Koetsier T., Bergmans L. (eds.) Mathematics and the Divine: A Historical Study

Elsevier Science, 2005. — 716 p. — ISBN 0-444-50328-5.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 isnt 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 Mans quest for the Absolute in the course of history.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 informationThe 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 aftermathChinese Number MysticismThe 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 commentsDerivation 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 SiddhantasBibliographical notesThe PythagoreansPythagoreanism in Plato and Aristotle
Pythagoreanism: some evidence from the Pythagoreans
Mathematics and the divine in the Pythagoreans: a suggestion
Notice for further readingMathematics and the Divine in Plato
Preliminary remarksThe Timaeus
The RepublicAppendix A. The division of the stuff of the world soul (Timaeus 35b-36b)Nicomachus of Gerasa and the Arithmetic Scale of the DivineTheologoumena ArithmeticaGeometry 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 AntiquityReligious architecture and heavenly measurements
Religious architecture and geometrical measurements
The building in its Earth-Heaven dialectic, or the circle above the squareThe Sacred Geography of IslamThe 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«Number Mystique» in Early Medieval Computus TextsThe 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 Plotinus' 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 prayerMathematics and the Divine: Ramon LullThe arbor elementalis
Lull's dynamic understanding of reality
The disciplines as productive arts
Geometry as an «art»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 CusaThe place of mathematics in human knowledge and its symbolic value
The problem of squaring the circleMichael Stifel and his NumerologyThe end of the world and the Antichrist
The autumn of the Middle Ages
Stifel's numerology in 1532
Stifel's mathematics
Concluding remarksBetween Rosicrucians and Cabbala-Johannes Faulhaber's Mathematics of Biblical NumbersPyramidal 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 theologyGalileo, God and MathematicsThe 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 GodPascal's Views on Mathematics and the DivineCharacteristics of God
God's Salvation-Plan
Heart and reason
The Wager argument (418)
Mathematical aspects of presentationSpinoza 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 bonumJohn 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 fluxionsGod and Mathematics in Leibniz's ThoughtThe best of all possible worlds
The binary system and creation
A staircase leading to God
The existence of God
Concluding remarkBerkeley'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 mathematicsLeonhard Euler
Historical background
Life
Euler on religion
Physico-theological arguments in EulerGeorg Cantor
The mathematician Cantor
Short vita of Cantor
Mathematics and metaphysics
Mathematics and religion
Paradoxes and truth
Religious denominationGerrit 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 dialogueArthur Schopenhauer and L.E.J. Brouwer: A ComparisonFrom 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
AcknowledgementOn 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 peopleHusserl and Impossible Numbers: A Sceptical ExperienceBeyond 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 scienceSymbol and Space According to René Guénon
Life and work of René Guénon (Blois 1886 - Cairo 1951)
The symbolism of spaceEddington, Science and the Unseen WorldAstronomer and physicist
Quakerism
The problem
The four-dimensional world
Eddington's idealism
Mind stuff
Concluding remarks
AcknowledgementThe Divined ProportionNo logo
Elemental truths
Potentia mirabilis
Stupendous effects
The blueprint of the universe
Unity in variety
Author Index
Subject Index