Distinctions of Reason and Reasonable Distinctions

The Academic Life of John Wallis (1616–1703)


Distinctions of Reason and Reasonable Distinctions is an intellectual biography of John Wallis (1616-1703), professor of mathematics at Oxford for over half a century. His career spans the political tumult of the English Civil Wars, the religious upheaval of the Church of England, and the fascinating developments in mathematics and natural philosophy. His ability to navigate this terrain and advance human learning in the academic world was facilitated by his use of the Jesuit Francisco Suarez’s theory of distinctions. This Roman Catholic’s philosophy in the hands of a Protestant divine fostered an instrumentalism necessary to bridge the old and new. With this tool, Wallis brought modern science into the university and helped form the Royal Society.

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Biographical Note

Jason M. Rampelt is a Fellow in Christianity and Science at the Greystone Theological Institute in Pittsburgh, Pennsylvania. He writes on early-modern natural philosophy and theology and the intersecting domains of Christianity and the natural sciences.

Table of contents

List of Illustrations

1 Introduction
 1 John Wallis’s “Mottled Soul”: The Interpretative Challenge
 2 The Salve of the “Town Doctor”: the Interpretive Approach

PART 1: John Wallis’s Academic Formation

Introduction to Part 1

2 John Wallis’s Autobiography: Text and Context
 1 John Wallis and Thomas Smith
 2 John Wallis’s Manuscript Copies of His Autobiography
 3 John Wallis, Anthony Wood, and the Memory of the Town Doctor

3 Early Life and Education
 1 At Home and at School, 1616–32
 2 Cambridge University, 1632–40

4 The Foundation of a Career
 1 Ecclesiastical Service, 1640–49
 2 Natural Philosophy in London, 1645–49
 3 Conclusion

Conclusion to Part 1

PART 2: John Wallis’s Academic Career

Introduction to Part 2

5 Mathematical Lecturer
 1 The Savilian Statutes
 2 Lectures on Arithmetic and Algebra
 3 Lectures on Geometry
 4 Conclusion

6 Doctor of Divinity
 1 Dogmatics and the Distinctions of Reason
 2 Reason and Revelation
 3 Conclusion: the Hermeneutic of Suspension

7 Pedagogue, Pastor, and Protector
 1 Geometry as Solidior Philosophia
 2 The Care of Scholars
 3 A University in Its Own Right
 4 Conclusion

Conclusion to Part 2

PART 3: John Wallis’s Philosophical Method

Introduction to Part 3

8 Mathematical Method
 1 Geometry, Algebra, and Arithmetic
 2 Arithmetica Infinitorum, 1656
 3 Hobbes and Wallis
 4 Imaginary Numbers
 5 The Angle of Contact
 6 Conclusion

9 The Languages of Philosophy
 1 Logic
 2 Language
 3 Conclusion

Conclusion to Part 3

10 Conclusion


Early-modern history of science, also historical theology in the post-Reformation period, especially Protestant scholastics; history of the English universities, mathematics, and pedagogy. Keywords are natural philosophy; history of science; theology; scholastic; Jesuit; Francisco Suarez; scientific revolution; history of mathematics; Royal Society; university lecture; Cambridge; Oxford; Westminster Assembly; logic; grammar.

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