An accidental blog

"If God is sovereign, then his lordship must extend over all of life, and it cannot be restricted to the walls of the church or within the Christian orbit." Abraham Kuyper Common Grace 1.1.

Sunday, 18 March 2012

Neo-Calvinism and the French Revolution Conference, Paris August 2012

The French Revolution was the scene of much intellectual and social upheaval. Its impact touched a wide range of subjects: the relationship of the church to the state, social relationships, science, literature, fashion, philosophy and theology. Although the French Revolution’s momentum was felt across Europe and North America, it met a particularly interesting response in the Netherlands, at that time the scene of a burgeoning neo- Calvinist movement. In that context, the likes of Groen van Prinsterer, Abraham Kuyper and Herman Bavinck responded to the French Revolution’s ideals and influence in a variety of intellectual and practical ways.

This conference will focus on the historical and theological aspects of this neo-Calvinist response to the French Revolution.

Call for Papers

The conference organisers welcome proposals for short papers. Proposals (approximately 300 words) should be sent to by May 4th. Conference papers will be in English.


The conference registration fee is €40. Conference places must be reserved by email ( by May 30th.

Location and Accommodation
The conference will be held at:
The Library The American Church in Paris 65 quai d’Orsay 75007 Paris France
Participants are responsible for finding their own accommodation. The organisers suggest the Adveniat Youth Hostel ( as a well-priced, comfortable and convenient option.

For further details see here.

Music for a Sunday morning: EST + Pat Metheny

Friday, 16 March 2012

Christian mathematicians on

Over at the God and math website, maintained by Josh Wilkinson, I have begun a sereis on Christin mathematicians.

Appeared so far are short biographies on:

Soon to appear are:

Thursday, 15 March 2012

Abraham Kuyper from George H. Dryer History of the Christian Church Vol. V

Abraham Kuyper, born in 1837, is the other evangelical leader in Holland. He was educated at Leyden - under Scholten and Kuenen. He knew from personal experience the lack of vitality and spiritual power in their teachings, and he represents the strongest reaction against them. This came from his finding, studying, and winning a prize for an edition of the works of John a Lasco, the Polish Reformer of the sixteenth century. From that time he has been a sturdy Calvinist. As pastor at Beest and Utrecht he stood by the side of Groen as leader of the Old Reform party in the State Church from 1869. On Groen's death in 1876, he succeeded to the leadership of the party. He became editor of the Standard in 1870, and later founded the Herald.

Since 1874 he has been Deputy in the National Legislature. In 1878 he founded a Union to support free Christian schools. It has an income of $50,000 a year. In 1880 he founded a free university, independent of the State. Preachers who followed him were excluded from the National Synod; but in 1885 one hundred and fifty Churches followed the example of Amsterdam in welcoming these preachers as their pastors. They have their independent organization but there is no formal breach with the State Church.

These Churches, under the lead of Kuyper, have entered into an alliance with the Roman Catholics. Their point of contact is religious instruction in the schools of the land. The opening of the new century saw this leader of the Calvinistic reaction against the naturalism and Free Religion of Scholten and Kuenen the Prime Minister of Holland.

Sunday, 11 March 2012

Michael Schutt: Vocation the Mask of God

Mike Schutt on Vocation the mask of God

Schutt looks at why Luther called vocation the 'mask of God' and how we can be disciples over all of life.

How do we know what we are called to? "Listen to the Caller. It's not about being fulfilled or self-actualisation. It's about following a Caller".

Well worth checking out.
Mike blogs regularly here.

Music for a Sunday morning

SUSANNA - FREEZE from TRÆR on Vimeo.

Friday, 9 March 2012

More of Kuyper's children

 Jan Frederik Hendrik Kuyper 1866-1933
Fredrick moved to Michigan and attended Hope College. He became a dentist and practiced dentistry in the Badung and Padang in the East indies.

Abraham Kuyper Jr. b. 1872
Married Miss H. Van Oort in March 1899. He was a Reformed Church pastor in Makkum (1899-1906), Vlissingen (1906-1910) and Rotterdam (1910-1939).
He wrote a book on Johannes Maccovius (Leyden: D. Donner, 1899), a Polish reformed theologian.

 Hendrika Johanna Kuyper (1875-1948)
Became a nurse.

Catharina Maria Eunice Kuyper (1876-1955)
A nurse and became director of nursing at the Vrije Universiteit (1927-1932).
She wrote a short piece on her father Abraham Kuper’s  early years.

