De L'Infini Mathematique (2 volumes)

Louis Couturat

Paris: Felix Alcan, 1896

[Infinity - Number Theory] 2 volumes Bound in contemporary leather-backed speckled boards. Original wraps bound in. XXIV, 667 p. Figures in text.  These pour le Doctorat presentee a la Faculte des lettres de Paris par Louis Couturat. Couturat was a French mathematician who "sought a universal language and symbolic-logic system to study the history of philosopjy and philosophy of mathematics." - Britannica.  In this work, "On Mathematical Infinity" he argued for the actual infinite. "For him the actual infinite was a generalisation of number, in the same way that negative numbers, fractions, irrational numbers and complex numbers had all been seen at extending the concept of number. Couturat argued that all of these generalisations had at first encountered strong opposition, but had become accepted in the end because they were suitable for representing new magnitudes and they allowed a calculus of operations which was impossible before their introduction. Infinite numbers, he claimed, were necessary in order to maintain the continuity of magnitudes."  - J J O'Connor and E F Robertson, St. Andrews, Dept of Mathematics.