This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.
Sample Chapter(s)
Chapter 1: On the Nature and Origin of Algebraic Symbolism (699 KB)
Contents:
- On the Nature and Origin of Algebraic Symbolism (A Heeffer)
- Reading Diophantos (A Meskens)
- What Did the Abbacus Teachers Aim at When They (Sometimes) Ended Up Doing Mathematics? An Investigation of the Incentives and Norms of a Distinct Mathematical Practice (J Høyrup)
- Philosophical Method and Galileo's Paradox of Infinity (M Parker)
- Representations as Means and Ends: Representability and Habituation in Mathematical Analysis During the First Part of the Nineteenth Century (H Kragh Sørensen)
- Nineteenth-Century Analysis as Philosophy of Mathematics (J J Gray)
- Dedekind, Structural Reasoning, and Mathematical Understanding (E H Reck)
- A Mathematician and a Philosopher on the Science-Likeness of Mathematics: Klein's and Lakatos' Methodologies Compared (E Glas)
- An Enhanced Argument for Innate Elementary Geometric Knowledge and Its Philosophical Implications (H De Cruz)
- The Serpent in Russell's Paradise (R Desmet)
- Bridging Theories with Axioms: Boole, Stone, and Tarski (D Schlimm)
Readership: Philosophers and historians of science.
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WHAT DID THE ABBACUS TEACHERS AIM AT WHEN THEY (SOMETIMES) ENDED UP DOING MATHEMATICS? AN INVESTIGATION OF THE INCENTIVES AND NORMS OF A DISTINCT MATHEMATICAL PRACTICE
- Pages:47–75
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REPRESENTATIONS AS MEANS AND ENDS: REPRESENTABILITY AND HABITUATION IN MATHEMATICAL ANALYSIS DURING THE FIRST PART OF THE NINETEENTH CENTURY
- Pages:114–137
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A MATHEMATICIAN AND A PHILOSOPHER ON THE SCIENCE-LIKENESS OF MATHEMATICS: KLEIN'S AND LAKATOS' METHODOLOGIES COMPARED
- Pages:174–184
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AN ENHANCED ARGUMENT FOR INNATE ELEMENTARY GEOMETRIC KNOWLEDGE AND ITS PHILOSOPHICAL IMPLICATIONS
- Pages:185–206
Sample Chapter(s)
Chapter 1: On the Nature and Origin of Algebraic Symbolism (699k)
