Heeffer A., Van Dyck M. (Eds.) Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics

London, UK: College Publications, 2010. — 326 p. — (Studies in Logic 26). — ISBN: 978-1-84890-017-2.The novel use of symbolism in early modern mathematics poses both philosophical and historical questions. How can we trace its development and transmission through manuscript sources? Is it intrinsically related to the emergence of symbolic algebra? How does symbolism relate to the use of diagrams? What are the consequences of symbolic reasoning on our understanding of nature? Can a symbolic language enable new forms of reasoning? Does a universal symbolic language exists which enables us to express all knowledge? This book brings together a collection of papers that address all these and related questions ? which were initially posed on a conference held in Ghent (Belgium) in August 2009. Scholars working on philosophy of science, history of philosophy and history of mathematics provide an insight into the role and function of symbolic representations in the development of early modern mathematics. The papers cover the period from early abbaco arithmetic and algebra (14th century) up to Leibniz (early 18th century).The development of algebraic symbolism
Hesitating progress – the slow development toward algebraic symbolization in abbacus-and related manuscripts, c. 1300 to c. 1550
From the second unknown to the symbolic equation
Symbolic revolution, scientific revolution: mathematical and philosophical aspects
The interplay between diagrams and symbolism
Translating Euclid’s diagrams into English, 1551–1571
The symbolic treatment of Euclid’s Elements in H´erigone’s Cursus mathematicus (1634, 1637, 1642)
What more there is in early modern algebra than its literal Formalism
The geometry of the unknown: Bombelli’s algebra linearia
Mathesis universalis and charateristica universalis
The “merely mechanical” vs. the “scab of symbols”: seventeenth century disputes over the criteria of mathematical rigor
Leibniz between ars characteristica and ars inveniendi: Unknown news about Cajori’s ‘master-builder of mathematical notations’