Guillaume Kuyper (1878 -1941)
Guillaume was named after Guillaume Groen Van Prinsterer. He married Henrietta van Leeuwen Storm. They had three daughters. The second daughter was named Johanna (b. 29 Dec 1909).
Guillaume became a major in the Dutch army (1902-1932) and then became mayor of Stedum (1932-1941).

Wilhelm (1883-1892)
Willy died aged 9. According to Praamsma he was named after Levinus Wilhelminus Keuchenius.

See also H. H. Kuyper
and  Henrietta Kuyper

For a diagram of the Kuyper family tree.

Another use for an iPad

Saturday, 3 March 2012

Revealing Arithmetic - a review

Revealing Arithmetic
Math Concepts from a Biblical Worldview
Katherine A. Loop
Fairfax, VA: Christian Perspective

In a sense this book fills out some details and builds upon Loop's earlier book Beyond Numbers . This is not quite a full-blown Christian mathematics curriculum but it provides hints and helps towards a Christian approach to mathematics education. Loop describes it as 'a supplemental handbook', it focuses on elementary arithmetic. It will be invaluable to home-schoolers and Christian educators.

Four main 'tactics' are used to develop a Christian approach:

  • Rewording the presentation
  • Sharing the history of the concept
  • Applying the concept in a real-life situation
  • Using the concepts to explore an aspect of creation.

Each chapter follows a similar format. There is an introduction, usually looking at historical examples and thus emphasising, rightly, that the symbols or names we give concepts are only one way to express things. This helps undermine the idea that maths is a human creation. The emphasis is continually on the idea that we can only do mathematics because God has created a consistent universe and that God is faithful in keeping his covenant. Maths is seen as a God-given tool, dependent upon God and not as independent facts.

The teaching suggestions and ideas have an objective and specific points to communicate. Usually one of these is to stress the idea that mathematics is dependent upon God and not independent of him.

An example from a textbook is shown and then reworded so that the children see maths as a language system to describe aspects of creation.

Ideas are then provided. These usually contain some real-life example and historical aspects to look at.

Two key points pervade this approach: mathematics is dependent upon God and that we can do mathematics only because God has created a consistent universe. As she states:

Counting, written numbers, comparing and grouping numbers, addition, subtraction, multiplication, division, fractions, decimals, percents, ratios, proportions, number sets, exponents, roots—all the concepts we refer to as “arithmetic” are useful methods to help us count and work with quantities! These methods only work because a faithful, all-powerful God holds all things together predictably.

The book is aimed at Christian home schoolers and so these points need no justification. She rightly states that:
Teaching math from a biblical worldview means so much more that saying over and again "God created and sustains a consistent universe and math records it". 
And yet at times, there is a tendency for Loop to do exactly that.

Occasionally she overstates the point; for example: "Most modern math books present fractions exclusively as ways of representing partial quantity, without letting students know they also represent division." This is certainly not the case in the UK. Here the emphasis has been on a connectionist approach to maths that stresses the connections between different areas of maths (see for example Mike Askew et al.  Effective Teachers of Numeracy in Primary Schools: Teachers' Beliefs, Practices and Pupils' Learning).

The use of manipulatives are continually encouraged here, particularly the abacus and Napier's bones. Worksheets on using and making an abacus are included as well as on using and constructing Napier's bones.

I was particulalry pleased to see that a number of different approaches to the four rules were discussed and advocated. For example, eight different methods for multiplication were examined. This book provides a great starting point for all those who want to think Christianly about mathematics education. It is explicitly Christian and is aimed at Christian homeschoolers and for those working in Christian schools. The ideas will take some adapting and modifying to make it applicable for Christian teachers in schools that are not explicitly Christian.

Reflecting on the book it did make me wonder how much of this approach is distinctively Christian -  would a Jews or Muslim happily concur with the approaches here (and does that matter)? What difference does Jesus make to mathematics? As G. K. Chesterton so brilliantly put it:
You cannot evade the issue of God, whether you talk about pigs or the binomial theory, you are still talking about Him. Now if Christianity be. . . a fragment of metaphysical nonsense invented by a few people, then, of course, defending it will simply mean talking that metaphysical nonsense over and over. But if Christianity should happen to be true - then defending it may mean talking about anything or everything. Things can be irrelevant to the proposition that Christianity is false, but nothing can be irrelevant to the proposition that Christianity is true.
Mathematics is relevant because in Jesus everything matters.

