mathematics and categorial connections
De facto truth and the need of a science of science
References
Symbol and Space According to René Guénon
Life and work of René Guénon (Blois 1886 - Cairo 1951)
The symbolism of space
References
Eddington, Science and the Unseen World
Introduction
Astronomer and physicist
Quakerism
The problem
The four-dimensional world
Eddington's idealism
Mind stuff
Concluding remarks
Acknowledgement
References
The Divined Proportion
Introduction
No logo
Elemental truths
Potentia mirabilis
Stupendous effects
The blueprint of the universe
Unity in variety
Author Index
Subject Index

Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable ?<br>The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history.<br><br>· Mathematics and man's quest for the Absolute<br>· A selective history highlighting key figures, schools and trains of thought <br>· An international team of historians presenting specific new findings as well as general overviews<br>· Confronting and uniting otherwise compartmentalized information

2024-01-07