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Book contents
- Frontmatter
- Contents
- Acknowledgments
- Introduction
- 1 Setting the Scene
- 2 William Oughtred and Thomas Harriot
- 3 John Collins's Campaign for a Current English Algebra Textbook
- 4 John Pell's English Edition of Rahn's Algebra and John Kersey's Algebra
- 5 The Arithmetic Formulation of Algebra in John Wallis's Treatise of Algebra
- 6 English Mathematical Thinkers Take Sides on Early Modern Algebra
- 7 The Mixed Mathematical Legacy of Newton's Universal Arithmetick
- 8 George Berkeley at the Intersection of Algebra and Philosophy
- 9 The Scottish Response to Newtonian Algebra
- 10 Algebra “Considered As the Logical Institutes of the Mathematician”
- Epilogue
- Index
8 - George Berkeley at the Intersection of Algebra and Philosophy
Published online by Cambridge University Press: 05 December 2011
- Frontmatter
- Contents
- Acknowledgments
- Introduction
- 1 Setting the Scene
- 2 William Oughtred and Thomas Harriot
- 3 John Collins's Campaign for a Current English Algebra Textbook
- 4 John Pell's English Edition of Rahn's Algebra and John Kersey's Algebra
- 5 The Arithmetic Formulation of Algebra in John Wallis's Treatise of Algebra
- 6 English Mathematical Thinkers Take Sides on Early Modern Algebra
- 7 The Mixed Mathematical Legacy of Newton's Universal Arithmetick
- 8 George Berkeley at the Intersection of Algebra and Philosophy
- 9 The Scottish Response to Newtonian Algebra
- 10 Algebra “Considered As the Logical Institutes of the Mathematician”
- Epilogue
- Index
Summary
The British intellectual tradition produced three major thinkers, in addition to Newton, who published on algebra in the first half of the eighteenth century: George Berkeley, Colin MacLaurin, and Nicholas Saunderson. Berkeley's writings on algebra were the most philosophical of the works produced by the three men and, in their time, the most neglected. Berkeley was also the only of the three to draw significant inspiration from Wallis, for MacLaurin and Saunderson began their algebras as commentaries on Universal Arithmetick. Berkeley wove Wallis's algebraic reflections with the arithmetic insights of Barrow and possibly Hobbes into a coherent philosophy of arithmetic and algebra as sciences of signs, in contrast to his philosophy of geometry as the science of perceptible finite extension.
As Berkeley's general philosophical concerns affected his understanding of early modern mathematics, so mathematics presented him with problems and insights that helped to shape his philosophy. His earliest notebooks referred to Barrow's view of number as a “note” or “sign,” and number, so understood, became one of his stock examples against abstraction. Berkeley, moreover, was the first major British (and perhaps European) philosopher to come to terms with the symbolical style of early modern algebra. His early acceptance of symbolical reasoning and Barrow's view of number helped to raise in him “semiotic consciousness” – or “the explicit awareness of the role of the sign as that role is played in a given respect” – and thus contributed toward his innovative theory of language.
- Type
- Chapter
- Information
- Symbols, Impossible Numbers, and Geometric EntanglementsBritish Algebra through the Commentaries on Newton's Universal Arithmetick, pp. 209 - 241Publisher: Cambridge University PressPrint publication year: 1997