Math Concepts from a Biblical Worldview?    
Written Numbers         
Place Value               
Comparing Numbers           
Addition: Foundational Concept       
Subtraction: Foundational Concept      
Addition & Subtraction: Multi-Digit Operations         
Multiplication: Foundational Concept   
Division: Foundational Concept   
Multiplication: Multi-Digit Operations   
Division: Multi-Digit Operations    
Fractions: Foundational Concept      
Fractions: Operations          
Ratios & Proportions  
Types of Numbers (Number Sets)
Exponents & Roots     
Math & the Gospel 
Answer Key  
Appendix A: Mathematicians
Appendix B: Different Number Systems 
Appendix C: Abacuses
Appendix D: Math Methods
Appendix E: Resources for Further Study  

Mathematics and the Divine - a brief review

Mathematics and the Divine
A Historical Study
Edited by Teun Koetsier, Vrije Universiteit, Amsterdam, The Netherlands and 
Luc Bergmans, University of Paris IV Sorbonne, Paris, France

Amsterdam: Elsevier, 2004
hbk, 716 Pages
ISBN  978-0-444-50328-2

In 35 chapters, with 34 authors and 716 pages this is book explores history, philosophy, theology and the metaphysics of mathematics. I know of no other book that does just that.

Most of the usual suspects are here: Descartes, Pascal, Kepler, Galileo, Euler and Cantor. Others less 'usual' are  Nicomachus of Gerasa, Nicholas of Cusa, Johannes Faulhaber, Athanasius Kircher, John Wallis, Gerrit Mannoury and René Guénon. The emphasis is on people and movements rather than topics in maths  - except where individuals are involved, e.g. infinity in the context of Cantor. The one exception is on 'divined proportion' which takes a look at the Golden ratio. The chapters are in topic chronological order.

It is good to see that it is not only Western mathematicians that are included; so we have chapters on Chinese number mysticism, mathematical models in Indian cosmology and geography in Islam. 

1. Ho Peng-Yoke, Chinese Number Mysticism 
2. Kim Plofker, Derivation and Revelation: the Legitimacy of Mathematical Models in Indian Cosmology 
3. Reviel Netz, The Pythagoreans 
4. Ian Mueller, Mathematics and the Divine in Plato 
5. Jean-François Mattei, Nicomachus of Gerasa and the Divine Arithmetical Ladder 
6. Dominic J. O'Meara, Geometry and the Divine in Proclus 
7. Marie-Pierre Terrien, Religious Architecture and Mathematics during Late Antiquity 
8. David A. King, The Sacred Geography of Islam 
9. Faith Wallis, 'Number Mystique' in early medieval computus texts
10. Maurice-Ruben Hayoun, Is the Divine Universe Divisible 
11. Charles Lohr, Mathematics and the Divine: Ramon Lull 
12. Hugue Garcia, Christian Gnosis 
13. Edith Dudley Sylla, Swester Katrei and Gregory of Rimini: Angels, God and Mathematics in the Fourteenth Century 
14. Jean-Michel Counet, Mathematics and the Divine in Nicholas of Cusa 
15. Teun Koetsier and Karin Reich, Michael Stifel and his Numerology 
16. Ivo Schneider, Between Rosicrucians and Kabbala - the Mathematics of the Biblical Numbers of Johannes Faulhaber 
17. Eberhard Knobloch, Mathematics and the Divine: Athanasius Kircher 
18. Volker R. Remmert, Galileo, God and Mathematics 
19. André Charrak, The Mathematical Model of Creation According to Kepler 
20. Jean-Marie Nicolle, The Mathematical Analogy in the Proof of God's Existence by Descartes
21. Donald Adamson, Pascal's Views on Mathematics and the Divine 
22. Ger Harmsen, Spinoza and the Geometrical Method of Proof 
23. Philip Beeley and Siegmund Probst, John Wallis (1616-1703): Mathematician and Divine 
24. Kees de Pater, Newton and the Ocean of Truth 
25. Herbert Breger, Leibniz: Mathematics and the Divine 
26. Wolfgang Breidert, Berkeley's Defence of the Infinite God in Contrast to the Infinite in Mathematics 
27. Ruediger Thiele, Leonhard Euler and the Divine 
28. Ruediger Thiele, Georg Cantor and the Divine 
29. Luc Bergmans, Gerrit Mannoury and his Fellow Significians on Mathematics and Mysticism 
30. Teun Koetsier, Arthur Schopenhauer and L. E. J. Brouwer: A Comparison 
31. Sergei S. Demidov and Charles E. Ford, On the Road to a Unified View: Priest Pavel Florensky - Theologian, Philosopher and Scientist 
32. François De Gandt, Husserl and Impossible Numbers: a Sceptical Experience 
33. Bruno Pinchard, Symbol and Space According to René Guénon 
34. Teun Koetsier, Eddington: Science and the Unseen World 
35. Albert van der Schoot, The Divined Proportion